Finite Group DatabasebetaFinite Group Databasebeta| order | 11748 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×D11×D89 |
| unambiguous semidirect product | (D11×C89)⋊(C2×C3) |
| unambiguous semidirect product | (C11×D89)⋊(C2×C3) |
| unambiguous semidirect product | D979⋊(C2×C3) |
| Fitting, socle, Hall | C3×C11×C89 ⋊ C22 |
| derived, Hall | C11×C89 ⋊ C22×C3 |
| Hall | C3×C89 ⋊ C2×D11 |
| Sylow | C89 ⋊ C2×C3×D11 |
| Hall | C3×C11 ⋊ C2×D89 |
| Sylow | C11 ⋊ C2×C3×D89 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D11×D89 |
| commutator, cosocle, hypocenter | C11×C89 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C11×C89 | C22 |
| LCS | G ▷ C11×C89 | |
| UCS | C1 ◁ C3 | |
40 conjugacy classes of subgroups.
966 conjugacy classes — view the full character table.
| maximal subgroup of | C9×D11×D89, C32×D11×D89, C3×D33×D89, … |
| maximal normal subgroup of | C9×D11×D89, C32×D11×D89 |
| maximal quotient of | C9×D11×D89, C32×D11×D89, C3×D33×D89, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11748, 24);