Finite Group DatabasebetaFinite Group Databasebeta| order | 780 |
| isoclinism | isoclinic class of D5×C13⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×D5×C13⋊C3 |
| unambiguous semidirect product | C5⋊(C22×C13⋊C3) |
| unambiguous semidirect product | (C2×C5)⋊(C2×C13⋊C3) |
| unambiguous semidirect product | (C2×D5×C13)⋊C3 |
| Fitting, socle | C2×C5×C13 ⋊ C2×C3 |
| derived, Hall | C5×C13 ⋊ C22×C3 |
| Hall | C2×D5×C13 ⋊ C3 |
| Hall | C5×C13⋊C3 ⋊ C22 |
| Sylow | C13 ⋊ C2×C3×D5 |
| Sylow | C5 ⋊ C22×C13⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D5×C13⋊C3 |
| commutator, cosocle, hypocenter | C5×C13 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C13 | C2×C3 |
| LCS | G ▷ C5×C13 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 130 |
56 conjugacy classes — view the full character table.
| maximal subgroup of | D5×Dic13⋊C3, #10587070⋊C3, #10587072⋊C3, … |
| maximal normal subgroup of | D5×Dic13⋊C3, #10587070⋊C3, #10587072⋊C3, … |
| maximal quotient of | C13⋊C3×Dic10, C4×D5×C13⋊C3, C13⋊C3×D20, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(780, 22);