Finite Group DatabasebetaFinite Group Databasebeta| order | 22959 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3 |
| direct product | C3×C2551⋊C3 |
| unambiguous semidirect product | C2551⋊C32 |
| unambiguous semidirect product | (C3×C2551)⋊C3 |
| Fitting, socle | C3×C2551 ⋊ C3 |
| derived, Sylow | C2551 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C2551⋊C3 |
| commutator, cosocle, hypocenter | C2551 | C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C2551 | C3 |
| LCS | G ▷ C2551 | |
| UCS | C1 ◁ C3 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7653 |
2559 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22959, 3);