Finite Group DatabasebetaFinite Group Databasebeta| order | 780 |
| isoclinism | isoclinic class of D3×D13 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×D3×D13 |
| unambiguous semidirect product | (D3×C13)⋊(C2×C5) |
| unambiguous semidirect product | (C3×D13)⋊(C2×C5) |
| unambiguous semidirect product | D39⋊(C2×C5) |
| Fitting, socle, Hall | C3×C5×C13 ⋊ C22 |
| derived, Hall | C3×C13 ⋊ C22×C5 |
| Hall | C5×C13 ⋊ C2×D3 |
| Hall | C3×C5 ⋊ C2×D13 |
| Sylow | C13 ⋊ C2×C5×D3 |
| Sylow | C3 ⋊ C2×C5×D13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D3×D13 |
| commutator, cosocle, hypocenter | C3×C13 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C13 | C22 |
| LCS | G ▷ C3×C13 | |
| UCS | C1 ◁ C5 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 195 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | C5×D3×#261, D3×#63118, D3×D5×D13, … |
| maximal normal subgroup of | C5×D3×#261, D3×#63118, D3×D5×D13, … |
| maximal quotient of | C5×Dic3×D13, C5×D3×Dic13, C5×#64601, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(780, 37);