Finite Group DatabasebetaFinite Group Databasebeta| order | 22050 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C5 |
No aliases for this group.
| derived, Hall | C52×C49 ⋊ C2×C9 |
| Hall | C49×C52⋊C9 ⋊ C2 |
| Hall | C5⋊D245 ⋊ C9 |
| Hall | C52⋊C9 ⋊ D49 |
| Sylow | C49 ⋊ (C5⋊D5)⋊C9 |
| Sylow | C52 ⋊ C9×D49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #20301201 |
| commutator, hypocenter | C52×C49 | C2×C9 |
| Frattini | C3×C7 | #11760384 |
| Fitting, cosocle | C3×C52×C49 | C2×C3 |
| socle | C3×C52×C7 | C3×D7 |
| prime radical | C3×C5⋊D245 | C3 |
| LCS | G ▷ C52×C49 | |
| UCS | C1 ◁ C3 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2205 |
Polycyclic presentation:
2,3,5^2,7,3,7|b^3=f,e^7=g^6,c^a=c^4,d^a=d^4,e^a=e^6g,g^a=g^6,c^b=cd,d^b=c^2d^3822 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22050, 44);