Finite Group DatabasebetaFinite Group Databasebeta| order | 17622 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C32×D979 |
| unambiguous semidirect product | C11⋊(C32×D89) |
| unambiguous semidirect product | C89⋊(C32×D11) |
| Fitting, socle, Hall | C32×C11×C89 ⋊ C2 |
| derived, Hall | C11×C89 ⋊ C2×C32 |
| Hall | C32×C89 ⋊ D11 |
| Hall | C32×C11 ⋊ D89 |
| Sylow | C89 ⋊ C32×D11 |
| Sylow | C11 ⋊ C32×D89 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | D979 |
| commutator, cosocle, hypocenter | C11×C89 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C32×C11×C89 | C2 |
| LCS | G ▷ C11×C89 | |
| UCS | C1 ◁ C32 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8811 |
4419 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×D11×D89, C3×D3×D979, C3×D33⋊D89, … |
| maximal normal subgroup of | C32×D11×D89, C3×D3×D979, C3×D33⋊D89, … |
| maximal quotient of | C32×Dic979, C2×C32×D979 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17622, 28);