Finite Group DatabasebetaFinite Group Databasebeta| order | 24684 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×C121⋊#595 |
| unambiguous semidirect product | C121⋊(C3×#595) |
| Fitting, Hall | C3×C17×C121 ⋊ C4 |
| derived, Hall | C17×C121 ⋊ C3×C4 |
| Hall | C3×C121 ⋊ #595 |
| Sylow | C121 ⋊ C3×#595 |
| Hall | C3×C17 ⋊ Dic121 |
| Sylow | C17 ⋊ C3×Dic121 |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6171 |
1824 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24684, 11);