Finite Group DatabasebetaFinite Group Databasebeta| order | 850 |
| isoclinism | isoclinic class of D17 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C52 · Schur multiplier (H2) = C5 |
| direct product | C52×D17 |
| unambiguous semidirect product | C17⋊(C2×C52) |
| Fitting, socle, Hall | C52×C17 ⋊ C2 |
| derived, Sylow | C17 ⋊ C2×C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52 | D17 |
| commutator, cosocle, hypocenter | C17 | C2×C52 |
| Frattini | C1 | G |
| Fitting, socle | C52×C17 | C2 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C52 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 425 |
250 conjugacy classes — view the full character table.
| maximal subgroup of | C52×#595, C5×#66772, #13133353, … |
| maximal normal subgroup of | C52×#595, C5×#66772, #13133353, … |
| maximal quotient of | C52×Dic17, C2×C52×D17, C3×C52×D17, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(850, 5);