Finite Group DatabasebetaFinite Group Databasebeta| order | 32850 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C73 · Schur multiplier (H2) = C3×C5 |
| direct product | C3×C73×(C5⋊D5)⋊C3 |
| unambiguous semidirect product | (C5⋊D5)⋊(C32×C73) |
| unambiguous semidirect product | (C3×C5⋊D5)⋊(C3×C73) |
| Fitting, socle | C3×C52×C73 ⋊ C2×C3 |
| derived, Sylow | C52 ⋊ C2×C32×C73 |
| Hall | C3×C73×C52⋊C3 ⋊ C2 |
| Hall | C5⋊D5×C73 ⋊ C32 |
| Hall | C52×C73 ⋊ C2×C32 |
| Hall | C3×C52⋊C3 ⋊ C2×C73 |
| Hall | C5⋊D5 ⋊ C32×C73 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C73 | (C5⋊D5)⋊C3 |
| commutator, cosocle, hypocenter | C52 | C2×C32×C73 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C73 | C2×C3 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C3×C73 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3285 |
2190 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32850, 86);