Finite Group DatabasebetaFinite Group Databasebeta| order | 9108 |
| isoclinism | isoclinic class of D99 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C23 · Schur multiplier (H2) = C1 |
| direct product | C23×Dic99 |
| unambiguous semidirect product | C9⋊(C23×Dic11) |
| unambiguous semidirect product | C11⋊(C23×Dic9) |
| derived, Hall | C9×C11 ⋊ C4×C23 |
| Hall | C9×C11×C23 ⋊ C4 |
| Hall | C11×C23 ⋊ Dic9 |
| Hall | C9×C23 ⋊ Dic11 |
| Sylow | C11 ⋊ C23×Dic9 |
| Sylow | C9 ⋊ C23×Dic11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C23 | D99 |
| commutator, hypocenter | C9×C11 | C4×C23 |
| Frattini | C2×C3 | C23×D33 |
| Fitting | C2×C9×C11×C23 | C2 |
| socle | C2×C3×C11×C23 | D3 |
| LCS | G ▷ C9×C11 | |
| UCS | C1 ◁ C2×C23 | |
36 conjugacy classes of subgroups.
2346 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9108, 11);