Finite Group DatabasebetaFinite Group Databasebeta| order | 9108 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D33⋊D69 |
| Fitting, socle, derived, Hall | C32×C11×C23 ⋊ C22 |
| Hall | C11×C23 ⋊ D32 |
| Hall | C32×C23 ⋊ C2×D11 |
| Hall | C32×C11 ⋊ C2×D23 |
| Sylow | C23 ⋊ (C3⋊D3)⋊D11 |
| Sylow | C11 ⋊ D3×D69 |
| Sylow | C32 ⋊ D11×D23 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C11×C23 | C22 |
| LCS | G ▷ C32×C11×C23 | |
| UCS | C1 | |
88 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3^2,11,23|c^a=c^2,d^a=d^2,f^a=f^22,d^b=d^2,e^b=e^10633 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9108, 89);