Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | C3×#65187 |
| Fitting | C3×C5×#108 ⋊ C2 |
| Hall | C3×C5 ⋊ #471 |
| Sylow | C5 ⋊ C3×#471 |
208 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 74 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)(9,12,13,22,14,23,24,15)(10,16,17,21,19,11,18,20);(9,11,13,20,14,16,24,21)(10,15,18,23,19,22,17,12);(5,6)(7,8)(9,10)(11,15)(12,21)(13,18)(14,19)(16,22)(17,24)(20,23)132 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D5×#471, C2×C3×#65187, #14429308, … |
| maximal normal subgroup of | C3×D5×#471, C2×C3×#65187, #14429308, … |
| maximal quotient of | C3×#10599329, C3×#10599339, C3×#10599330, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 3990);