Finite Group DatabasebetaFinite Group Databasebeta| order | 8932 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C29 · Schur multiplier (H2) = C2 |
| direct product | D7×D11×C29 |
| unambiguous semidirect product | (C11×D7)⋊(C2×C29) |
| unambiguous semidirect product | (C7×D11)⋊(C2×C29) |
| unambiguous semidirect product | D77⋊(C2×C29) |
| Fitting, socle, Hall | C7×C11×C29 ⋊ C22 |
| derived, Hall | C7×C11 ⋊ C22×C29 |
| Hall | C11×C29 ⋊ C2×D7 |
| Hall | C7×C29 ⋊ C2×D11 |
| Sylow | C11 ⋊ C2×D7×C29 |
| Sylow | C7 ⋊ C2×D11×C29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C29 | D7×D11 |
| commutator, hypocenter | C7×C11 | C22×C29 |
| Frattini | C1 | G |
| Fitting, socle | C7×C11×C29 | C22 |
| LCS | G ▷ C7×C11 | |
| UCS | C1 ◁ C29 | |
40 conjugacy classes of subgroups.
1015 conjugacy classes — view the full character table.
| maximal subgroup of | D11×C29×AGL(1,𝔽7), C3×D7×D11×C29, D11×C29×D21, … |
| maximal normal subgroup of | D11×C29×AGL(1,𝔽7), C3×D7×D11×C29 |
| maximal quotient of | C3×D7×D11×C29, D11×C29×D21, D7×C29×D33, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8932, 28);