Finite Group DatabasebetaFinite Group Databasebeta| order | 15642 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C3 |
| direct product | C11×C3⋊D237 |
| unambiguous semidirect product | C3⋊(C11×D237) |
| unambiguous semidirect product | C79⋊(C11×C3⋊D3) |
| Fitting, socle, Hall | C32×C11×C79 ⋊ C2 |
| derived, Hall | C32×C79 ⋊ C2×C11 |
| Hall | C11×C79 ⋊ C3⋊D3 |
| Hall | C32×C11 ⋊ D79 |
| Sylow | C79 ⋊ C11×C3⋊D3 |
| Sylow | C32 ⋊ C11×D79 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | C3⋊D237 |
| commutator, cosocle, hypocenter | C32×C79 | C2×C11 |
| Frattini | C1 | G |
| Fitting, socle | C32×C11×C79 | C2 |
| LCS | G ▷ C32×C79 | |
| UCS | C1 ◁ C11 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7821 |
3927 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×C11×D237, D33⋊D237, C11×C3⋊D3×D79, … |
| maximal normal subgroup of | D3×C11×D237, D33⋊D237, C11×C3⋊D3×D79, … |
| maximal quotient of | C11×C3⋊Dic237, C2×C11×C3⋊D237 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15642, 24);