Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of A5 |
| automorphism | ? |
| homology | Abelianization (H1) = C16 · Schur multiplier (H2) = C2 |
| direct product | C16×A5 |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C16 | A5 |
| commutator, hypocenter | A5 | C16 |
| Frattini, cosocle | C8 | C2×A5 |
| socle, prime radical | C2×A5 | C8 |
| LCS | G ▷ A5 | |
| UCS | C1 ◁ C16 | |
61 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 80 |
80 conjugacy classes — view the full character table.
| maximal subgroup of | A5⋊C32, C32×A5, C16×S5, … |
| maximal normal subgroup of | A5⋊C32, C32×A5, C16×S5, … |
| maximal quotient of | C32×A5, C2×C16×A5, C16×SL(2,𝔽5), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 640);