Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C22×C42 |
| direct product | C3×#66017 |
| Fitting | C3×C5×#124 ⋊ C2 |
| Hall | C3×C5 ⋊ H(3,𝔽4) |
| Sylow | C5 ⋊ C3×H(3,𝔽4) |
520 conjugacy classes of subgroups; only the 182 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 182 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 — 4 generators on 24 points:
(1,2,3)(4,5,7,8,6)(9,11,12,16)(10,14,13,15)(18,22)(19,23);(10,13)(11,16)(17,19)(18,21)(20,23)(22,24);(11,16)(14,15)(17,18)(19,24)(20,22)(21,23);(5,6)(7,8)(9,10)(11,15)(12,13)(14,16)(19,23)(21,24)141 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10602119, C3×#10599143, #14290889, … |
| maximal normal subgroup of | C3×#10602119, C3×#10599143, #14290889, … |
| maximal quotient of | C3×#10608165, C3×#10607571, C3×#10607224, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 9889);