Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | Aut(G) = D4×S5 (order 960) · Inn(G) = C2×S5 · Out(G) = C22 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C4⋊S5 |
| Fitting | C4 ⋊ S5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×S5 |
| commutator, socle, cosocle | C2×A5 | C22 |
| Fitting, hypercenter | C4 | S5 |
| hypocenter | A5 | D4 |
| LCS | G ▷ C2×A5 ▷ A5 | |
| UCS | C1 ◁ C2 ◁ C4 | |
96 conjugacy classes of subgroups.
| minimal degree | μ(G) = 9 |
| transitive degree | μt(G) = 20 |
A minimal faithful permutation representation — 2 generators on 9 points:
(2,3)(5,6);(1,2)(3,4)(6,7,8,9)19 conjugacy classes — view the full character table.
| maximal subgroup of | #11751487, #11751488, #11751518, … |
| maximal normal subgroup of | #11751487, #11751488, #11751518, … |
| maximal quotient of | #11751487, #11751488, #11751489, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 944);