Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of A5 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
| direct product | C23×A5 |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C23 | A5 |
| commutator, hypocenter | A5 | C23 |
| Frattini | C1 | G |
| LCS | G ▷ A5 | |
| UCS | C1 ◁ C23 | |
312 conjugacy classes of subgroups.
| minimal degree | μ(G) = 11 |
| transitive degree | μt(G) = 40 |
A minimal faithful permutation representation — 3 generators on 11 points:
(1,2)(5,6)(7,8,11);(3,4)(8,10,9);(5,6)(8,10,9)40 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 1187);