Finite Group DatabasebetaFinite Group Databasebeta| order | 8932 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C11 · Schur multiplier (H2) = C2 |
| direct product | C11×D7×D29 |
| unambiguous semidirect product | (D7×C29)⋊(C2×C11) |
| unambiguous semidirect product | (C7×D29)⋊(C2×C11) |
| unambiguous semidirect product | D203⋊(C2×C11) |
| Fitting, socle, Hall | C7×C11×C29 ⋊ C22 |
| derived, Hall | C7×C29 ⋊ C22×C11 |
| Hall | C11×C29 ⋊ C2×D7 |
| Hall | C7×C11 ⋊ C2×D29 |
| Sylow | C29 ⋊ C2×C11×D7 |
| Sylow | C7 ⋊ C2×C11×D29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D7×D29 |
| commutator, hypocenter | C7×C29 | C22×C11 |
| Frattini | C1 | G |
| Fitting, socle | C7×C11×C29 | C22 |
| LCS | G ▷ C7×C29 | |
| UCS | C1 ◁ C11 | |
40 conjugacy classes of subgroups.
880 conjugacy classes — view the full character table.
| maximal subgroup of | C11×AGL(1,𝔽7)×D29, C3×C11×D7×D29, C11×D21×D29, … |
| maximal normal subgroup of | C11×AGL(1,𝔽7)×D29, C3×C11×D7×D29 |
| maximal quotient of | C3×C11×D7×D29, C11×D21×D29, C11×D7×D87, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8932, 25);