Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C3×#65516 |
| Fitting | C22×C3×C5×Q8 ⋊ C2 |
| Hall | C3×C5 ⋊ #448 |
| Sylow | C5 ⋊ C3×#448 |
316 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 102 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)(13,14,16,18)(15,20,19,17);(10,12);(5,6)(7,8)(9,10)(11,12)(14,17)(15,19)(18,20)177 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10601765, C3×#10600492, #14287973, … |
| maximal normal subgroup of | C3×#10601765, C3×#10600492, #14287973, … |
| maximal quotient of | C3×#10602685, C3×#10602695, C3×#10602683, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4319);