Finite Group DatabasebetaFinite Group Databasebeta| order | 32850 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C5⋊D3285 |
| unambiguous semidirect product | C9⋊(C5⋊D365) |
| unambiguous semidirect product | C73⋊(C5⋊D45) |
| Fitting, derived, Hall | C52×C9×C73 ⋊ C2 |
| Hall | C52×C73 ⋊ D9 |
| Hall | C9×C73 ⋊ C5⋊D5 |
| Hall | C52×C9 ⋊ D73 |
| Sylow | C73 ⋊ C5⋊D45 |
| Sylow | C52 ⋊ D657 |
| Sylow | C9 ⋊ C5⋊D365 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C52×C9×C73 | C2 |
| Frattini | C3 | C3⋊(C5⋊D365) |
| socle | C3×C52×C73 | D3 |
| LCS | G ▷ C52×C9×C73 | |
| UCS | C1 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16425 |
Polycyclic presentation:
2,3,5^2,73,3|b^3=f^2,b^a=b^2f,c^a=c^4,d^a=d^4,e^a=e^72,f^a=f^28214 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32850, 54);