Finite Group DatabasebetaFinite Group Databasebeta| order | 22932 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×C22⋊#14274255 |
| unambiguous semidirect product | (C22×C3)⋊#14274255 |
| Fitting | C22×C3×C13×C49 ⋊ C3 |
| 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 ⋊ C3×C22⋊(C13⋊C3) |
| Sylow | C13 ⋊ C3×C22⋊(C49⋊C3) |
| Sylow | C22 ⋊ C3×#14274255 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C22⋊#14274255 |
| commutator, cosocle, hypocenter | C22×C13×C49 | C32 |
| Frattini | C7 | C3×C22⋊#63271 |
| Fitting | C22×C3×C13×C49 | C3 |
| socle | C22×C3×C7×C13 | ΓL(1,𝔽8) |
| LCS | G ▷ C22×C13×C49 | |
| UCS | C1 ◁ C3 | |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7644 |
2556 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22932, 249);