Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| isoclinism | isoclinic class of D3×A5 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C22 |
| direct product | C2×D3×A5 |
| unambiguous semidirect product | C3⋊(C22×A5) |
| unambiguous semidirect product | (C2×C3)⋊(C2×A5) |
| Fitting | C2×C3 ⋊ C2×A5 |
| socle | C2×C3×A5 ⋊ C2 |
| derived | C3×A5 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D3×A5 |
| commutator, hypocenter | C3×A5 | C22 |
| Frattini | C1 | G |
| Fitting | C2×C3 | C2×A5 |
| socle | C2×C3×A5 | C2 |
| cosocle | C3 | C22×A5 |
| LCS | G ▷ C3×A5 | |
| UCS | C1 ◁ C2 | |
149 conjugacy classes of subgroups; only the 14 normal subgroups are shown.
This group has 149 conjugacy classes of subgroups — too many to draw. Only its 14 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 30 |
30 conjugacy classes — view the full character table.
| maximal subgroup of | D3×A5⋊C4, #13088285, #13088288, … |
| maximal normal subgroup of | D3×A5⋊C4, #13088285, #13088288, … |
| maximal quotient of | Dic6×A5, C4×D3×A5, D12×A5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 771);