Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of #700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C3×D5⋊M16 |
| unambiguous semidirect product | D5⋊(C3×M16) |
| Hall | C3×C5 ⋊ C2×M16 |
| Sylow | C5 ⋊ C2×C3×M16 |
136 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 72 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)(7,11)(10,13)(14,15,16);(6,12,9,8)(7,13,11,10);(2,5,4,3)(6,10,12,7,9,13,8,11)84 conjugacy classes — view the full character table.
| maximal subgroup of | #11746520, #11746521, #11746525, … |
| maximal normal subgroup of | #11746520, #11746521, #11746525, … |
| maximal quotient of | C3×#65676, C3×C4×#700, C3×#65678, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 1049);