Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C8 · Schur multiplier (H2) = C22 |
| direct product | C3×#65196 |
| Fitting | C3×C5×M32 ⋊ C2 |
| Hall | C3×C5 ⋊ #504 |
| Sylow | C5 ⋊ C3×#504 |
168 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 102 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)(9,11,12,20,13,21,22,33,14,19,23,31,24,32,34,39)(10,16,17,28,18,29,30,38,15,25,26,35,27,36,37,40);(10,15)(11,19)(17,26)(18,27)(20,31)(21,32)(30,37)(33,39);(5,6)(7,8)(9,10)(11,16)(12,17)(13,18)(14,15)(19,25)(20,28)(21,29)(22,30)(23,26)(24,27)(31,35)(32,36)(33,38)(34,37)(39,40)240 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10598669, #14279283, C3×#10599915, … |
| maximal normal subgroup of | C3×#10598669, #14279283, C3×#10599915, … |
| maximal quotient of | C3×#10599865, C3×#10602212, C3×#10599900, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 3999);