Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C8 · Schur multiplier (H2) = C2 |
| direct product | C3×#64773 |
| Hall | C3×C5 ⋊ #349 |
| Sylow | C5 ⋊ C3×#349 |
116 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 116 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)(10,14)(11,17)(16,21)(18,23);(5,6)(7,8)(9,10,11,15,12,16,18,22,13,14,17,20,19,21,23,24)186 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10598021, C3×#10598172, #14277617, … |
| maximal normal subgroup of | C3×#10598021, C3×#10598172, #14277617, … |
| maximal quotient of | C3×#10598164, C3×#10598200, C3×#10598252, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 325);