Finite Group DatabasebetaFinite Group Databasebeta| order | 22932 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C7×C13 · Schur multiplier (H2) = C1 |
| direct product | C7×C13×C3⋊(ΓL(1,𝔽8)⋊C4) |
| unambiguous semidirect product | C3⋊(C7×C13×ΓL(1,𝔽8)⋊C4) |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊(C7×Dic3×C13) |
| unambiguous semidirect product | Dic21⋊(C3×C7×C13) |
| derived | C3×C7 ⋊ C3×C4×C7×C13 |
| Hall | C3×C7×C13×ΓL(1,𝔽8) ⋊ C4 |
| Hall | C72×C13 ⋊ C3×Dic3 |
| Hall | C3×C7×ΓL(1,𝔽8) ⋊ C4×C13 |
| Sylow | C72 ⋊ C3×Dic3×C13 |
120 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 3276 |
2184 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22932, 697);