Finite Group DatabasebetaFinite Group Databasebeta| order | 8932 |
| isoclinism | isoclinic class of C29⋊C7 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7×C11 · Schur multiplier (H2) = C2 |
| direct product | C22×C11×C29⋊C7 |
| unambiguous semidirect product | (C22×C29)⋊(C7×C11) |
| unambiguous semidirect product | (C22×C11×C29)⋊C7 |
| Fitting, socle, Hall | C22×C11×C29 ⋊ C7 |
| derived, Sylow | C29 ⋊ C22×C7×C11 |
| Hall | C11×C29 ⋊ C22×C7 |
| Hall | C22×C29 ⋊ C7×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C11 | C29⋊C7 |
| commutator, hypocenter | C29 | C22×C7×C11 |
| Frattini | C1 | G |
| Fitting, socle | C22×C11×C29 | C7 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C22×C11 | |
40 conjugacy classes of subgroups.
484 conjugacy classes — view the full character table.
| maximal subgroup of | C11×A4×C29⋊C7, C2×D3×C11×C29⋊C7, C22×C3×C11×C29⋊C7 |
| maximal normal subgroup of | C11×A4×C29⋊C7, C22×C3×C11×C29⋊C7 |
| maximal quotient of | C2×D3×C11×C29⋊C7, C22×C3×C11×C29⋊C7 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8932, 20);