Finite Group DatabasebetaFinite Group Databasebeta| order | 11868 |
| isoclinism | isoclinic class of C43⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C23 · Schur multiplier (H2) = C1 |
| direct product | C4×C23×C43⋊C3 |
| unambiguous semidirect product | (C4×C43)⋊(C3×C23) |
| unambiguous semidirect product | (C4×C23×C43)⋊C3 |
| Fitting, Hall | C4×C23×C43 ⋊ C3 |
| derived, Sylow | C43 ⋊ C3×C4×C23 |
| Hall | C23×C43 ⋊ C3×C4 |
| Hall | C4×C43 ⋊ C3×C23 |
24 conjugacy classes of subgroups.
1564 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Dic3×C23×C43⋊C3, C3×C4×C23×C43⋊C3 |
| maximal normal subgroup of | C3×C4×C23×C43⋊C3 |
| maximal quotient of | C4×C23×C43⋊C9, Dic3×C23×C43⋊C3, C3×C4×C23×C43⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11868, 2);