Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#932 |
| Fitting | C2×C3×C5×D4 ⋊ C2 |
| Hall | C3×C5 ⋊ AGL(1,ℤ/8) |
| Sylow | C3 ⋊ C5×AGL(1,ℤ/8) |
136 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 58 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)(5,10)(6,7)(9,11)(12,13,14,15,16);(4,6,8,7)(5,9,11,10);(2,3)(4,5)(6,9)(7,10)(8,11)105 conjugacy classes — view the full character table.
| maximal subgroup of | #11749135, #11749136, #11749139, … |
| maximal normal subgroup of | #11749135, #11749136, #11749139, … |
| maximal quotient of | C5×#4964, C5×#4966, C5×#4968, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 811);