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) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C3×D4×AGL(1,𝔽5) |
| Fitting | C3×C5×D4 ⋊ C4 |
| Hall | C3×C5 ⋊ C4×D4 |
| Sylow | C5 ⋊ C3×C4×D4 |
188 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 76 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:
(2,5,4,3)(10,11,12);(1,2,3,5,4)(7,9);(6,7)(8,9)75 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#213, #11751940, AGL(1,𝔽5)×#214, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#213, #11751940, AGL(1,𝔽5)×#214, … |
| maximal quotient of | C3×#65692, C3×#65693, C3×#65694, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 1054);