Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of #64945 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | C3×#65275 |
| Hall | C3×C5 ⋊ #400 |
| Sylow | C5 ⋊ C3×#400 |
268 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 118 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 28 |
| transitive degree | μt(G) = 960 |
A minimal faithful permutation representation — 3 generators on 28 points:
(1,2,3)(4,5,7,8,6)(10,12)(21,23,24,27)(22,25,26,28);(13,15,16,20)(14,17,18,19)(23,27)(25,28);(5,6)(7,8)(9,10)(11,12)(13,14,16,18)(15,19,20,17)(21,22,24,26)(23,25,27,28)186 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10597987, C3×#10597950, #14278314, … |
| maximal normal subgroup of | C3×#10597987, C3×#10597950, #14278314, … |
| maximal quotient of | C3×#10602358, C3×#10600208, C3×#10602360, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4078);