Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C2×C4 |
| direct product | C3×#65001 |
| Fitting | C3×C5×#97 ⋊ C2 |
| Hall | C3×C5 ⋊ #496 |
| Sylow | C5 ⋊ C3×#496 |
288 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 288 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) = 20 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 3 generators on 20 points:
(1,2,3)(4,5,7,8,6)(13,14,15,17,16,18,19,20);(9,10,11,12)(14,18)(17,20);(5,6)(7,8)(10,12)(14,17)(15,19)(18,20)168 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10598540, #14279398, C3×#10599143, … |
| maximal normal subgroup of | C3×#10598540, #14279398, C3×#10599143, … |
| maximal quotient of | C3×#10598883, C3×#10598884, C3×#10598885, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 3804);