Finite Group DatabasebetaFinite Group Databasebeta| order | 22932 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×ΓL(1,𝔽8)⋊(ΓL(1,𝔽8)⋊D13) |
| unambiguous semidirect product | (C2×ΓL(1,𝔽8))⋊(ΓL(1,𝔽8)⋊D13) |
| Fitting, socle | C2×C72×C13 ⋊ C2×C32 |
| derived, Hall | C72×C13 ⋊ C22×C32 |
| Hall | C13×ΓL(1,𝔽8)2 ⋊ C22 |
| Hall | C2×C7⋊D91 ⋊ C32 |
| Hall | ΓL(1,𝔽8)2 ⋊ C2×D13 |
| Sylow | C72 ⋊ C2×C32×D13 |
| Sylow | C13 ⋊ C2×ΓL(1,𝔽8)⋊AGL(1,𝔽7) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | ΓL(1,𝔽8)⋊(ΓL(1,𝔽8)⋊D13) |
| commutator, cosocle, hypocenter | C72×C13 | C22×C32 |
| Frattini | C1 | G |
| Fitting, socle | C2×C72×C13 | C2×C32 |
| LCS | G ▷ C72×C13 | |
| UCS | C1 ◁ C2 | |
280 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 62 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 546 |
A minimal faithful permutation representation — 2 generators on 29 points:
(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,20)(22,25,26,23,24,27);(1,2,4,6,8,10,12,13,11,9,7,5,3)(15,17,19)(16,18,20)(21,22,24,27,26,25,23)(28,29)352 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22932, 953);