Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of #64757 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | C3×#64760 |
| Hall | C3×C5 ⋊ #329 |
| Sylow | C5 ⋊ C3×#329 |
140 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 54 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 — 2 generators on 24 points:
(1,2,3)(4,5,7,8,6)(10,13)(11,15)(17,18)(19,23)(20,22)(21,24);(5,6)(7,8)(9,10,11,14,12,13,15,16)(18,21,22,23)141 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10598037, C3×#10598263, #14279331, … |
| maximal normal subgroup of | C3×#10598037, C3×#10598263, #14279331, … |
| maximal quotient of | C3×#10598130, C3×#10598133, C3×#10598121, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 312);