[ 1 1]
[ 1 -]

Permutation group acting on a set of cardinality 4
Order = 8 = 2^3
  (1, 2)(3, 4)
  (2, 4)
Automorphism group has centre of order: 2
Number of regular subgroups: 1
Number of regular subgroups containing zeta: 1
Matrix is cocyclic over /Expanded matrix is group developed over:
<2, 1> <4, 1>


[ 1 1 1 1]
[ 1 1 - -]
[ 1 - 1 -]
[ 1 - - 1]

Permutation group acting on a set of cardinality 8
Order = 192 = 2^6 * 3
  (1, 2)(5, 6)
  (2, 3)(6, 7)
  (3, 7)(4, 8)
  (3, 4)(7, 8)
Order of automorphism group: 192
Automorphism group has centre of order: 2
Number of regular subgroups: 5
Number of regular subgroups containing zeta: 4
Matrix is cocyclic over /Expanded matrix is group developed over:
<4, 2> <8, 5>
<4, 2> <8, 4>
<4, 2> <8, 2>
<4, 1> <8, 2>


[ 1 1 1 1 1 1 1 1]
[ 1 1 1 1 - - - -]
[ 1 1 - - 1 1 - -]
[ 1 1 - - - - 1 1]
[ 1 - 1 - 1 - 1 -]
[ 1 - 1 - - 1 - 1]
[ 1 - - 1 1 - - 1]
[ 1 - - 1 - 1 1 -]

Permutation group acting on a set of cardinality 16
Order = 21504 = 2^10 * 3 * 7
  (1, 2)(7, 8)(9, 10)(15, 16)
  (2, 3)(6, 7)(10, 11)(14, 15)
  (5, 15)(6, 16)(7, 13)(8, 14)
  (3, 5)(4, 6)(11, 13)(12, 14)
  (5, 7)(6, 8)(13, 15)(14, 16)
  (5, 6)(7, 8)(13, 14)(15, 16)
Automorphism group has centre of order: 2
Number of regular subgroups: 10
Number of regular subgroups containing zeta: 10
Matrix is cocyclic over /Expanded matrix is group developed over:
<8, 5> <16, 10>
<8, 5> <16, 12>
<8, 5> <16, 11>
<8, 5> <16, 13>
<8, 2> <16, 4>
<8, 2> <16, 2>
<8, 3> <16, 3>
<8, 3> <16, 4>
<8, 2> <16, 5>
<8, 3> <16, 9>


[ 1 1 1 1 1 1 1 1 1 1 1 1]
[ 1 1 1 1 1 1 - - - - - -]
[ 1 1 1 - - - 1 1 1 - - -]
[ 1 1 - 1 - - 1 - - 1 1 -]
[ 1 1 - - 1 - - 1 - 1 - 1]
[ 1 1 - - - 1 - - 1 - 1 1]
[ 1 - - - 1 1 1 1 - - 1 -]
[ 1 - 1 1 - - - 1 - - 1 1]
[ 1 - 1 - - 1 1 - - 1 - 1]
[ 1 - - 1 - 1 - 1 1 1 - -]
[ 1 - - 1 1 - 1 - 1 - - 1]
[ 1 - 1 - 1 - - - 1 1 1 -]

Permutation group acting on a set of cardinality 24
Order = 190080 = 2^7 * 3^3 * 5 * 11
  (1, 2)(5, 6)(9, 12)(10, 11)(13, 14)(17, 18)(21, 24)(22, 23)
  (2, 3)(5, 6)(7, 10)(8, 9)(14, 15)(17, 18)(19, 22)(20, 21)
  (5, 6)(7, 20)(8, 19)(9, 22)(10, 21)(11, 24)(12, 23)(17, 18)
  (3, 4)(5, 6)(9, 11)(10, 12)(15, 16)(17, 18)(21, 23)(22, 24)
  (4, 12)(5, 8)(6, 9)(7, 10)(16, 24)(17, 20)(18, 21)(19, 22)
  (4, 5, 6)(7, 10, 11)(8, 12, 9)(16, 17, 18)(19, 22, 23)(20, 24, 21)
Automorphism group has centre of order: 2
Number of regular subgroups: 3
Number of regular subgroups containing zeta: 3
Matrix is cocyclic over /Expanded matrix is group developed over:
<12, 5> <24, 11>
<12, 3> <24, 3>
<12, 4> <24, 4>