Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | ΓL(1,𝔽16)⋊Q8 |
| Hall | C3×C5 ⋊ C4×Q8 |
| Sylow | C5 ⋊ #887 |
| Sylow | C3 ⋊ Q8×AGL(1,𝔽5) |
140 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 52 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:
(1,2,3,5,4)(6,7,8)(9,11,12,15)(10,13,14,16);(7,8)(9,10,12,14)(11,16,15,13);(2,3,4,5)(11,15)(13,16)Polycyclic presentation:
2^5,3,5|a^2=d,b^2=e,c^2=e,c^a=ce,g^a=g^2,c^b=ce,f^b=f^2,g^d=g^439 conjugacy classes — view the full character table.
| maximal subgroup of | #11751663, #11751666, #11751669, … |
| maximal normal subgroup of | #11751663, #11751666, #11751669, … |
| maximal quotient of | #11751747, #11751752, #11751755, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 984);