Finite Group DatabasebetaFinite Group Databasebeta| order | 22050 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C3 |
| direct product | C7×C3⋊D525 |
| unambiguous semidirect product | C3⋊(C7×D525) |
| unambiguous semidirect product | C7⋊(C7×C3⋊D75) |
| unambiguous semidirect product | C25⋊(C7×C3⋊D21) |
| Fitting, Hall | C32×C72×C25 ⋊ C2 |
| derived | C32×C7×C25 ⋊ C2×C7 |
| Hall | C72×C25 ⋊ C3⋊D3 |
| Hall | C32×C72 ⋊ D25 |
| Hall | C32×C25 ⋊ C7×D7 |
| Sylow | C72 ⋊ C3⋊D75 |
| Sylow | C25 ⋊ C7×C3⋊D21 |
| Sylow | C32 ⋊ C7×D175 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | C3⋊D525 |
| commutator, cosocle, hypocenter | C32×C7×C25 | C2×C7 |
| Frattini | C5 | C7×C3⋊D105 |
| Fitting | C32×C72×C25 | C2 |
| socle | C32×C5×C72 | D5 |
| LCS | G ▷ C32×C7×C25 | |
| UCS | C1 ◁ C7 | |
198 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3150 |
5523 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22050, 219);