Finite Group DatabasebetaFinite Group Databasebeta| order | 24684 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C121 · Schur multiplier (H2) = C1 |
| direct product | C121×C3⋊#595 |
| unambiguous semidirect product | C3⋊(#595×C121) |
| Fitting, Hall | C3×C17×C121 ⋊ C4 |
| derived, Hall | C3×C17 ⋊ C4×C121 |
| Hall | C17×C121 ⋊ Dic3 |
| Hall | C3×C121 ⋊ #595 |
| Sylow | C17 ⋊ Dic3×C121 |
| Sylow | C3 ⋊ #595×C121 |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6171 |
2178 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24684, 13);