Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | D3×#689 |
| Hall | C3×C5 ⋊ C2×Q16 |
| Sylow | C5 ⋊ D3×Q16 |
| Sylow | C3 ⋊ C2×#689 |
120 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 3 generators on 24 points:
(1,2,4,5,3)(6,8,10,16)(7,11,13,20)(9,18,19,15)(12,21,17,14)(22,23,24);(2,3)(4,5)(6,7,10,13)(8,14,16,21)(9,17,19,12)(11,18,20,15);(23,24)51 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#4061, D3×#4062, #11754086, … |
| maximal normal subgroup of | D3×#4061, D3×#4062, #11754086, … |
| maximal quotient of | #11747146, #11747178, #11747198, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 585);