Finite Group DatabasebetaFinite Group Databasebeta| order | 32850 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C52×C9 · Schur multiplier (H2) = C5 |
| direct product | C52×#10620321⋊C2 |
| unambiguous semidirect product | #10620321⋊(C2×C52) |
| derived, Sylow | C73 ⋊ C2×C52×C9 |
| Hall | C52×#10620321 ⋊ C2 |
| Hall | C52×D73 ⋊ C9 |
| Hall | C52×C73 ⋊ C2×C9 |
| Hall | #10620321 ⋊ C2×C52 |
| Hall | D73 ⋊ C52×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C52 | D73⋊C3 |
| commutator, hypocenter | C73 | C2×C52×C9 |
| Frattini | C3 | C52×D73⋊C3 |
| Fitting, socle | C3×C52×C73 | C2×C3 |
| prime radical | C3×C52×D73 | C3 |
| cosocle | C3×C73 | C2×C3×C52 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C3×C52 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16425 |
1350 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32850, 38);