Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C24 |
| direct product | C3×#66022 |
| Fitting | C3×C5×#125 ⋊ C2 |
| Hall | C3×C5 ⋊ #533 |
| Sylow | C5 ⋊ C3×#533 |
444 conjugacy classes of subgroups; only the 214 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 214 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) = 480 |
A minimal faithful permutation representation — 4 generators on 24 points:
(1,2,3)(4,5,7,8,6)(9,11)(10,13)(12,15)(14,16)(17,19,20,24)(18,21,22,23);(11,15)(13,16)(17,18,20,22)(19,23,24,21);(9,10,12,14)(11,16,15,13);(5,6)(7,8)(11,15)(13,16)168 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10599155, #14284020, C3×#10599158, … |
| maximal normal subgroup of | C3×#10599155, #14284020, C3×#10599158, … |
| maximal quotient of | C3×#10605879, C3×#10606669, C3×#10607694, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 9894);