Finite Group DatabasebetaFinite Group Databasebeta| order | 32850 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3×C5 |
| direct product | C2×C52⋊C3×C73⋊C3 |
| unambiguous semidirect product | (C2×C52⋊(C73⋊C3))⋊C3 |
| unambiguous semidirect product | (C2×C73×C52⋊C3)⋊C3 |
| unambiguous semidirect product | (C2×C52×C73⋊C3)⋊C3 |
| Fitting, socle, Hall | C2×C52×C73 ⋊ C32 |
| derived, Hall | C52×C73 ⋊ C2×C32 |
| Hall | C2×C73 ⋊ C3×C52⋊C3 |
| Sylow | C73 ⋊ C2×C3×C52⋊C3 |
| Hall | C2×C52 ⋊ C3×C73⋊C3 |
| Sylow | C52 ⋊ C2×C3×C73⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C52⋊C3×C73⋊C3 |
| commutator, cosocle, hypocenter | C52×C73 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C2×C52×C73 | C32 |
| LCS | G ▷ C52×C73 | |
| UCS | C1 ◁ C2 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2190 |
594 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32850, 80);