Finite Group DatabasebetaFinite Group Databasebeta| order | 780 |
| isoclinism | isoclinic class of D15 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×Dic15 |
| unambiguous semidirect product | C3⋊(C13×Dic5) |
| derived, Hall | C3×C5 ⋊ C4×C13 |
| Hall | C3×C5×C13 ⋊ C4 |
| Hall | C5×C13 ⋊ Dic3 |
| Hall | C3×C13 ⋊ Dic5 |
| Sylow | C5 ⋊ Dic3×C13 |
| Sylow | C3 ⋊ C13×Dic5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C13 | D15 |
| commutator, hypocenter | C3×C5 | C4×C13 |
| Frattini | C2 | C13×D15 |
| Fitting, socle, prime radical | C2×C3×C5×C13 | C2 |
| cosocle | C2×C3×C5 | C2×C13 |
| LCS | G ▷ C3×C5 | |
| UCS | C1 ◁ C2×C13 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 780 |
234 conjugacy classes — view the full character table.
| maximal subgroup of | D13×Dic15, #13095634, #13095636, … |
| maximal normal subgroup of | D13×Dic15, #13095634, #13095636, … |
| maximal quotient of | C13×C3⋊#168, C2×C13×Dic15, C13×Dic45, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(780, 10);