Finite Group DatabasebetaFinite Group Databasebeta| order | 22932 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×ΓL(1,𝔽8)⋊((C13⋊C3)⋊D7) |
| unambiguous semidirect product | (C2×ΓL(1,𝔽8))⋊((C13⋊C3)⋊D7) |
| unambiguous semidirect product | (C2×C13⋊C3)⋊(ΓL(1,𝔽8)⋊D7) |
| Fitting, socle | C2×C72×C13 ⋊ C2×C32 |
| derived, Hall | C72×C13 ⋊ C22×C32 |
| Hall | C7×ΓL(1,𝔽8)×C13⋊C3 ⋊ C22 |
| Hall | C2×C7⋊D91 ⋊ C32 |
| Sylow | C72 ⋊ C2×C3×D13⋊C3 |
| Sylow | C13 ⋊ C2×C3×ΓL(1,𝔽8)⋊D7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | ΓL(1,𝔽8)⋊((C13⋊C3)⋊D7) |
| 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:
(1,2)(3,5)(4,9)(6,8)(7,11)(10,13)(15,18,19,16,17,20)(22,23)(24,25)(26,27);(2,4,7)(3,6,8)(5,10,11)(9,12,13)(14,15,17,20,19,18,16)(21,22,24,26,27,25,23)(28,29)272 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22932, 916);