Finite Group DatabasebetaFinite Group Databasebeta| order | 22050 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C7 · Schur multiplier (H2) = C3 |
| direct product | C32×C7×D175 |
| unambiguous semidirect product | C25⋊(C32×C7×D7) |
| Fitting, Hall | C32×C72×C25 ⋊ C2 |
| derived | C7×C25 ⋊ C2×C32×C7 |
| Hall | C72×C25 ⋊ C2×C32 |
| Hall | C32×C72 ⋊ D25 |
| Hall | C32×C25 ⋊ C7×D7 |
| Sylow | C72 ⋊ C32×D25 |
| Sylow | C25 ⋊ C32×C7×D7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32×C7 | D175 |
| commutator, cosocle, hypocenter | C7×C25 | C2×C32×C7 |
| Frattini | C5 | C32×C7×D35 |
| Fitting | C32×C72×C25 | C2 |
| socle | C32×C5×C72 | D5 |
| LCS | G ▷ C7×C25 | |
| UCS | C1 ◁ C32×C7 | |
198 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3150 |
5607 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22050, 207);