Finite Group DatabasebetaFinite Group Databasebeta| order | 22932 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×ΓL(1,𝔽8)×C3⋊#261 |
| unambiguous semidirect product | C3⋊(C7×ΓL(1,𝔽8)×#261) |
| Fitting, socle | C3×C72×C13 ⋊ C3×C4 |
| derived | C3×C7×C13 ⋊ C3×C4×C7 |
| Hall | C3×C7×C13×ΓL(1,𝔽8) ⋊ C4 |
| Hall | C72×C13 ⋊ C3×Dic3 |
| Hall | C3×C7×ΓL(1,𝔽8) ⋊ #261 |
| Sylow | C72 ⋊ C3×C3⋊#261 |
| Sylow | C13 ⋊ C7×Dic3×ΓL(1,𝔽8) |
136 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 42 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 819 |
525 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22932, 1104);