Finite Group DatabasebetaFinite Group Databasebeta| order | 22878 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C31 · Schur multiplier (H2) = C1 |
| direct product | C3×C31×D123 |
| unambiguous semidirect product | C3⋊(C3×C31×D41) |
| unambiguous semidirect product | C41⋊(C3×D3×C31) |
| Fitting, socle, Hall | C32×C31×C41 ⋊ C2 |
| derived | C3×C41 ⋊ C2×C3×C31 |
| Hall | C31×C41 ⋊ C3×D3 |
| Hall | C32×C41 ⋊ C2×C31 |
| Hall | C32×C31 ⋊ D41 |
| Sylow | C41 ⋊ C3×D3×C31 |
| Sylow | C32 ⋊ C31×D41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C31 | D123 |
| commutator, cosocle, hypocenter | C3×C41 | C2×C3×C31 |
| Frattini | C1 | G |
| Fitting, socle | C32×C31×C41 | C2 |
| LCS | G ▷ C3×C41 | |
| UCS | C1 ◁ C3×C31 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7626 |
5859 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22878, 26);