Finite Group DatabasebetaFinite Group Databasebeta| order | 8932 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×Dic29⋊C7 |
| unambiguous semidirect product | Dic29⋊(C7×C11) |
| unambiguous semidirect product | (C11×Dic29)⋊C7 |
| derived, Sylow | C29 ⋊ C4×C7×C11 |
| Hall | C11×C29⋊C7 ⋊ C4 |
| Hall | C11×Dic29 ⋊ C7 |
| Hall | C11×C29 ⋊ C4×C7 |
| Hall | C29⋊C7 ⋊ C4×C11 |
| Hall | Dic29 ⋊ C7×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C11 | D29⋊C7 |
| commutator, hypocenter | C29 | C4×C7×C11 |
| Frattini | C2 | C11×D29⋊C7 |
| Fitting, socle | C2×C11×C29 | C2×C7 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C2×C11 | |
24 conjugacy classes of subgroups.
352 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C11×Dic29⋊C7, C11×C3⋊(Dic29⋊C7) |
| maximal normal subgroup of | C3×C11×Dic29⋊C7 |
| maximal quotient of | C3×C11×Dic29⋊C7, C11×C3⋊(Dic29⋊C7) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8932, 10);