Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C25 |
| direct product | C3×#66087 |
| Fitting | C3×C5×#131 ⋊ C2 |
| Hall | C3×C5 ⋊ #578 |
| Sylow | C5 ⋊ C3×#578 |
496 conjugacy classes of subgroups; only the 214 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 214 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 — 4 generators on 40 points:
(1,2,3)(4,5,7,8,6)(9,13,12,24,15,27,14,26)(10,18,28,38,19,33,17,25)(11,21,23,37,22,36,20,34)(16,30,29,39,32,40,31,35);(9,12,15,14)(10,17,19,28)(11,20,22,23)(13,24,27,26)(16,29,32,31)(18,25,33,38)(21,34,36,37)(30,39,40,35);(9,11,15,22)(10,16,19,32)(12,23,14,20)(13,21,27,36)(17,31,28,29)(18,30,33,40)(24,37,26,34)(25,35,38,39);(5,6)(7,8)(9,10)(11,16)(12,17)(13,25)(14,28)(15,19)(18,26)(20,29)(21,35)(22,32)(23,31)(24,33)(27,38)(30,34)(36,39)(37,40)186 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10601888, C3×#10599920, #14316472, … |
| maximal normal subgroup of | C3×#10601888, C3×#10599920, #14316472, … |
| maximal quotient of | C3×#10615537, C3×#10615516, C3×#10610302, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 9959);