Finite Group DatabasebetaFinite Group Databasebeta| order | 650 |
| isoclinism | isoclinic class of D13 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C25 · Schur multiplier (H2) = C1 |
| direct product | C25×D13 |
| unambiguous semidirect product | C13⋊(C2×C25) |
| Fitting, Hall | C13×C25 ⋊ C2 |
| derived, Sylow | C13 ⋊ C2×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | D13 |
| commutator, hypocenter | C13 | C2×C25 |
| Frattini | C5 | C5×D13 |
| Fitting | C13×C25 | C2 |
| socle, cosocle | C5×C13 | C2×C5 |
| prime radical | C5×D13 | C5 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C25 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 325 |
200 conjugacy classes — view the full character table.
| maximal subgroup of | C25×#261, #13049904, D13×D25, … |
| maximal normal subgroup of | C25×#261, #13049904, D13×D25, … |
| maximal quotient of | C25×Dic13, C2×C25×D13, C3×C25×D13, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(650, 2);