Finite Group DatabasebetaFinite Group Databasebeta| order | 15642 |
| isoclinism | isoclinic class of D99 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C79 · Schur multiplier (H2) = C1 |
| direct product | C79×D99 |
| unambiguous semidirect product | C9⋊(D11×C79) |
| unambiguous semidirect product | C11⋊(D9×C79) |
| Fitting, Hall | C9×C11×C79 ⋊ C2 |
| derived, Hall | C9×C11 ⋊ C2×C79 |
| Hall | C11×C79 ⋊ D9 |
| Hall | C9×C79 ⋊ D11 |
| Sylow | C11 ⋊ D9×C79 |
| Sylow | C9 ⋊ D11×C79 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C79 | D99 |
| commutator, cosocle, hypocenter | C9×C11 | C2×C79 |
| Frattini | C3 | D33×C79 |
| Fitting | C9×C11×C79 | C2 |
| socle | C3×C11×C79 | D3 |
| LCS | G ▷ C9×C11 | |
| UCS | C1 ◁ C79 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7821 |
4029 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D79×D99, D9×D11×C79, D99⋊D79, … |
| maximal normal subgroup of | D79×D99, D9×D11×C79, D99⋊D79, … |
| maximal quotient of | C79×Dic99, C2×C79×D99 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15642, 8);