Finite Group DatabasebetaFinite Group Databasebeta| order | 24804 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C3×Dic689⋊C3 |
| unambiguous semidirect product | Dic689⋊C32 |
| unambiguous semidirect product | (C3×Dic689)⋊C3 |
| derived, Hall | C13×C53 ⋊ C32×C4 |
| Hall | C3×C13⋊C3×C53 ⋊ C4 |
| Hall | Dic689 ⋊ C32 |
| Hall | C3×C13⋊C3 ⋊ Dic53 |
| Sylow | C53 ⋊ C3×Dic13⋊C3 |
| Sylow | C13 ⋊ C32×Dic53 |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8268 |
1140 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24804, 73);