Finite Group DatabasebetaFinite Group Databasebeta| order | 8932 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D29×D77 |
| unambiguous semidirect product | (C7×D29)⋊D11 |
| unambiguous semidirect product | (C11×D29)⋊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 ⋊ C2×D77 |
| 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.
640 conjugacy classes — view the full character table.
| maximal subgroup of | D29×C11⋊AGL(1,𝔽7), C3×D29×D77, D29×D231, … |
| maximal normal subgroup of | D29×C11⋊AGL(1,𝔽7), C3×D29×D77 |
| maximal quotient of | C3×D29×D77, D29×D231, D77×D87, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8932, 27);