Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | Aut(G) = C22×D4×AGL(1,𝔽5) (order 640) · Inn(G) = C22⋊AGL(1,𝔽5) · Out(G) = C23 |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C3×#4007 |
| Fitting | C3×C5×D4 ⋊ C4 |
| Hall | C3×C5 ⋊ #102 |
| Sylow | C5 ⋊ C3×#102 |
100 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 100 conjugacy classes of subgroups — too many to draw. Only its 36 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 — 2 generators on 16 points:
(1,2,3,5,4)(7,10)(8,13)(11,12)(14,15,16);(2,5,4,3)(6,7)(8,10)(9,12)(11,13)57 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#4007, #11751937, #11751938, … |
| maximal normal subgroup of | D3×#4007, #11751937, #11751938, … |
| maximal quotient of | C3×#64868, C3×#64871, C3×#64873, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 287);