Finite Group DatabasebetaFinite Group Databasebeta| order | 22050 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | (C5⋊D5)⋊#89204 |
| derived, Hall | C52×C72 ⋊ C2×C9 |
| Hall | C52⋊#89204 ⋊ C2 |
| Hall | C72×C5⋊D5 ⋊ C9 |
| Hall | C5⋊D5 ⋊ #89204 |
| Sylow | C72 ⋊ (C5⋊D5)⋊C9 |
| Sylow | C52 ⋊ C2×#89204 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | (C5⋊D5)⋊#3861 |
| commutator, hypocenter | C52×C72 | C2×C9 |
| Fitting, socle, cosocle | C3×C52×C72 | C2×C3 |
| prime radical | C3×C72×C5⋊D5 | C3 |
| LCS | G ▷ C52×C72 | |
| UCS | C1 ◁ C3 | |
200 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2205 |
Polycyclic presentation:
2,3,5^2,7^2,3|b^3=g,c^a=c^4,d^a=d^4,c^b=cd^3,d^b=c^4d^3,e^b=e^2,f^b=f^2702 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22050, 265);