Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C3×#1402 ⋊ C2 |
| Sylow | C3 ⋊ #13560 |
486 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 59 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|a^2=e,c^2=h,f^2=h,b^a=bd,d^a=df,f^a=fg,g^a=gh,e^b=efh,f^b=fh,g^b=gh,i^c=i^2,e^d=egh,f^d=fh,f^e=fh51 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 89785);