Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | D4×ΓL(1,𝔽16) |
| Fitting | C3×C5×D4 ⋊ C4 |
| Hall | C3×C5 ⋊ C4×D4 |
| Sylow | C5 ⋊ D4×Dic3 |
| Sylow | C3 ⋊ D4×AGL(1,𝔽5) |
188 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 63 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)(7,8);(1,2,5,3,4)(6,7,8)(10,12);(9,10)(11,12)45 conjugacy classes — view the full character table.
| maximal subgroup of | #11751941, #11751942, #11751945, … |
| maximal normal subgroup of | #11751941, #11751942, #11751945, … |
| maximal quotient of | #11752351, #11752352, #11752353, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 1067);