Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C23 |
| direct product | C5×#5046 |
| Fitting | C3×C5×C22⋊Q8 ⋊ C2 |
| Hall | C3×C5 ⋊ #450 |
| Sylow | C3 ⋊ C5×#450 |
376 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 376 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) = 240 |
A minimal faithful permutation representation — 3 generators on 20 points:
(1,2,3,4,5)(6,7,8)(10,12)(13,14,16,18)(15,20,19,17);(9,10)(11,12);(7,8)(14,17)(15,19)(18,20)165 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#71892, C5×#68316, #14287732, … |
| maximal normal subgroup of | C5×#71892, C5×#68316, #14287732, … |
| maximal quotient of | C5×#69699, C5×#69706, C5×#69714, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4740);