Finite Group DatabasebetaFinite Group Databasebeta| order | 780 |
| isoclinism | isoclinic class of D5×C13⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | Dic5×C13⋊C3 |
| unambiguous semidirect product | (C13×Dic5)⋊C3 |
| derived, Hall | C5×C13 ⋊ C3×C4 |
| Hall | C13×Dic5 ⋊ C3 |
| Hall | C5×C13⋊C3 ⋊ C4 |
| Sylow | C13 ⋊ C3×Dic5 |
| Sylow | C5 ⋊ C4×C13⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D5×C13⋊C3 |
| commutator, hypocenter | C5×C13 | C3×C4 |
| Fitting, socle, cosocle | C2×C5×C13 | C2×C3 |
| prime radical | C2×C5×C13⋊C3 | C2 |
| LCS | G ▷ C5×C13 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 260 |
56 conjugacy classes — view the full character table.
| maximal subgroup of | C13⋊C3×#170, #10587064⋊C3, Dic5×D13⋊C3, … |
| maximal normal subgroup of | C13⋊C3×#170, #10587064⋊C3, Dic5×D13⋊C3, … |
| maximal quotient of | C13⋊C3×#168, C2×Dic5×C13⋊C3, Dic5×C13⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(780, 2);