Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of A5 |
| automorphism | Aut(G) = D4×S5 (order 960) · Inn(G) = A5 · Out(G) = C2×D4 |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| direct product | C2×C4×A5 |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C2×C4 | A5 |
| commutator, hypocenter | A5 | C2×C4 |
| Frattini, cosocle | C2 | C22×A5 |
| socle, prime radical | C22×A5 | C2 |
| LCS | G ▷ A5 | |
| UCS | C1 ◁ C2×C4 | |
120 conjugacy classes of subgroups.
| minimal degree | μ(G) = 11 |
| transitive degree | μt(G) = 40 |
A minimal faithful permutation representation — 2 generators on 11 points:
(1,2)(7,10,11);(1,2)(3,4,5,6)(7,8,9,10,11)40 conjugacy classes — view the full character table.
| maximal subgroup of | #11751496, C2×A5⋊C8, C4⋊(A5⋊C4), … |
| maximal normal subgroup of | #11751496, C2×A5⋊C8, C4⋊(A5⋊C4), … |
| maximal quotient of | C42×A5, C4×#6732, C22⋊C4×A5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 954);