Finite Group DatabasebetaFinite Group Databasebeta| order | 780 |
| isoclinism | isoclinic class of D3×D65 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D3×D65 |
| unambiguous semidirect product | (C5×D3)⋊D13 |
| unambiguous semidirect product | (D3×C13)⋊D5 |
| Fitting, socle, derived, Hall | C3×C5×C13 ⋊ C22 |
| Hall | C5×C13 ⋊ C2×D3 |
| Hall | C3×C13 ⋊ C2×D5 |
| Hall | C3×C5 ⋊ C2×D13 |
| Sylow | C13 ⋊ D3×D5 |
| Sylow | C5 ⋊ D3×D13 |
| Sylow | C3 ⋊ C2×D65 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C5×C13 | C22 |
| LCS | G ▷ C3×C5×C13 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 195 |
102 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#63121, D3×#63122, D3×D5×D13, … |
| maximal normal subgroup of | D3×#63121, D3×#63122, D3×D5×D13, … |
| maximal quotient of | Dic3×D65, D3×Dic65, #13095655, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(780, 41);