Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| isoclinism | isoclinic class of D3×A5 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C2 |
| direct product | Dic3×A5 |
| unambiguous semidirect product | C3⋊(C4×A5) |
| derived | C3×A5 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D3×A5 |
| commutator, hypocenter | C3×A5 | C4 |
| Fitting, cosocle | C2×C3 | C2×A5 |
| socle, prime radical | C2×C3×A5 | C2 |
| LCS | G ▷ C3×A5 | |
| UCS | C1 ◁ C2 | |
75 conjugacy classes of subgroups.
| minimal degree | μ(G) = 12 |
| transitive degree | μt(G) = 60 |
30 conjugacy classes — view the full character table.
| maximal subgroup of | #13088282, ΓL(2,𝔽4)⋊C4, Dic3×S5, … |
| maximal normal subgroup of | #13088282, ΓL(2,𝔽4)⋊C4, Dic3×S5, … |
| maximal quotient of | C3⋊C8×A5, C3⋊#91145, Dic3×SL(2,𝔽5), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 416);