Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | Q8×A5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, cosocle | C2 | C22×A5 |
| commutator, socle, prime radical | C2×A5 | C22 |
| Fitting, hypercenter | Q8 | A5 |
| hypocenter | A5 | Q8 |
| LCS | G ▷ C2×A5 ▷ A5 | |
| UCS | C1 ◁ C2 ◁ Q8 | |
84 conjugacy classes of subgroups.
| minimal degree | μ(G) = 13 |
| transitive degree | μt(G) = 40 |
A minimal faithful permutation representation — 2 generators on 13 points:
(1,2,4,6)(3,7,8,5)(9,13,12,11,10);(1,3,4,8)(2,5,6,7)(9,10,11,13,12)25 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 958);