Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | Aut(G) = D4×S5 (order 960) · Inn(G) = C22×A5 · Out(G) = C22 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C22 |
| direct product | D4×A5 |
| unambiguous semidirect product | C4⋊(C2×A5) |
| unambiguous semidirect product | C22⋊(C2×A5) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, cosocle | C2 | C22×A5 |
| commutator, socle | C2×A5 | C22 |
| Fitting, hypercenter | D4 | A5 |
| hypocenter | A5 | D4 |
| LCS | G ▷ C2×A5 ▷ A5 | |
| UCS | C1 ◁ C2 ◁ D4 | |
120 conjugacy classes of subgroups.
| minimal degree | μ(G) = 9 |
| transitive degree | μt(G) = 20 |
A minimal faithful permutation representation — 2 generators on 9 points:
(2,4)(6,8)(7,9);(1,2)(3,4)(5,9,8)25 conjugacy classes — view the full character table.
| maximal subgroup of | #11751518, #11751519, D8×A5, … |
| maximal normal subgroup of | #11751518, #11751519, D8×A5, … |
| maximal quotient of | C22⋊C4×A5, C22⋊#6732, C4⋊C4×A5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 956);