Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C23 |
| direct product | C5×#5238 |
| Fitting | C2×C3×C5×#41 ⋊ C2 |
| Hall | C3×C5 ⋊ #449 |
| Sylow | C3 ⋊ C5×#449 |
324 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 324 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)(6,7,8)(10,12)(13,15,16,17)(14,18,19,20);(13,14)(15,18)(16,19)(17,20);(7,8)(9,10)(11,12)(14,18)(15,17)(19,20)195 conjugacy classes — view the full character table.
| maximal subgroup of | C5×D3×#449, C2×C5×#5238, D5×#5238, … |
| maximal normal subgroup of | C5×D3×#449, C2×C5×#5238, D5×#5238, … |
| maximal quotient of | C5×#71888, C5×#71884, C5×#71886, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4932);