Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of #686 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C8 · Schur multiplier (H2) = C2 |
| direct product | C3×Q8⋊#168 |
| Hall | C3×C5 ⋊ Q8⋊C8 |
| Sylow | C5 ⋊ C3×Q8⋊C8 |
140 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 78 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 — 2 generators on 24 points:
(1,2,3)(4,5,7,8,6)(17,18,20,22)(19,24,23,21);(5,6)(7,8)(9,10,11,13,12,14,15,16)(18,21)(19,23)(22,24)204 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D5×Q8⋊C8, C2×C3×Q8⋊#168, #14281533, … |
| maximal normal subgroup of | C3×D5×Q8⋊C8, C2×C3×Q8⋊#168, #14281533, … |
| maximal quotient of | C3×#10598129, C3×#10598133, C3×#10598110, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 307);