Finite Group DatabasebetaFinite Group Databasebeta| order | 850 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C17 · Schur multiplier (H2) = C1 |
| direct product | C5×D5×C17 |
| unambiguous semidirect product | C5⋊(C2×C5×C17) |
| Fitting, socle, Hall | C52×C17 ⋊ C2 |
| derived | C5 ⋊ C2×C5×C17 |
| Sylow | C52 ⋊ C2×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C17 | D5 |
| commutator, cosocle, hypocenter | C5 | C2×C5×C17 |
| Frattini | C1 | G |
| Fitting, socle | C52×C17 | C2 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C5×C17 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 170 |
340 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×C17×AGL(1,𝔽5), C5×#66774, C17×#1042, … |
| maximal normal subgroup of | C5×C17×AGL(1,𝔽5), C5×#66774, C17×#1042, … |
| maximal quotient of | C5×C17×Dic5, C2×C5×D5×C17, C3×C5×D5×C17, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(850, 6);