Finite Group DatabasebetaFinite Group Databasebeta| order | 7953 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×C241⋊C3 |
| unambiguous semidirect product | C241⋊(C3×C11) |
| unambiguous semidirect product | (C11×C241)⋊C3 |
| Fitting, socle, Hall | C11×C241 ⋊ C3 |
| derived, Sylow | C241 ⋊ C3×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | C241⋊C3 |
| commutator, hypocenter | C241 | C3×C11 |
| Frattini | C1 | G |
| Fitting, socle | C11×C241 | C3 |
| LCS | G ▷ C241 | |
| UCS | C1 ◁ C11 | |
8 conjugacy classes of subgroups.
913 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C11×C241⋊C3, C11×D241⋊C3, D11×C241⋊C3, … |
| maximal normal subgroup of | C2×C11×C241⋊C3, C11×D241⋊C3, D11×C241⋊C3, … |
| maximal quotient of | C2×C11×C241⋊C3, C11×C241⋊C9, C3×C11×C241⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7953, 1);