Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of D3×AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C4×D3×AGL(1,𝔽5) |
| Fitting | C3×C4×C5 ⋊ C2×C4 |
| derived, Hall | C3×C5 ⋊ C2×C42 |
| Sylow | C5 ⋊ C42×D3 |
| Sylow | C3 ⋊ C2×C4×AGL(1,𝔽5) |
216 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 80 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 12 |
| transitive degree | μt(G) = 60 |
A minimal faithful permutation representation — 3 generators on 12 points:
(2,3,4,5)(6,7,8);(1,2,3,5,4)(7,8);(9,10,11,12)60 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 994);