Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of #64945 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C24 |
| direct product | C3×#65248 |
| Fitting | C2×C3×C5×C22⋊C4 ⋊ C2 |
| Hall | C3×C5 ⋊ #394 |
| Sylow | C5 ⋊ C3×#394 |
476 conjugacy classes of subgroups.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 3 generators on 20 points:
(1,2,3)(4,5,7,8,6)(10,12)(14,16)(17,19,20,18);(13,14)(15,16)(17,18)(19,20);(5,6)(7,8)(9,10)(11,12)(18,19)186 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D5×#394, C2×C3×#65248, #14331541, … |
| maximal normal subgroup of | C3×D5×#394, C2×C3×#65248, #14331541, … |
| maximal quotient of | C3×#10602343, C3×#10602340, C3×#10600221, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4051);