Finite Group DatabasebetaFinite Group Databasebeta| order | 11868 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C23 · Schur multiplier (H2) = C1 |
| direct product | C23×Dic129 |
| unambiguous semidirect product | C3⋊(C23×Dic43) |
| unambiguous semidirect product | C43⋊(Dic3×C23) |
| derived, Hall | C3×C43 ⋊ C4×C23 |
| Hall | C3×C23×C43 ⋊ C4 |
| Hall | C23×C43 ⋊ Dic3 |
| Hall | C3×C23 ⋊ Dic43 |
| Sylow | C43 ⋊ Dic3×C23 |
| Sylow | C3 ⋊ C23×Dic43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C23 | D129 |
| commutator, hypocenter | C3×C43 | C4×C23 |
| Frattini | C2 | C23×D129 |
| Fitting, socle, prime radical | C2×C3×C23×C43 | C2 |
| cosocle | C2×C3×C43 | C2×C23 |
| LCS | G ▷ C3×C43 | |
| UCS | C1 ◁ C2×C23 | |
24 conjugacy classes of subgroups.
3036 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C23×Dic387, C23×C3⋊((C43⋊C3)⋊C4), C23×C3⋊Dic129, … |
| maximal normal subgroup of | C23×C3⋊((C43⋊C3)⋊C4), C3×C23×Dic129 |
| maximal quotient of | C23×Dic387, C23×C3⋊Dic129, C3×C23×Dic129 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11868, 7);