Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C3×#65182 |
| Fitting | C3×C5×#108 ⋊ C2 |
| Hall | C3×C5 ⋊ #430 |
| Sylow | C5 ⋊ C3×#430 |
204 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 204 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) = 24 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 3 generators on 24 points:
(1,2,3)(4,5,7,8,6)(9,11,12,20,14,21,13,22)(10,16,17,19,15,23,18,24);(9,10,13,18,14,15,12,17)(11,19,20,23,21,24,22,16);(5,6)(7,8)(10,15)(16,23)(17,18)(19,24)150 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10600050, C3×#10600106, #14318538, … |
| maximal normal subgroup of | C3×#10600050, C3×#10600106, #14318538, … |
| maximal quotient of | C3×#10599321, C3×#10599361, C3×#10599324, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 3985);