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Aliases
Splittings
Subgroups
2672 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 5 generators on 23 points:
(2,3,4)(5,7,6)(9,13)(10,17)(14,22)(15,16)(18,19)(21,23);(1,2,4,6,3,5,7)(8,9,11,13)(10,14,19,21)(12,16,20,15)(17,23,18,22);(8,10,12,17)(9,14,16,23)(11,19,20,18)(13,21,15,22);(9,15)(10,17)(13,16)(14,21)(18,19)(22,23);(9,13)(10,18)(14,23)(15,16)(17,19)(21,22)
Conjugacy classes & character table
190 conjugacy classes — view the full character table.
Relationships
| maximal subgroup of | ΓL(1,𝔽8)×#3532⋊C3, ΓL(1,𝔽8)×#62817, AGL(1,𝔽7)×#3532 |
| maximal normal subgroup of | ΓL(1,𝔽8)×#3532⋊C3, ΓL(1,𝔽8)×#62817, AGL(1,𝔽7)×#3532 |
GAP
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((2,3,4)(5,7,6)(9,13)(10,17)(14,22)(15,16)(18,19)(21,23), (1,2,4,6,3,5,7)(8,9,11,13)(10,14,19,21)(12,16,20,15)(17,23,18,22), (8,10,12,17)(9,14,16,23)(11,19,20,18)(13,21,15,22), (9,15)(10,17)(13,16)(14,21)(18,19)(22,23), (9,13)(10,18)(14,23)(15,16)(17,19)(21,22));
Finite Group Databasebeta