Finite Group DatabasebetaFinite Group Databasebeta| order | 32850 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C73 · Schur multiplier (H2) = C1 |
| direct product | C3×C73×#3874 |
| Fitting, socle | C3×C52×C73 ⋊ D3 |
| derived | C52⋊C3 ⋊ C2×C3×C73 |
| Hall | C3×C73×C52⋊C3 ⋊ C2 |
| Hall | C52×C73 ⋊ C3×D3 |
| Hall | C3×C52⋊C3 ⋊ C2×C73 |
| Sylow | C52 ⋊ C3×D3×C73 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C73 | #3874 |
| commutator, cosocle, hypocenter | C52⋊C3 | C2×C3×C73 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C73 | D3 |
| LCS | G ▷ C52⋊C3 | |
| UCS | C1 ◁ C3×C73 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3285 |
2847 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32850, 84);