Finite Group DatabasebetaFinite Group Databasebeta| order | 11748 |
| isoclinism | isoclinic class of D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C89 · Schur multiplier (H2) = C1 |
| direct product | C3×Dic11×C89 |
| unambiguous semidirect product | C11⋊(C3×C4×C89) |
| derived, Sylow | C11 ⋊ C3×C4×C89 |
| Hall | C3×C11×C89 ⋊ C4 |
| Hall | C11×C89 ⋊ C3×C4 |
| Hall | C3×C11 ⋊ C4×C89 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C89 | D11 |
| commutator, hypocenter | C11 | C3×C4×C89 |
| Frattini | C2 | C3×D11×C89 |
| Fitting, socle, prime radical | C2×C3×C11×C89 | C2 |
| cosocle | C2×C11 | C2×C3×C89 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C2×C3×C89 | |
24 conjugacy classes of subgroups.
3738 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C9×Dic11×C89, C3×C89×Dic33, C32×Dic11×C89 |
| maximal normal subgroup of | C9×Dic11×C89, C32×Dic11×C89 |
| maximal quotient of | C9×Dic11×C89, C3×C89×Dic33, C32×Dic11×C89 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11748, 4);