Finite Group DatabasebetaFinite Group Databasebeta| order | 650 |
| isoclinism | isoclinic class of D13 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C52 · Schur multiplier (H2) = C5 |
| direct product | C52×D13 |
| unambiguous semidirect product | C13⋊(C2×C52) |
| Fitting, socle, Hall | C52×C13 ⋊ C2 |
| derived, Sylow | C13 ⋊ C2×C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52 | D13 |
| commutator, cosocle, hypocenter | C13 | C2×C52 |
| Frattini | C1 | G |
| Fitting, socle | C52×C13 | C2 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C52 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 325 |
200 conjugacy classes — view the full character table.
| maximal subgroup of | C52×#261, C5×#63118, #13049937, … |
| maximal normal subgroup of | C52×#261, C5×#63118, #13049937, … |
| maximal quotient of | C52×Dic13, C2×C52×D13, C3×C52×D13, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(650, 5);