Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | C3×#65138 |
| Hall | C3×C5 ⋊ #462 |
| Sylow | C5 ⋊ C3×#462 |
216 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 90 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)(13,15,22,26,17,24,16,23)(14,18,25,28,20,27,19,21);(9,10,11,12);(5,6)(7,8)(13,14,17,20)(15,21,24,28)(16,25,22,19)(18,26,27,23)177 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10599199, C3×#10599047, #14289979, … |
| maximal normal subgroup of | C3×#10599199, C3×#10599047, #14289979, … |
| maximal quotient of | C3×#10599340, C3×#10599381, C3×#10599382, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 3941);