Finite Group DatabasebetaFinite Group Databasebeta| order | 8932 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D77⋊D29 |
| unambiguous semidirect product | D203⋊D11 |
| unambiguous semidirect product | D319⋊D7 |
| Fitting, socle, derived, Hall | C7×C11×C29 ⋊ C22 |
| Hall | C11×C29 ⋊ C2×D7 |
| Hall | C7×C29 ⋊ C2×D11 |
| Hall | C7×C11 ⋊ C2×D29 |
| Sylow | C29 ⋊ D7×D11 |
| Sylow | C11 ⋊ D7×D29 |
| Sylow | C7 ⋊ D11×D29 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C11×C29 | C22 |
| LCS | G ▷ C7×C11×C29 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,7,11,29|d^a=d^10,e^a=e^28,c^b=c^6,d^b=d^10595 conjugacy classes — view the full character table.
| maximal subgroup of | (C11⋊AGL(1,𝔽7))⋊D29, C3×D77⋊D29, D319⋊D21, … |
| maximal normal subgroup of | (C11⋊AGL(1,𝔽7))⋊D29, C3×D77⋊D29 |
| maximal quotient of | C3×D77⋊D29, D319⋊D21, D203⋊D33, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8932, 31);