Finite Group DatabasebetaFinite Group Databasebeta| order | 32850 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1 |
| direct product | C5×C5⋊(#10620323⋊C2) |
| unambiguous semidirect product | C5⋊(C5×#10620323⋊C2) |
| unambiguous semidirect product | #10620323⋊(C5×D5) |
| Fitting, socle, Hall | C52×C73 ⋊ C2×C9 |
| derived | C5×C73 ⋊ C2×C5×C9 |
| Hall | C52×#10620323 ⋊ C2 |
| Hall | C5×D365 ⋊ C9 |
| Hall | #10620323 ⋊ C5×D5 |
| Sylow | C73 ⋊ C5×C9×D5 |
| Sylow | C52 ⋊ #10620323⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C5⋊(#10620323⋊C2) |
| commutator, hypocenter | C5×C73 | C2×C5×C9 |
| Frattini | C1 | G |
| Fitting, socle | C52×C73 | C2×C9 |
| prime radical | C5×C5⋊(D73⋊C3) | C3 |
| cosocle | C5×C73⋊C3 | C2×C3×C5 |
| LCS | G ▷ C5×C73 | |
| UCS | C1 ◁ C5 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 730 |
280 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32850, 75);