Finite Group DatabasebetaFinite Group Databasebeta| order | 32550 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C7×C25 · Schur multiplier (H2) = C1 |
| direct product | C2×C7×C25×C31⋊C3 |
| unambiguous semidirect product | (C2×C25×C31)⋊(C3×C7) |
| Fitting, Hall | C2×C7×C25×C31 ⋊ C3 |
| derived, Sylow | C31 ⋊ C2×C3×C7×C25 |
| Hall | C7×C25×C31 ⋊ C2×C3 |
| Hall | C2×C25×C31 ⋊ C3×C7 |
| Hall | C25×C31 ⋊ C2×C3×C7 |
| Hall | C2×C7×C31 ⋊ C3×C25 |
| Hall | C7×C31 ⋊ C2×C3×C25 |
| Hall | C2×C31 ⋊ C3×C7×C25 |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10850 |
4550 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32550, 3);