Finite Group DatabasebetaFinite Group Databasebeta| order | 22050 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C5⋊(C5⋊#11725075) |
| derived, Hall | C52×C72 ⋊ C2×C9 |
| Hall | C52×#89205 ⋊ C2 |
| Hall | C7×C5⋊D35 ⋊ C9 |
| Hall | #89205 ⋊ C5⋊D5 |
| Sylow | C72 ⋊ C9×C5⋊D5 |
| Sylow | C52 ⋊ #11725075 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C5⋊(C5⋊#64422) |
| commutator, hypocenter | C52×C72 | C2×C9 |
| Fitting, socle, cosocle | C3×C52×C72 | C2×C3 |
| prime radical | C3×C7×C5⋊D35 | C3 |
| LCS | G ▷ C52×C72 | |
| UCS | C1 ◁ C3 | |
208 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 3150 |
Polycyclic presentation:
2,3,5^2,7^2,3|b^3=g,c^a=c^4,d^a=d^4,e^a=e^6,e^b=e^2,f^b=f^4735 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22050, 246);