Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C2×C4 |
| direct product | C3×#65348 |
| Fitting | C3×C5×#124 ⋊ C2 |
| Hall | C3×C5 ⋊ #495 |
| Sylow | C5 ⋊ C3×#495 |
260 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 260 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) = 28 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 3 generators on 28 points:
(1,2,3)(4,5,7,8,6)(10,12)(14,19)(15,23)(16,25)(18,26)(20,21)(22,27);(9,10,11,12)(13,15)(14,18)(16,24)(17,23)(19,27)(20,26)(21,22)(25,28);(5,6)(7,8)(10,12)(13,14)(15,22)(16,19)(17,21)(18,23)(20,25)(24,26)(27,28)150 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D5×#495, C2×C3×#65348, #14438845, … |
| maximal normal subgroup of | C3×D5×#495, C2×C3×#65348, #14438845, … |
| maximal quotient of | C3×#10601973, C3×#10602005, C3×#10601974, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4151);