Finite Group DatabasebetaFinite Group Databasebeta| order | 15642 |
| isoclinism | isoclinic class of D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11×C79 · Schur multiplier (H2) = C1 |
| direct product | C11×D9×C79 |
| unambiguous semidirect product | C9⋊(C2×C11×C79) |
| Fitting, Hall | C9×C11×C79 ⋊ C2 |
| derived, Sylow | C9 ⋊ C2×C11×C79 |
| Hall | C9×C79 ⋊ C2×C11 |
| Hall | C9×C11 ⋊ C2×C79 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11×C79 | D9 |
| commutator, cosocle, hypocenter | C9 | C2×C11×C79 |
| Frattini | C3 | D3×C11×C79 |
| Fitting | C9×C11×C79 | C2 |
| socle | C3×C11×C79 | D3 |
| LCS | G ▷ C9 | |
| UCS | C1 ◁ C11×C79 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7821 |
5214 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C11×D9×D79, D9×D11×C79, D9×D869, … |
| maximal normal subgroup of | C11×D9×D79, D9×D11×C79, D9×D869, … |
| maximal quotient of | C11×Dic9×C79, C2×C11×D9×C79 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15642, 6);