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×#64758 |
| Hall | C3×C5 ⋊ #328 |
| Sylow | C5 ⋊ C3×#328 |
160 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 160 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)(17,18,20,22)(19,23,24,21);(5,6)(7,8)(9,10)(11,15,16,13)(12,14)(18,21,22,23)141 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D5×#328, C2×C3×#64758, #14282725, … |
| maximal normal subgroup of | C3×D5×#328, C2×C3×#64758, #14282725, … |
| maximal quotient of | C3×#10598129, C3×#10598133, C3×#10598115, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 310);