Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C25 |
| direct product | C3×#66169 |
| Fitting | C3×C5×H(5,𝔽2) ⋊ C2 |
| Hall | C3×C5 ⋊ #576 |
| Sylow | C5 ⋊ C3×#576 |
536 conjugacy classes of subgroups; only the 214 normal subgroups are shown.
This group has 536 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) = 240 |
A minimal faithful permutation representation — 4 generators on 24 points:
(1,2,3)(4,5,7,8,6)(10,15)(12,20)(14,22)(16,17)(19,24)(21,23);(11,18)(14,21)(19,24)(22,23);(9,11)(10,14)(12,19)(13,18)(15,22)(16,23)(17,21)(20,24);(5,6)(7,8)(9,10)(11,14)(12,15)(13,17)(16,20)(18,21)(19,22)(23,24)168 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10612011, C3×#10615746, C3×#10615740, … |
| maximal normal subgroup of | C3×#10612011, C3×#10615746, C3×#10615740, … |
| maximal quotient of | C3×#10614294, C3×#10615830, C3×#10614293, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 10041);