Finite Group DatabasebetaFinite Group Databasebeta| order | 22962 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C89⋊(D43⋊C3) |
| unambiguous semidirect product | (C43⋊C3)⋊D89 |
| unambiguous semidirect product | D3827⋊C3 |
| Fitting, socle, derived, Hall | C43×C89 ⋊ C2×C3 |
| Hall | C89×C43⋊C3 ⋊ C2 |
| Hall | D3827 ⋊ C3 |
| Hall | C43⋊C3 ⋊ D89 |
| Sylow | C89 ⋊ D43⋊C3 |
| Sylow | C43 ⋊ C3×D89 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C43×C89 | C2×C3 |
| LCS | G ▷ C43×C89 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3827 |
Polycyclic presentation:
2,3,43,89|c^a=c^42,d^a=d^88,c^b=c^36761 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22962, 12);