Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | #60666⋊C3 |
| Fitting, Sylow | #60666 ⋊ C3 |
422 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 81 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 256 |
Polycyclic presentation:
3,2^8|b^2=g,c^2=gi,d^2=h,h^2=i,b^a=bfh,e^a=fg,f^a=efghi,c^b=cg,d^b=dh,h^b=hi,f^e=fi80 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1084818);