Finite Group DatabasebetaFinite Group Databasebeta| order | 850 |
| isoclinism | isoclinic class of D85 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D85 |
| unambiguous semidirect product | C5⋊(C5×D17) |
| unambiguous semidirect product | C17⋊(C5×D5) |
| Fitting, socle, Hall | C52×C17 ⋊ C2 |
| derived | C5×C17 ⋊ C2×C5 |
| Sylow | C52 ⋊ D17 |
| Sylow | C17 ⋊ C5×D5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D85 |
| commutator, cosocle, hypocenter | C5×C17 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C52×C17 | C2 |
| LCS | G ▷ C5×C17 | |
| UCS | C1 ◁ C5 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 170 |
220 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#66775, C5×#66776, #13133350, … |
| maximal normal subgroup of | C5×#66775, C5×#66776, #13133350, … |
| maximal quotient of | C5×Dic85, C2×C5×D85, C3×C5×D85, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(850, 7);