Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| isoclinism | isoclinic class of A5 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C2 |
| direct product | C3×C4×A5 |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C3×C4 | A5 |
| commutator, hypocenter | A5 | C3×C4 |
| Frattini, cosocle | C2 | C2×C3×A5 |
| socle, prime radical | C2×C3×A5 | C2 |
| LCS | G ▷ A5 | |
| UCS | C1 ◁ C3×C4 | |
79 conjugacy classes of subgroups.
| transitive degree | μt(G) = 60 |
60 conjugacy classes — view the full character table.
| maximal subgroup of | C3×A5⋊C8, C3⋊(A5⋊C8), C3⋊C8×A5, … |
| maximal normal subgroup of | C3×A5⋊C8, C3⋊(A5⋊C8), C3⋊C8×A5, … |
| maximal quotient of | C3×C8×A5, C3×#91145, C3×C4×SL(2,𝔽5), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 419);