Finite Group DatabasebetaFinite Group Databasebeta| order | 32850 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C25⋊(#10620321⋊C2) |
| unambiguous semidirect product | #10620321⋊D25 |
| derived, Hall | C25×C73 ⋊ C2×C9 |
| Hall | C25×#10620321 ⋊ C2 |
| Hall | D1825 ⋊ C9 |
| Hall | #10620321 ⋊ D25 |
| Sylow | C73 ⋊ C9×D25 |
| Sylow | C25 ⋊ #10620321⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C25⋊(D73⋊C3) |
| commutator, hypocenter | C25×C73 | C2×C9 |
| Frattini | C3×C5 | C5⋊(D73⋊C3) |
| Fitting, cosocle | C3×C25×C73 | C2×C3 |
| socle | C3×C5×C73 | C3×D5 |
| prime radical | C3×D1825 | C3 |
| LCS | G ▷ C25×C73 | |
| UCS | C1 ◁ C3 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16425 |
Polycyclic presentation:
2,3,5,73,3,5|b^3=e,c^5=f^4,c^a=c^4f,d^a=d^72,f^a=f^4,d^b=d^81026 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32850, 12);