Finite Group DatabasebetaFinite Group Databasebeta| order | 22716 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×C22⋊(C631⋊C3) |
| unambiguous semidirect product | (C22×C3)⋊(C631⋊C3) |
| unambiguous semidirect product | (C3×C631)⋊A4 |
| Fitting, socle | C22×C3×C631 ⋊ C3 |
| derived, Hall | C22×C631 ⋊ C32 |
| Sylow | C631 ⋊ C3×A4 |
| Sylow | C22 ⋊ C3×C631⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C22⋊(C631⋊C3) |
| commutator, cosocle, hypocenter | C22×C631 | C32 |
| Frattini | C1 | G |
| Fitting, socle | C22×C3×C631 | C3 |
| LCS | G ▷ C22×C631 | |
| UCS | C1 ◁ C3 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7572 |
2532 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22716, 45);