Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×#65311 |
| Hall | C3×C5 ⋊ #479 |
| Sylow | C5 ⋊ C3×#479 |
180 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 86 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) = 960 |
A minimal faithful permutation representation — 3 generators on 32 points:
(1,2,3)(4,5,7,8,6)(17,19,21,27)(18,23,22,31)(20,29,30,26)(24,32,28,25);(9,11,12,16)(10,13,14,15)(18,22)(23,31)(24,28)(25,32);(5,6)(7,8)(9,10,12,14)(11,15,16,13)(17,18,21,22)(19,25,27,32)(20,28,30,24)(23,29,31,26)177 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D5×#479, C2×C3×#65311, #14430151, … |
| maximal normal subgroup of | C3×D5×#479, C2×C3×#65311, #14430151, … |
| maximal quotient of | C3×#10602420, C3×#10602421, C3×#10602422, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4114);