Finite Group DatabasebetaFinite Group Databasebeta| order | 15300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C25 · Schur multiplier (H2) = C2×C3 |
| direct product | C3⋊D3×C25×D17 |
| unambiguous semidirect product | (C3×D17)⋊(D3×C25) |
| Fitting, Hall | C32×C17×C25 ⋊ C22 |
| derived, Hall | C32×C17 ⋊ C22×C25 |
| Hall | C17×C25 ⋊ C2×C3⋊D3 |
| Hall | C32×C25 ⋊ C2×D17 |
| Sylow | C17 ⋊ C2×C3⋊D3×C25 |
| Sylow | C32 ⋊ C2×C25×D17 |
180 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3825 |
1500 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15300, 88);