Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | AGL(1,𝔽5)×Dic6 |
| unambiguous semidirect product | (C3×AGL(1,𝔽5))⋊Q8 |
| Hall | C3×C5 ⋊ C4×Q8 |
| Sylow | C5 ⋊ C4×Dic6 |
| Sylow | C3 ⋊ Q8×AGL(1,𝔽5) |
140 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 54 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)(4,6,7,11)(5,8,9,10)(12,13,14,16,15);(2,3)(4,5,7,9)(6,10,11,8);(13,14,15,16)45 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#204, #11751661, AGL(1,𝔽5)×Dic12, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#204, #11751661, AGL(1,𝔽5)×Dic12, … |
| maximal quotient of | #11751745, #11751749, Dic6×#170, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 982);