Finite Group DatabasebetaFinite Group Databasebeta| order | 32850 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C5 |
| direct product | D73×C52⋊C9 |
| derived, Hall | C52×C73 ⋊ C2×C9 |
| Hall | C73×C52⋊C9 ⋊ C2 |
| Hall | C52×D73 ⋊ C9 |
| Sylow | C73 ⋊ C2×C52⋊C9 |
| Sylow | C52 ⋊ C9×D73 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C52⋊C3×D73 |
| commutator, hypocenter | C52×C73 | C2×C9 |
| Fitting, socle, cosocle | C3×C52×C73 | C2×C3 |
| prime radical | C3×C52×D73 | C3 |
| LCS | G ▷ C52×C73 | |
| UCS | C1 ◁ C3 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3285 |
1254 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32850, 50);