Finite Group DatabasebetaFinite Group Databasebeta| order | 22050 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | (C5⋊D5)⋊(C49⋊C9) |
| derived, Hall | C52×C49 ⋊ C2×C9 |
| Hall | C52⋊(C49⋊C9) ⋊ C2 |
| Hall | C49×C5⋊D5 ⋊ C9 |
| Hall | C5⋊D5 ⋊ C49⋊C9 |
| Sylow | C49 ⋊ (C5⋊D5)⋊C9 |
| Sylow | C52 ⋊ C2×C49⋊C9 |
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^4,c^a=c^4,d^a=d^4,c^b=cd^3,d^b=c^4d^3,e^b=e^4g,g^b=g^4702 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22050, 45);