Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | C3×#4064 |
| Fitting | C3×C5×Q16 ⋊ C2 |
| Hall | C3×C5 ⋊ #137 |
| Sylow | C5 ⋊ C3×#137 |
120 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 54 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)(6,14,10,8)(7,20,13,11)(9,16,19,18)(12,15,17,21)(22,23,24);(6,13,10,7)(8,21,14,15)(9,12,19,17)(11,16,20,18);(2,3)(4,5)(8,14)(11,20)(15,21)(16,18)75 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#4064, #11754099, #11754101, … |
| maximal normal subgroup of | D3×#4064, #11754099, #11754101, … |
| maximal quotient of | C3×#65078, C3×#65080, C3×#65084, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 711);