Finite Group DatabasebetaFinite Group Databasebeta| order | 22050 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C25 · Schur multiplier (H2) = C3 |
| direct product | C7×C25×C3⋊D21 |
| unambiguous semidirect product | C3⋊(C7×C25×D21) |
| unambiguous semidirect product | C7⋊(C7×C3⋊D3×C25) |
| Fitting, Hall | C32×C72×C25 ⋊ C2 |
| derived | C32×C7 ⋊ C2×C7×C25 |
| Hall | C72×C25 ⋊ C3⋊D3 |
| Hall | C32×C72 ⋊ C2×C25 |
| Hall | C32×C25 ⋊ C7×D7 |
| Sylow | C72 ⋊ C3⋊D3×C25 |
| Sylow | C32 ⋊ C7×D7×C25 |
198 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3150 |
5775 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22050, 216);