Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of #64757 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C3×#64757 |
| Hall | C3×C5 ⋊ #327 |
| Sylow | C5 ⋊ C3×#327 |
180 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 62 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 — 2 generators on 24 points:
(1,2,3)(4,5,7,8,6)(9,11)(10,13)(12,16)(14,15)(18,21)(19,24)(22,23);(5,6)(7,8)(9,10)(11,15,16,13)(12,14)(17,18)(19,21)(20,23)(22,24)141 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D5×#327, C2×C3×#64757, #14282682, … |
| maximal normal subgroup of | C3×D5×#327, C2×C3×#64757, #14282682, … |
| maximal quotient of | C3×#10598130, C3×#10598129, C3×#10598115, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 309);