Finite Group DatabasebetaFinite Group Databasebeta| order | 22050 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C7×C25 · Schur multiplier (H2) = C1 |
| direct product | D3×C7×ΓL(1,𝔽8)×C25 |
| unambiguous semidirect product | C3⋊(C2×C7×ΓL(1,𝔽8)×C25) |
| unambiguous semidirect product | (D3×C7)⋊(C3×C7×C25) |
| unambiguous semidirect product | (D3×C7×C25)⋊(C3×C7) |
| Fitting | C3×C72×C25 ⋊ C2×C3 |
| derived | C3×C7 ⋊ C2×C3×C7×C25 |
| Hall | C3×C7×ΓL(1,𝔽8)×C25 ⋊ C2 |
| Hall | C72×C25 ⋊ C3×D3 |
| Hall | C3×C7×ΓL(1,𝔽8) ⋊ C2×C25 |
| Sylow | C72 ⋊ C3×D3×C25 |
132 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1575 |
2625 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22050, 180);