Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C24 |
| direct product | C3×#66031 |
| Fitting | C3×C5×#125 ⋊ C2 |
| Hall | C3×C5 ⋊ #541 |
| Sylow | C5 ⋊ C3×#541 |
384 conjugacy classes of subgroups; only the 190 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 190 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 32 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 4 generators on 32 points:
(1,2,3)(4,5,7,8,6)(9,11,12,16)(10,14,13,15)(18,24)(20,29)(22,31)(25,28);(9,10,12,13)(11,15,16,14)(17,20)(18,23)(19,25)(21,29)(22,30)(24,27)(26,28)(31,32);(17,19,21,26)(18,22,24,31)(20,28,29,25)(23,32,27,30);(5,6)(7,8)(10,13)(14,15)(17,18)(19,22)(20,27)(21,24)(23,29)(25,32)(26,31)(28,30)150 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10612876, C3×#10612940, #14436255, … |
| maximal normal subgroup of | C3×#10612876, C3×#10612940, #14436255, … |
| maximal quotient of | C3×#10605955, C3×#10607701, C3×#10607928, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 9903);