Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C8 · Schur multiplier (H2) = C22 |
| direct product | C3×#65725 |
| Hall | C3×C5 ⋊ #504 |
| Sylow | C5 ⋊ C3×#504 |
168 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 96 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 40 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 3 generators on 40 points:
(1,2,3)(4,5,6,8,7)(9,12,14,26,15,13,25,27)(10,17,19,33,20,18,32,34)(11,21,22,35,23,24,36,37)(16,28,29,38,30,31,39,40);(9,11)(10,16)(12,24)(13,21)(14,22)(15,23)(17,31)(18,28)(19,29)(20,30)(25,36)(26,37)(27,35)(32,39)(33,40)(34,38);(5,6,7,8)(9,10,13,18,14,19,27,34,15,20,12,17,25,32,26,33)(11,16,21,28,22,29,35,38,23,30,24,31,36,39,37,40)150 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10603999, C3×#10604083, #14315231, … |
| maximal normal subgroup of | C3×#10603999, C3×#10604083, #14315231, … |
| maximal quotient of | C3×#10604741, C3×#10603868, C3×#10604742, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 6453);