Finite Group DatabasebetaFinite Group Databasebeta| order | 22716 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | C2×C9×D631 |
| Fitting | C2×C9×C631 ⋊ C2 |
| derived, Sylow | C631 ⋊ C22×C9 |
| Hall | C9×C631 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C9 | D631 |
| commutator, hypocenter | C631 | C22×C9 |
| Frattini | C3 | C2×C3×D631 |
| Fitting | C2×C9×C631 | C2 |
| socle | C2×C3×C631 | C2×C3 |
| prime radical | C2×C3×D631 | C3 |
| cosocle | C3×C631 | C22×C3 |
| LCS | G ▷ C631 | |
| UCS | C1 ◁ C2×C9 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11358 |
5706 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22716, 15);