Finite Group DatabasebetaFinite Group Databasebeta| order | 780 |
| isoclinism | isoclinic class of C5⋊(D13⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | Dic65⋊C3 |
| derived, Hall | C5×C13 ⋊ C3×C4 |
| Hall | Dic65 ⋊ C3 |
| Hall | C5×C13⋊C3 ⋊ C4 |
| Hall | C13⋊C3 ⋊ Dic5 |
| Sylow | C13 ⋊ C3×Dic5 |
| Sylow | C5 ⋊ Dic13⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C5⋊(D13⋊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 |
Polycyclic presentation:
2,3,2,5,13|a^2=c,d^a=d^4,e^a=e^12,e^b=e^344 conjugacy classes — view the full character table.
| maximal subgroup of | #10587066⋊C3, #10587065⋊C3, Dic5×D13⋊C3, … |
| maximal normal subgroup of | #10587066⋊C3, #10587065⋊C3, Dic5×D13⋊C3, … |
| maximal quotient of | #10587059⋊C3, C2×Dic65⋊C3, Dic65⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(780, 3);