the 4 isometry classes of irreducible [36,32,3]_3 codes are:

code no       1:
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1 1 1 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 1 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 0 1 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 1 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 1 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 1 1 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 2 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 2 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 2 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0
2 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0
2 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0
0 2 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0
1 2 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0
2 2 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0
0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0
1 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0
2 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0
0 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0
1 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
the automorphism group has order 648
and is strongly generated by the following 7 elements:
(
1 0 0 0 
0 1 0 0 
0 0 2 0 
0 0 1 1 
, 
1 0 0 0 
0 2 0 0 
0 0 2 0 
2 0 0 2 
, 
2 0 0 0 
0 2 0 0 
1 1 1 0 
1 1 2 2 
, 
1 0 0 0 
0 1 0 0 
1 2 0 2 
1 2 2 0 
, 
1 0 0 0 
0 1 0 0 
2 0 1 1 
2 0 0 2 
, 
2 0 0 0 
1 0 1 2 
2 2 1 1 
1 1 1 1 
, 
2 0 0 0 
2 0 1 2 
2 2 1 1 
0 1 1 1 
)
acting on the columns of the generator matrix as follows (in order):
(4, 24)(5, 19)(8, 9)(10, 13)(11, 15)(12, 14)(16, 25)(17, 26)(18, 27)(20, 28)(21, 29)(22, 30)(23, 31), 
(4, 16)(5, 27)(6, 7)(8, 9)(11, 12)(14, 15)(18, 19)(21, 22)(24, 25)(29, 30)(32, 33)(35, 36), 
(3, 11)(4, 31)(5, 23)(8, 10)(9, 12)(13, 14)(16, 29)(17, 30)(18, 26)(19, 24)(20, 25)(21, 28)(22, 27), 
(3, 20)(4, 12)(5, 27)(8, 19)(9, 18)(10, 17)(11, 16)(13, 23)(14, 22)(15, 21)(24, 30)(25, 29)(26, 31), 
(3, 26)(4, 16)(5, 12)(8, 24)(9, 25)(10, 28)(11, 27)(13, 31)(14, 29)(15, 30)(18, 22)(19, 21)(20, 23), 
(2, 34)(3, 31)(4, 5)(6, 32)(7, 33)(8, 30)(9, 29)(13, 20)(14, 18)(15, 19)(16, 27)(17, 28), 
(2, 33)(3, 29, 9, 30, 8, 31)(4, 5, 17, 28, 16, 27)(6, 34)(7, 32)(10, 11, 12)(13, 20, 15, 19, 14, 18)(21, 22, 23)(24, 26, 25)
orbits: { 1 }, { 2, 34, 33, 6, 32, 7 }, { 3, 11, 20, 26, 31, 15, 12, 16, 27, 10, 28, 25, 23, 13, 17, 18, 24, 4, 8, 14, 21, 30, 19, 9, 5, 29, 22 }, { 35, 36 }

code no       2:
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1 1 1 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 1 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 0 1 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 1 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 1 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 1 1 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 2 1 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 2 1 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 2 1 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 2 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 2 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 2 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0
2 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0
2 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0
0 2 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0
1 2 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0
2 2 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0
0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0
1 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0
2 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0
0 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0
0 2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
the automorphism group has order 1296
and is strongly generated by the following 8 elements:
(
1 0 0 0 
0 2 0 0 
0 0 2 0 
0 0 0 2 
, 
1 0 0 0 
0 2 0 0 
0 0 1 0 
0 0 0 1 
, 
1 0 0 0 
0 1 0 0 
0 0 2 0 
0 0 1 1 
, 
2 0 0 0 
0 2 0 0 
2 2 2 2 
2 2 0 1 
, 
1 0 0 0 
0 1 0 0 
2 0 2 0 
2 0 1 1 
, 
1 0 0 0 
0 1 0 0 
1 0 1 1 
1 0 0 2 
, 
2 0 0 0 
0 0 1 2 
0 2 1 1 
0 1 1 1 
, 
0 2 0 0 
0 0 2 1 
1 0 2 0 
0 0 2 0 
)
acting on the columns of the generator matrix as follows (in order):
(5, 28)(6, 7)(8, 9)(11, 12)(14, 15)(16, 17)(19, 20)(22, 23)(25, 26)(30, 31)(33, 34), 
(5, 30)(6, 7)(10, 13)(11, 14)(12, 15)(18, 21)(19, 22)(20, 23)(27, 29)(28, 31)(35, 36), 
(4, 24)(5, 19)(8, 9)(10, 13)(11, 15)(12, 14)(16, 25)(17, 26)(18, 27)(20, 28)(21, 29)(22, 30)(23, 31), 
(3, 5)(4, 23)(8, 28)(9, 27)(10, 30)(11, 31)(12, 29)(13, 25)(14, 26)(15, 24)(16, 22)(17, 21)(18, 20), 
(3, 8)(4, 26)(5, 20)(10, 14)(11, 13)(12, 15)(16, 24)(17, 25)(18, 28)(19, 27)(21, 31)(22, 29)(23, 30), 
(3, 25)(4, 17)(5, 10)(8, 26)(9, 24)(11, 28)(12, 27)(13, 30)(14, 31)(15, 29)(18, 23)(19, 22)(20, 21), 
(2, 32)(3, 29)(4, 27)(5, 17)(6, 33)(7, 34)(8, 31)(9, 30)(13, 18)(14, 19)(15, 20)(16, 28), 
(1, 32, 2)(3, 4, 21, 23, 15, 9)(5, 12, 8, 24, 18, 22)(6, 33, 36)(7, 34, 35)(10, 16, 27, 20, 14, 25)(11, 26, 29, 19, 28, 30)(13, 17)
orbits: { 1, 2, 32 }, { 3, 5, 8, 25, 29, 9, 28, 30, 19, 20, 10, 17, 22, 26, 31, 12, 16, 13, 14, 27, 21, 15, 24, 18, 11, 23, 4 }, { 6, 7, 33, 36, 34, 35 }

code no       3:
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1 1 1 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 1 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 0 1 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 1 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 1 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 1 1 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 2 1 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 2 1 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 2 1 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 2 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 2 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 2 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0
2 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0
2 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0
0 2 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0
1 2 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0
0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0
1 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0
2 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0
0 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0
1 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0
0 2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
the automorphism group has order 192
and is strongly generated by the following 4 elements:
(
2 0 0 0 
0 2 0 0 
2 2 0 1 
2 2 1 0 
, 
2 0 0 0 
0 1 0 2 
2 1 0 0 
2 1 2 0 
, 
2 0 0 0 
0 0 1 2 
0 1 0 2 
0 0 0 2 
, 
1 0 2 0 
0 2 2 1 
0 0 2 1 
0 0 1 1 
)
acting on the columns of the generator matrix as follows (in order):
(3, 23)(4, 15)(5, 24)(8, 22)(9, 21)(10, 20)(11, 19)(12, 18)(13, 17)(14, 16)(25, 27)(26, 28)(29, 30), 
(2, 9, 33, 21)(3, 31, 23, 7)(4, 15, 16, 14)(5, 18, 12, 24)(6, 8, 32, 22)(10, 25, 28, 19)(11, 26, 27, 20)(13, 17)(29, 34, 30, 35), 
(2, 31)(3, 21)(5, 12)(6, 32)(7, 33)(8, 22)(9, 23)(10, 27)(11, 28)(18, 24)(19, 26)(20, 25), 
(1, 33, 17, 9)(2, 13, 21, 36)(3, 31)(4, 24)(5, 12, 15, 14)(6, 28, 19, 30)(7, 23)(8, 32, 26, 25)(10, 27, 29, 34)(11, 22, 35, 20)
orbits: { 1, 9, 21, 2, 23, 17, 33, 3, 13, 31, 36, 7 }, { 4, 15, 14, 24, 12, 16, 5, 18 }, { 6, 22, 32, 30, 8, 11, 29, 34, 19, 25, 20, 28, 35, 27, 26, 10 }

code no       4:
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1 1 1 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 1 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 0 1 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 1 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 1 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 1 1 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 2 1 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 2 1 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 0 1 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 0 0 1 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 2 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 2 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0
2 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0
2 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0
0 2 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0
1 2 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0
2 2 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0
0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0
1 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0
0 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0
1 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0
2 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0
0 2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0
1 2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0
2 2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
the automorphism group has order 93312
and is strongly generated by the following 8 elements:
(
1 0 0 0 
0 1 0 0 
0 0 1 0 
2 0 2 2 
, 
1 0 0 0 
0 1 0 0 
0 0 1 0 
1 2 0 2 
, 
1 0 0 0 
0 2 0 0 
0 0 0 2 
2 0 1 1 
, 
1 0 0 0 
0 1 0 0 
0 2 0 2 
0 2 2 0 
, 
1 0 0 0 
1 2 2 0 
1 0 2 2 
2 1 0 0 
, 
1 0 0 0 
2 1 2 2 
1 2 1 2 
0 2 2 1 
, 
1 2 1 0 
0 1 2 2 
1 2 2 1 
0 0 0 2 
, 
0 2 2 1 
1 2 1 2 
0 2 0 2 
2 1 1 1 
)
acting on the columns of the generator matrix as follows (in order):
(4, 23)(5, 20)(15, 22)(16, 24)(17, 27)(18, 26)(19, 28)(21, 25)(29, 30)(31, 35)(32, 34)(33, 36), 
(4, 19)(5, 30)(15, 18)(16, 17)(20, 21)(22, 33)(23, 32)(24, 31)(25, 29)(26, 36)(27, 35)(28, 34), 
(3, 23, 16, 8, 24, 4)(5, 21, 14, 25, 20, 13)(6, 7)(9, 22, 15)(10, 27, 19, 11, 28, 17)(12, 26, 18)(29, 30)(31, 32)(34, 35), 
(3, 17)(4, 10)(5, 25)(8, 19)(9, 18)(11, 16)(12, 15)(13, 20)(14, 21)(22, 26)(23, 28)(24, 27), 
(2, 15, 33, 12)(3, 17, 27, 24)(4, 32, 10, 7)(5, 29, 25, 30)(6, 16, 31, 11)(8, 19, 28, 23)(9, 18, 26, 22)(13, 21, 14, 20), 
(2, 24, 26, 6, 22, 27)(3, 18, 31, 9, 17, 33)(4, 10, 34)(5, 25)(7, 23, 28)(8, 19, 32)(11, 36, 16, 12, 35, 15)(13, 14)(20, 21)(29, 30), 
(1, 21, 13, 20, 25, 29, 30, 14)(2, 12, 22, 9, 33, 15, 18, 26)(3, 24, 27, 16, 6, 31, 17, 35)(7, 23, 34, 28, 19, 8, 10, 32), 
(1, 34)(2, 33)(3, 17)(4, 25)(5, 10)(7, 30)(8, 13)(9, 22)(11, 16)(14, 28)(18, 26)(19, 20)(21, 23)(24, 27)(29, 32)
orbits: { 1, 14, 34, 21, 13, 30, 28, 32, 35, 10, 23, 25, 20, 5, 8, 29, 7, 19, 11, 31, 4, 27, 12, 17, 3, 16, 6, 15, 24, 18, 22, 33, 2, 9, 36, 26 }