Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | D3×#700 |
| Hall | C3×C5 ⋊ C2×M16 |
| Sylow | C5 ⋊ D3×M16 |
| Sylow | C3 ⋊ C2×#700 |
136 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 50 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)(6,8,10,9)(7,11,12,13)(14,15,16);(2,3,4,5)(6,7,9,11,10,12,8,13);(15,16)42 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#3995, D3×#3996, #11751675, … |
| maximal normal subgroup of | D3×#3995, D3×#3996, #11751675, … |
| maximal quotient of | #11751756, #11751762, #11751763, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 988);