Finite Group DatabasebetaFinite Group Databasebeta| order | 32850 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3×C5 |
| Fitting, socle, derived, Hall | C52×C73 ⋊ C2×C32 |
| Hall | C52⋊C3×C73⋊C3 ⋊ C2 |
| Hall | C52×D73 ⋊ C32 |
| Hall | D73 ⋊ C3×C52⋊C3 |
| Sylow | C73 ⋊ C2×C3×C52⋊C3 |
| Sylow | C52 ⋊ C3×D73⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C52×C73 | C2×C32 |
| LCS | G ▷ C52×C73 | |
| UCS | C1 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1095 |
198 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32850, 67);