Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of #4656 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C23 |
| direct product | C5×#4676 |
| Fitting | C3×C5×#95 ⋊ C2 |
| Hall | C3×C5 ⋊ #396 |
| Sylow | C3 ⋊ C5×#396 |
372 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 118 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)(13,14,15,16)(17,18)(19,20);(9,10)(11,12)(14,16)(17,18,19,20);(7,8)(10,12)(14,16)(18,20)210 conjugacy classes — view the full character table.
| maximal subgroup of | C5×D3×#396, C2×C5×#4676, D5×#4676, … |
| maximal normal subgroup of | C5×D3×#396, C2×C5×#4676, D5×#4676, … |
| maximal quotient of | C5×#69428, C5×#69409, C5×#69416, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4370);