Finite Group DatabasebetaFinite Group Databasebeta| order | 32850 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9×C73 · Schur multiplier (H2) = C5 |
| direct product | C2×C73×C52⋊C9 |
| unambiguous semidirect product | (C2×C52)⋊(C9×C73) |
| derived, Sylow | C52 ⋊ C2×C9×C73 |
| Hall | C2×C52×C73 ⋊ C9 |
| Hall | C52×C73 ⋊ C2×C9 |
| Hall | C2×C52 ⋊ C9×C73 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C73 | C52⋊C3 |
| commutator, hypocenter | C52 | C2×C9×C73 |
| Frattini | C3 | C2×C73×C52⋊C3 |
| Fitting, socle, prime radical | C2×C3×C52×C73 | C3 |
| cosocle | C3×C52 | C2×C3×C73 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C2×C3×C73 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6570 |
4818 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32850, 52);