Finite Group DatabasebetaFinite Group Databasebeta| order | 32850 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C5 |
| direct product | C52⋊C3×D219 |
| unambiguous semidirect product | C3⋊(C52⋊C3×D73) |
| Fitting, socle, derived | C3×C52×C73 ⋊ C2×C3 |
| Hall | C3×C73×C52⋊C3 ⋊ C2 |
| Hall | C52×C73 ⋊ C3×D3 |
| Hall | C3×C52⋊C3 ⋊ D73 |
| Sylow | C73 ⋊ D3×C52⋊C3 |
| Sylow | C52 ⋊ C3×D219 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C52×C73 | C2×C3 |
| LCS | G ▷ C3×C52×C73 | |
| UCS | C1 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3285 |
1221 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32850, 98);