Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C2×C4 |
| direct product | C3×#65004 |
| Fitting | C3×C5×#97 ⋊ C2 |
| Hall | C3×C5 ⋊ #497 |
| Sylow | C5 ⋊ C3×#497 |
248 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 94 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) = 480 |
A minimal faithful permutation representation — 3 generators on 28 points:
(1,2,3)(4,5,7,8,6)(13,15,16,23,17,22,25,28)(14,19,20,21,18,26,24,27);(9,10,11,12)(14,18)(15,22)(20,24)(23,28);(5,6)(7,8)(10,12)(13,14)(15,21)(16,24)(17,18)(19,23)(20,25)(22,27)(26,28)168 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10598541, #14279421, C3×#10599145, … |
| maximal normal subgroup of | C3×#10598541, #14279421, C3×#10599145, … |
| maximal quotient of | C3×#10598883, C3×#10598888, C3×#10598889, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 3807);