Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×D3×Dic10 |
| Hall | C3×C5 ⋊ C22×Q8 |
| Sylow | C5 ⋊ C2×D3×Q8 |
| Sylow | C3 ⋊ C22×Dic10 |
312 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 132 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 4 generators on 18 points:
(3,4,5)(6,7,9,10,8)(11,13,14,18)(12,15,16,17);(1,2)(7,8)(9,10)(11,12,14,16)(13,17,18,15);(4,5);(1,2)78 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#3942, #11747489, #11747494, … |
| maximal normal subgroup of | D3×#3942, #11747489, #11747494, … |
| maximal quotient of | #11752462, #11752466, #11752470, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 1078);