Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of #686 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C3×#65433 |
| Fitting | C3×C5×#131 ⋊ C2 |
| Hall | C3×C5 ⋊ #443 |
| Sylow | C5 ⋊ C3×#443 |
212 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 212 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) = 24 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 3 generators on 24 points:
(1,2,3)(4,5,7,8,6)(9,12,13,15,14,20,23,24)(10,16,17,22,19,11,18,21);(9,11)(10,15)(12,18)(13,21)(14,16)(17,20)(19,24)(22,23);(5,6)(7,8)(9,10)(11,20)(12,16)(13,17)(14,19)(15,22)(18,23)(21,24)204 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10599915, C3×#10602245, #14315208, … |
| maximal normal subgroup of | C3×#10599915, C3×#10602245, #14315208, … |
| maximal quotient of | C3×C8×#686, C3×C8×#687, C3×C8×#688, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4236);