Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C3×#65434 |
| Fitting | C3×C5×#131 ⋊ C2 |
| Hall | C3×C5 ⋊ #444 |
| Sylow | C5 ⋊ C3×#444 |
208 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 208 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)(9,12,13,16,15,23,14,22)(10,11,17,19,18,20,21,24);(9,11)(10,16)(12,21)(13,19)(14,24)(15,20)(17,23)(18,22);(5,6)(7,8)(9,10)(11,12)(13,17)(14,21)(15,18)(16,19)(20,23)(22,24)186 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D5×#444, C2×C3×#65434, #14417949, … |
| maximal normal subgroup of | C3×D5×#444, C2×C3×#65434, #14417949, … |
| maximal quotient of | C3×#10601730, C3×#10601632, C3×#10601725, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4237);