Finite Group DatabasebetaFinite Group Databasebeta| order | 30225 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C25 · Schur multiplier (H2) = C1 |
| direct product | C25×#11925881 |
| Fitting, Hall | C13×C25×C31 ⋊ C3 |
| derived, Hall | C13×C31 ⋊ C3×C25 |
| Hall | C25×C31 ⋊ C13⋊C3 |
| Hall | C13×C25 ⋊ C31⋊C3 |
| Sylow | C31 ⋊ C25×C13⋊C3 |
| Sylow | C13 ⋊ C25×C31⋊C3 |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10075 |
3425 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30225, 6);