Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | D3×C4⋊AGL(1,𝔽5) |
| Fitting | C3×C4×C5 ⋊ C2×C4 |
| Hall | C3×C5 ⋊ C2×C4⋊C4 |
| Sylow | C5 ⋊ D3×C4⋊C4 |
| Sylow | C3 ⋊ C2×C4⋊AGL(1,𝔽5) |
184 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 184 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) = 12 |
| transitive degree | μt(G) = 60 |
A minimal faithful permutation representation — 3 generators on 12 points:
(1,2,3,5,4)(6,7,8,9)(10,11,12);(2,3,4,5)(7,9);(11,12)42 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#3993, D3×#3994, #11751653, … |
| maximal normal subgroup of | D3×#3993, D3×#3994, #11751653, … |
| maximal quotient of | D3×#3993, D3×#3994, #11751653, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 996);