Finite Group DatabasebetaFinite Group Databasebeta| order | 11748 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×Dic979 |
| unambiguous semidirect product | C11⋊(C3×Dic89) |
| derived, Hall | C11×C89 ⋊ C3×C4 |
| Hall | C3×C11×C89 ⋊ C4 |
| Hall | C3×C89 ⋊ Dic11 |
| Sylow | C89 ⋊ C3×Dic11 |
| Hall | C3×C11 ⋊ Dic89 |
| Sylow | C11 ⋊ C3×Dic89 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D979 |
| commutator, hypocenter | C11×C89 | C3×C4 |
| Frattini | C2 | C3×D979 |
| Fitting, socle, prime radical | C2×C3×C11×C89 | C2 |
| cosocle | C2×C11×C89 | C2×C3 |
| LCS | G ▷ C11×C89 | |
| UCS | C1 ◁ C2×C3 | |
24 conjugacy classes of subgroups.
2946 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C9×Dic979, C3×Dic2937, C32×Dic979 |
| maximal normal subgroup of | C9×Dic979, C32×Dic979 |
| maximal quotient of | C9×Dic979, C3×Dic2937, C32×Dic979 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11748, 5);