Finite Group DatabasebetaFinite Group Databasebeta| order | 22050 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C9 · Schur multiplier (H2) = C1 |
| direct product | C7×D25×C7⋊C9 |
| unambiguous semidirect product | C25⋊(C2×C7×C7⋊C9) |
| unambiguous semidirect product | (C7×D25)⋊(C7×C9) |
| derived | C7×C25 ⋊ C2×C7×C9 |
| Hall | C7×C25×C7⋊C9 ⋊ C2 |
| Hall | C72×D25 ⋊ C9 |
| Hall | C72×C25 ⋊ C2×C9 |
| Sylow | C72 ⋊ C9×D25 |
| Sylow | C25 ⋊ C2×C7×C7⋊C9 |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1575 |
1470 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22050, 72);