Finite Group DatabasebetaFinite Group Databasebeta| order | 22050 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3×C7 |
| unambiguous semidirect product | C3⋊(C3⋊(C7⋊D175)) |
| unambiguous semidirect product | C7⋊(C3⋊D525) |
| unambiguous semidirect product | C25⋊(C3⋊(C3⋊(C7⋊D7))) |
| Fitting, derived, Hall | C32×C72×C25 ⋊ C2 |
| Hall | C72×C25 ⋊ C3⋊D3 |
| Hall | C32×C72 ⋊ D25 |
| Hall | C32×C25 ⋊ C7⋊D7 |
| Sylow | C72 ⋊ C3⋊D75 |
| Sylow | C25 ⋊ C3⋊(C3⋊(C7⋊D7)) |
| Sylow | C32 ⋊ C7⋊D175 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C32×C72×C25 | C2 |
| Frattini | C5 | C3⋊(C3⋊(C5⋊(C7⋊D7))) |
| socle | C32×C5×C72 | D5 |
| LCS | G ▷ C32×C72×C25 | |
| UCS | C1 | |
360 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11025 |
Polycyclic presentation:
2,3^2,5,7^2,5|d^5=g^4,b^a=b^2,c^a=c^2,d^a=d^4g,e^a=e^6,f^a=f^6,g^a=g^45514 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22050, 220);