Finite Group DatabasebetaFinite Group Databasebeta| order | 32850 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | (C5⋊D5)⋊#10620323 |
| Fitting, socle, derived, Hall | C52×C73 ⋊ C2×C9 |
| Hall | C52⋊#10620323 ⋊ C2 |
| Hall | C5⋊D5×C73 ⋊ C9 |
| Sylow | C73 ⋊ (C5⋊D5)⋊C9 |
| Hall | C5⋊D5 ⋊ #10620323 |
| Sylow | C52 ⋊ C2×#10620323 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C73 | C2×C9 |
| prime radical | C5⋊D5×C73⋊C3 | C3 |
| cosocle | C52×C73⋊C3 | C2×C3 |
| LCS | G ▷ C52×C73 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1095 |
Polycyclic presentation:
2,3^2,5^2,73|b^3=c,d^a=d^4,e^a=e^4,d^b=de^3,e^b=d^4e^3,f^b=f^2,f^c=f^8142 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32850, 71);