Finite Group DatabasebetaFinite Group Databasebeta| order | 22932 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C13⋊C3×C22⋊(C49⋊C3) |
| unambiguous semidirect product | (C22×C13⋊C3)⋊(C49⋊C3) |
| unambiguous semidirect product | (C13⋊C3×C49)⋊A4 |
| Fitting, derived, Hall | C22×C13×C49 ⋊ C32 |
| Hall | C13×C49 ⋊ C3×A4 |
| Hall | C22×C49 ⋊ C3×C13⋊C3 |
| Hall | C22×C13 ⋊ C3×C49⋊C3 |
| Sylow | C49 ⋊ A4×C13⋊C3 |
| Sylow | C13 ⋊ C3×C22⋊(C49⋊C3) |
| Sylow | C22 ⋊ C13⋊C3×C49⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C22×C13×C49 | C32 |
| Frattini | C7 | C13⋊C3×C22⋊ΓL(1,𝔽8) |
| socle | C22×C7×C13 | C3×ΓL(1,𝔽8) |
| LCS | G ▷ C22×C13×C49 | |
| UCS | C1 | |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2548 |
476 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22932, 178);