Finite Group DatabasebetaFinite Group Databasebeta| order | 650 |
| isoclinism | isoclinic class of C5⋊D65 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C5⋊D65 |
| unambiguous semidirect product | C13⋊(C5⋊D5) |
| Fitting, socle, derived, Hall | C52×C13 ⋊ C2 |
| Sylow | C52 ⋊ D13 |
| Sylow | C13 ⋊ C5⋊D5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C52×C13 | C2 |
| LCS | G ▷ C52×C13 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 325 |
Polycyclic presentation:
2,5^2,13|b^a=b^4,c^a=c^4,d^a=d^12164 conjugacy classes — view the full character table.
| maximal subgroup of | #13049927, #13049928, #13049931, … |
| maximal normal subgroup of | #13049927, #13049928, #13049931, … |
| maximal quotient of | #13049918, C2×C5⋊D65, C3×C5⋊D65, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(650, 9);