Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C5 · Schur multiplier (H2) = C25 |
| direct product | C5×#5838 |
| Fitting | C3×C5×2−1+4 ⋊ C2 |
| Hall | C3×C5 ⋊ #578 |
| Sylow | C3 ⋊ C5×#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)(6,7,8)(10,17)(13,26)(15,28)(16,32)(18,19)(21,36)(24,38)(27,39)(29,30)(31,40)(33,34)(35,37);(9,12,14,25)(10,16,19,34)(11,20,22,23)(13,24,26,38)(15,27,30,31)(17,32,18,33)(21,35,36,37)(28,39,29,40);(9,11,14,22)(10,15,19,30)(12,23,25,20)(13,21,26,36)(16,31,34,27)(17,28,18,29)(24,37,38,35)(32,40,33,39);(7,8)(9,10)(11,15)(12,16)(13,17)(14,19)(18,26)(20,27)(21,28)(22,30)(23,31)(24,32)(25,34)(29,36)(33,38)(35,39)(37,40)195 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#80301, C5×#84019, C5×#84013, … |
| maximal normal subgroup of | C5×#80301, C5×#84019, C5×#84013, … |
| maximal quotient of | C5×#82570, C5×#84111, C5×#82562, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 10418);