Finite Group DatabasebetaFinite Group Databasebeta| order | 24684 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C17×C121 · Schur multiplier (H2) = C2 |
| direct product | C2×D3×C17×C121 |
| unambiguous semidirect product | C3⋊(C22×C17×C121) |
| unambiguous semidirect product | (C2×C3)⋊(C2×C17×C121) |
| Fitting | C2×C3×C17×C121 ⋊ C2 |
| derived, Sylow | C3 ⋊ C22×C17×C121 |
| Hall | C3×C17×C121 ⋊ C22 |
| Hall | C3×C121 ⋊ C22×C17 |
| Hall | C3×C17 ⋊ C22×C121 |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12342 |
12342 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24684, 25);