Finite Group DatabasebetaFinite Group Databasebeta| order | 650 |
| isoclinism | isoclinic class of C5⋊D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C13 · Schur multiplier (H2) = C5 |
| direct product | C13×C5⋊D5 |
| unambiguous semidirect product | C5⋊(D5×C13) |
| Fitting, socle, Hall | C52×C13 ⋊ C2 |
| derived, Sylow | C52 ⋊ C2×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | C5⋊D5 |
| commutator, cosocle, hypocenter | C52 | C2×C13 |
| Frattini | C1 | G |
| Fitting, socle | C52×C13 | C2 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C13 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 325 |
182 conjugacy classes — view the full character table.
| maximal subgroup of | C13×#1043, #13049929, C13×#1044, … |
| maximal normal subgroup of | C13×#1043, #13049929, C13×#1044, … |
| maximal quotient of | C13×#1039, C2×C13×C5⋊D5, C3×C13×C5⋊D5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(650, 8);