Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of #826 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#5194 |
| Fitting | C3×C5×#135 ⋊ C2 |
| Hall | C3×C5 ⋊ #508 |
| Sylow | C3 ⋊ C5×#508 |
168 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 70 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)(6,7,8)(10,16)(12,23)(13,24)(15,27)(17,18)(19,32)(20,33)(21,34)(25,37)(26,31)(28,29)(30,39)(35,40)(36,38);(9,11,14,22)(10,15,19,30)(12,20,25,35)(13,21,24,34)(16,27,32,39)(17,28,31,38)(18,29,26,36)(23,33,37,40);(7,8)(9,10)(11,15)(12,16)(13,26)(14,19)(17,23)(18,24)(20,27)(21,36)(22,30)(25,32)(28,33)(29,34)(31,37)(35,39)(38,40)180 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#69238, C5×#70921, #14315651, … |
| maximal normal subgroup of | C5×#69238, C5×#70921, #14315651, … |
| maximal quotient of | C5×#70651, C5×#72077, C5×#70648, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4888);