Finite Group DatabasebetaFinite Group Databasebeta| order | 850 |
| isoclinism | isoclinic class of D17 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C25 · Schur multiplier (H2) = C1 |
| direct product | C25×D17 |
| unambiguous semidirect product | C17⋊(C2×C25) |
| Fitting, Hall | C17×C25 ⋊ C2 |
| derived, Sylow | C17 ⋊ C2×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | D17 |
| commutator, hypocenter | C17 | C2×C25 |
| Frattini | C5 | C5×D17 |
| Fitting | C17×C25 | C2 |
| socle, cosocle | C5×C17 | C2×C5 |
| prime radical | C5×D17 | C5 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C25 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 425 |
250 conjugacy classes — view the full character table.
| maximal subgroup of | C25×#595, #13133320, D17×D25, … |
| maximal normal subgroup of | C25×#595, #13133320, D17×D25, … |
| maximal quotient of | C25×Dic17, C2×C25×D17, C3×C25×D17, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(850, 2);