Finite Group DatabasebetaFinite Group Databasebeta| order | 9108 |
| isoclinism | isoclinic class of D69 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C1 |
| direct product | C3×C11×Dic69 |
| unambiguous semidirect product | C3⋊(C3×C11×Dic23) |
| derived | C3×C23 ⋊ C3×C4×C11 |
| Hall | C32×C11×C23 ⋊ C4 |
| Hall | C11×C23 ⋊ C3×Dic3 |
| Hall | C32×C23 ⋊ C4×C11 |
| Hall | C32×C11 ⋊ Dic23 |
| Sylow | C23 ⋊ C3×C11×Dic3 |
| Sylow | C32 ⋊ C11×Dic23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C11 | D69 |
| commutator, hypocenter | C3×C23 | C3×C4×C11 |
| Frattini | C2 | C3×C11×D69 |
| Fitting, socle | C2×C32×C11×C23 | C2 |
| LCS | G ▷ C3×C23 | |
| UCS | C1 ◁ C2×C3×C11 | |
56 conjugacy classes of subgroups.
2376 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9108, 46);