Finite Group DatabasebetaFinite Group Databasebeta| order | 22878 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C41 · Schur multiplier (H2) = C1 |
| direct product | C41×D279 |
| unambiguous semidirect product | C9⋊(C41×D31) |
| unambiguous semidirect product | C31⋊(D9×C41) |
| Fitting, Hall | C9×C31×C41 ⋊ C2 |
| derived, Hall | C9×C31 ⋊ C2×C41 |
| Hall | C31×C41 ⋊ D9 |
| Hall | C9×C41 ⋊ D31 |
| Sylow | C31 ⋊ D9×C41 |
| Sylow | C9 ⋊ C41×D31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C41 | D279 |
| commutator, cosocle, hypocenter | C9×C31 | C2×C41 |
| Frattini | C3 | C41×D93 |
| Fitting | C9×C31×C41 | C2 |
| socle | C3×C31×C41 | D3 |
| LCS | G ▷ C9×C31 | |
| UCS | C1 ◁ C41 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11439 |
5781 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22878, 8);