Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C3×#65384 |
| Fitting | C3×C5×C4⋊Q8 ⋊ C2 |
| Hall | C3×C5 ⋊ #456 |
| Sylow | C5 ⋊ C3×#456 |
284 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 78 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)(9,12,14,11)(10,16,18,24)(13,19,23,21)(15,22,20,17);(9,11,14,12)(10,15,18,20)(13,21,23,19)(16,17,24,22);(5,6)(7,8)(9,10)(11,15)(12,20)(13,22)(14,18)(16,21)(17,23)(19,24)132 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10598041, C3×#10597954, #14279376, … |
| maximal normal subgroup of | C3×#10598041, C3×#10597954, #14279376, … |
| maximal quotient of | C3×#10600498, C3×#10600499, C3×#10600500, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4187);