Finite Group DatabasebetaFinite Group Databasebeta| order | 22050 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1 |
| direct product | C3×C7×D525 |
| unambiguous semidirect product | C3⋊(C3×C7×D175) |
| unambiguous semidirect product | C25⋊(C3×C7×D21) |
| Fitting, Hall | C32×C72×C25 ⋊ C2 |
| derived | C3×C7×C25 ⋊ C2×C3×C7 |
| Hall | C72×C25 ⋊ C3×D3 |
| Hall | C32×C72 ⋊ D25 |
| Hall | C32×C25 ⋊ C7×D7 |
| Sylow | C72 ⋊ C3×D75 |
| Sylow | C25 ⋊ C3×C7×D21 |
| Sylow | C32 ⋊ C7×D175 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C7 | D525 |
| commutator, cosocle, hypocenter | C3×C7×C25 | C2×C3×C7 |
| Frattini | C5 | C3×C7×D105 |
| Fitting | C32×C72×C25 | C2 |
| socle | C32×C5×C72 | D5 |
| LCS | G ▷ C3×C7×C25 | |
| UCS | C1 ◁ C3×C7 | |
162 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1050 |
5544 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22050, 213);