Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×#65080 |
| Hall | C3×C5 ⋊ #475 |
| Sylow | C5 ⋊ C3×#475 |
192 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 86 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) = 960 |
A minimal faithful permutation representation — 3 generators on 24 points:
(1,2,3)(4,5,7,8,6)(9,11,12,16)(10,13,14,15)(18,21)(19,24)(22,23);(17,18,20,23)(19,21,24,22);(5,6)(7,8)(9,10,12,14)(11,15,16,13)141 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D5×#475, C2×C3×#65080, #14430028, … |
| maximal normal subgroup of | C3×D5×#475, C2×C3×#65080, #14430028, … |
| maximal quotient of | C3×#10601014, C3×#10601030, C3×#10601031, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 3883);