Finite Group DatabasebetaFinite Group Databasebeta| order | 8932 |
| isoclinism | isoclinic class of #1181 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7×C11 · Schur multiplier (H2) = C1 |
| direct product | C7×C11×#1181 |
| Fitting, socle, Hall | C7×C11×C29 ⋊ C4 |
| derived, Sylow | C29 ⋊ C4×C7×C11 |
| Hall | C11×C29 ⋊ C4×C7 |
| Hall | C7×C29 ⋊ C4×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7×C11 | #1181 |
| commutator, hypocenter | C29 | C4×C7×C11 |
| Frattini | C1 | G |
| Fitting, socle | C7×C11×C29 | C4 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C7×C11 | |
24 conjugacy classes of subgroups.
847 conjugacy classes — view the full character table.
| maximal subgroup of | C11×ΓL(1,𝔽8)×#1181, C3×C7×C11×#1181, C7×C11×C3⋊#1181 |
| maximal normal subgroup of | C11×ΓL(1,𝔽8)×#1181, C3×C7×C11×#1181 |
| maximal quotient of | C3×C7×C11×#1181, C7×C11×C3⋊#1181 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8932, 21);