Finite Group DatabasebetaFinite Group Databasebeta| order | 22050 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C7×C25 · Schur multiplier (H2) = C1 |
| direct product | C3×C7×C25×D21 |
| unambiguous semidirect product | C3⋊(C3×C7×D7×C25) |
| Fitting, Hall | C32×C72×C25 ⋊ C2 |
| derived | C3×C7 ⋊ C2×C3×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 |
162 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1050 |
6300 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22050, 210);