Finite Group DatabasebetaFinite Group Databasebeta| order | 650 |
| isoclinism | isoclinic class of D65 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D65 |
| unambiguous semidirect product | C5⋊(C5×D13) |
| unambiguous semidirect product | C13⋊(C5×D5) |
| Fitting, socle, Hall | C52×C13 ⋊ C2 |
| derived | C5×C13 ⋊ C2×C5 |
| Sylow | C52 ⋊ D13 |
| Sylow | C13 ⋊ C5×D5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D65 |
| commutator, cosocle, hypocenter | C5×C13 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C52×C13 | C2 |
| LCS | G ▷ C5×C13 | |
| UCS | C1 ◁ C5 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 130 |
170 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#63121, C5×#63122, #13049934, … |
| maximal normal subgroup of | C5×#63121, C5×#63122, #13049934, … |
| maximal quotient of | C5×Dic65, C2×C5×D65, C3×C5×D65, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(650, 7);