Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | D4⋊(C3⋊#168) |
| Hall | C3×C5 ⋊ D4⋊C8 |
| Sylow | C5 ⋊ D4⋊(C3⋊C8) |
| Sylow | C3 ⋊ D4⋊#168 |
164 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 75 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=c,c^2=e,d^2=f,b^a=bd,d^a=df,g^a=g^2,h^a=h^4,d^b=df168 conjugacy classes — view the full character table.
| maximal subgroup of | D15×D4⋊C8, C2×D4⋊(C3⋊#168), D5×D4⋊(C3⋊C8), … |
| maximal normal subgroup of | D15×D4⋊C8, C2×D4⋊(C3⋊#168), D5×D4⋊(C3⋊C8), … |
| maximal quotient of | #14276641, #14276656, #14276795, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 550);