Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | C3×#65171 |
| Fitting | C3×C5×#107 ⋊ C2 |
| Hall | C3×C5 ⋊ #480 |
| Sylow | C5 ⋊ C3×#480 |
228 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 228 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) = 480 |
A minimal faithful permutation representation — 3 generators on 24 points:
(1,2,3)(4,5,7,8,6)(10,14)(13,16)(17,18,22,24,20,23,19,21);(9,11,12,15)(10,13,14,16)(18,21)(19,22)(23,24);(5,6)(7,8)(9,10)(11,13)(12,14)(15,16)141 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D5×#480, C2×C3×#65171, #14431426, … |
| maximal normal subgroup of | C3×D5×#480, C2×C3×#65171, #14431426, … |
| maximal quotient of | C3×#10599664, C3×#10601425, C3×#10599673, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 3974);