Finite Group DatabasebetaFinite Group Databasebeta| order | 9108 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4×C11 · Schur multiplier (H2) = C3 |
| derived, Sylow | C23 ⋊ C32×C4×C11 |
| Hall | C32×C23⋊C11 ⋊ C4 |
| Hall | C32×Dic23 ⋊ C11 |
| Hall | C23⋊C11 ⋊ C32×C4 |
| Hall | C32×C23 ⋊ C4×C11 |
| Hall | Dic23 ⋊ C32×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32 | AGL(1,𝔽23) |
| commutator, hypocenter | C23 | C32×C4×C11 |
| Frattini | C2 | C32×AGL(1,𝔽23) |
| Fitting, socle | C2×C32×C23 | C2×C11 |
| LCS | G ▷ C23 | |
| UCS | C1 ◁ C2×C32 | |
72 conjugacy classes of subgroups.
414 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9108, 36);