Finite Group DatabasebetaFinite Group Databasebeta| order | 780 |
| isoclinism | isoclinic class of D65 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×C3×D65 |
| unambiguous semidirect product | (C2×C5)⋊(C3×D13) |
| Fitting, socle | C2×C3×C5×C13 ⋊ C2 |
| derived, Hall | C5×C13 ⋊ C22×C3 |
| Hall | C3×C5×C13 ⋊ C22 |
| Hall | C3×C13 ⋊ C2×D5 |
| Hall | C3×C5 ⋊ C2×D13 |
| Sylow | C13 ⋊ C2×C3×D5 |
| Sylow | C5 ⋊ C2×C3×D13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D65 |
| commutator, cosocle, hypocenter | C5×C13 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C5×C13 | C2 |
| LCS | G ▷ C5×C13 | |
| UCS | C1 ◁ C2×C3 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 390 |
204 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10587069, C3×#10587071, C3×#10587072, … |
| maximal normal subgroup of | C3×#10587069, C3×#10587071, C3×#10587072, … |
| maximal quotient of | C3×Dic130, C3×C4×D65, C3×D260, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(780, 48);