Finite Group DatabasebetaFinite Group Databasebeta| order | 15642 |
| isoclinism | isoclinic class of D79 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9×C11 · Schur multiplier (H2) = C1 |
| direct product | C9×C11×D79 |
| Fitting, Hall | C9×C11×C79 ⋊ C2 |
| derived, Sylow | C79 ⋊ C2×C9×C11 |
| Hall | C11×C79 ⋊ C2×C9 |
| Hall | C9×C79 ⋊ C2×C11 |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7821 |
4059 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C9×D11×D79, C11×D9×D79, D79×D99, … |
| maximal normal subgroup of | C9×D11×D79, C11×D9×D79, D79×D99, … |
| maximal quotient of | C9×C11×Dic79, C2×C9×C11×D79 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15642, 3);