Finite Group DatabasebetaFinite Group Databasebeta| order | 24684 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×Dic363 |
| unambiguous semidirect product | C3⋊(C17×Dic121) |
| unambiguous semidirect product | C121⋊(Dic3×C17) |
| derived, Hall | C3×C121 ⋊ C4×C17 |
| Hall | C3×C17×C121 ⋊ C4 |
| Hall | C17×C121 ⋊ Dic3 |
| Sylow | C121 ⋊ Dic3×C17 |
| Hall | C3×C17 ⋊ Dic121 |
| Sylow | C3 ⋊ C17×Dic121 |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 24684 |
6222 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24684, 7);