Finite Group DatabasebetaFinite Group Databasebeta| order | 22050 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C25 · Schur multiplier (H2) = C7 |
| direct product | C3×C25×C3⋊(C7⋊D7) |
| unambiguous semidirect product | C3⋊(C3×C25×C7⋊D7) |
| Fitting, Hall | C32×C72×C25 ⋊ C2 |
| derived | C3×C72 ⋊ C2×C3×C25 |
| Hall | C72×C25 ⋊ C3×D3 |
| Hall | C32×C72 ⋊ C2×C25 |
| Hall | C32×C25 ⋊ C7⋊D7 |
| Sylow | C72 ⋊ C3×D3×C25 |
| Sylow | C32 ⋊ C25×C7⋊D7 |
270 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7350 |
5625 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22050, 211);