Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of D3×AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | D3×D5⋊C8 |
| unambiguous semidirect product | D5⋊(D3×C8) |
| unambiguous semidirect product | (D3×D5)⋊C8 |
| derived, Hall | C3×C5 ⋊ C22×C8 |
| Sylow | C5 ⋊ C2×D3×C8 |
| Sylow | C3 ⋊ C2×D5⋊C8 |
152 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 16 |
| transitive degree | μt(G) = 120 |
A minimal faithful permutation representation — 3 generators on 16 points:
(1,2,3,5,4)(6,7,8)(9,11,13,12)(10,14,16,15);(2,3,4,5)(9,10,12,15,13,16,11,14);(7,8)60 conjugacy classes — view the full character table.
| maximal subgroup of | D3×C8×AGL(1,𝔽5), D3×#3992, #11751671, … |
| maximal normal subgroup of | D3×C8×AGL(1,𝔽5), D3×#3992, #11751671, … |
| maximal quotient of | D3×D5⋊C16, #11751642, D3×#3990, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 986);