Finite Group DatabasebetaFinite Group Databasebeta| order | 22932 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4×C7 · Schur multiplier (H2) = C3 |
| direct product | C3×C7×ΓL(1,𝔽8)⋊#261 |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊(C3×C7×#261) |
| Fitting, socle | C3×C72×C13 ⋊ C3×C4 |
| derived | C7×C13 ⋊ C32×C4×C7 |
| Hall | C3×C7×C13×ΓL(1,𝔽8) ⋊ C4 |
| Hall | C7×C7⋊#261 ⋊ C32 |
| Hall | C72×C13 ⋊ C32×C4 |
| Hall | C3×C7×ΓL(1,𝔽8) ⋊ #261 |
| Sylow | C72 ⋊ C32×#261 |
| Sylow | C13 ⋊ C3×C7×ΓL(1,𝔽8)⋊C4 |
152 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1638 |
609 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22932, 994);