Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of AGL(1,𝔽5) |
| automorphism | Aut(G) = C22×D4×AGL(1,𝔽5) (order 640) · Inn(G) = AGL(1,𝔽5) · Out(G) = C22×D4 |
| homology | Abelianization (H1) = C3×C4×C8 · Schur multiplier (H2) = C4 |
| direct product | C3×C8×AGL(1,𝔽5) |
| Fitting | C3×C5×C8 ⋊ C4 |
| derived, Sylow | C5 ⋊ C3×C4×C8 |
| Hall | C3×C5 ⋊ C4×C8 |
88 conjugacy classes of subgroups.
| minimal degree | μ(G) = 16 |
| transitive degree | μt(G) = 120 |
A minimal faithful permutation representation — 2 generators on 16 points:
(2,5,4,3)(14,15,16);(1,2,3,5,4)(6,10,12,7,9,13,8,11)120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 271);