Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of D80 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | C3×#65193 |
| Fitting | C2×C3×C5×C16 ⋊ C2 |
| Hall | C3×C5 ⋊ #508 |
| Sylow | C5 ⋊ C3×#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)(4,5,7,8,6)(9,12,23,37,14,25,28,38,15,26,21,34,11,20,13,24)(10,17,27,33,16,30,32,36,19,31,40,39,29,35,18,22);(9,11,15,14)(10,16,19,29)(12,20,26,25)(13,21,28,23)(17,30,31,35)(18,27,32,40)(22,33,36,39)(24,34,38,37);(5,6)(7,8)(9,10)(11,16)(12,22)(13,27)(14,29)(15,19)(17,24)(18,23)(20,33)(21,32)(25,39)(26,36)(28,40)(30,34)(31,38)(35,37)258 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×#10598076, C3×#10598089, #14279612, … |
| maximal normal subgroup of | C3×#10598076, C3×#10598089, #14279612, … |
| maximal quotient of | C3×#10602205, C3×#10602197, C3×C4×D80, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 3996);