Finite Group DatabasebetaFinite Group Databasebeta| order | 9108 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C11 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊(C3⋊(Dic23⋊C11)) |
| unambiguous semidirect product | (C23⋊C11)⋊(C3⋊Dic3) |
| unambiguous semidirect product | (C3⋊Dic69)⋊C11 |
| derived, Hall | C32×C23 ⋊ C4×C11 |
| Hall | C32×C23⋊C11 ⋊ C4 |
| Hall | C3⋊Dic69 ⋊ C11 |
| Hall | C23⋊C11 ⋊ C3⋊Dic3 |
| Sylow | C23 ⋊ C11×C3⋊Dic3 |
| Sylow | C32 ⋊ Dic23⋊C11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊(C3⋊AGL(1,𝔽23)) |
| commutator, hypocenter | C32×C23 | C4×C11 |
| Fitting, socle | C2×C32×C23 | C2×C11 |
| LCS | G ▷ C32×C23 | |
| UCS | C1 ◁ C2 | |
72 conjugacy classes of subgroups.
Polycyclic presentation:
2,11,3^2,23,2|a^2=f,c^a=c^2,d^a=d^2,e^a=e^22,e^b=e^2150 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9108, 39);