Finite Group DatabasebetaFinite Group Databasebeta| order | 11748 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C1 |
| direct product | C3×#67063⋊C11 |
| unambiguous semidirect product | #67063⋊(C3×C11) |
| unambiguous semidirect product | (C3×#67063)⋊C11 |
| Fitting, socle, Hall | C3×C89 ⋊ C4×C11 |
| derived, Sylow | C89 ⋊ C3×C4×C11 |
| Hall | C3×C89⋊C11 ⋊ C4 |
| Hall | C3×#67063 ⋊ C11 |
| Hall | C89⋊C11 ⋊ C3×C4 |
| Hall | #67063 ⋊ C3×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #67063⋊C11 |
| commutator, hypocenter | C89 | C3×C4×C11 |
| Frattini | C1 | G |
| Fitting, socle | C3×C89 | C4×C11 |
| prime radical | C3×D89⋊C11 | C2 |
| cosocle | D89 | C2×C3×C11 |
| LCS | G ▷ C89 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
138 conjugacy classes — view the full character table.
| maximal subgroup of | C9×#67063⋊C11, C32×#67063⋊C11, C3×C3⋊(#67063⋊C11) |
| maximal normal subgroup of | C9×#67063⋊C11, C32×#67063⋊C11 |
| maximal quotient of | C9×#67063⋊C11, C32×#67063⋊C11, C3×C3⋊(#67063⋊C11) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11748, 14);