Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | #67⋊#168 |
| Hall | C3×C5 ⋊ C8×D4 |
| Sylow | C5 ⋊ #67⋊C8 |
| Sylow | C3 ⋊ D4×#168 |
268 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 480 |
Polycyclic presentation:
2^6,3,5|a^2=d,d^2=f,c^a=ce,h^a=h^4,c^b=ce,g^b=g^2132 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#67⋊C8, D3×D4×#168, C8×#6790, … |
| maximal normal subgroup of | D5×#67⋊C8, D3×D4×#168, C8×#6790, … |
| maximal quotient of | #14286094, #14286161, #14286176, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 2690);