Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3 ⋊ C8×Q32 |
226 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 85 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 768 |
Polycyclic presentation:
2^8,3|a^2=e,b^2=h,c^2=eh,d^2=fh,e^2=g,f^2=h,b^a=bd,d^a=df,f^a=fh,d^b=df,f^b=fh,i^b=i^2,i^c=i^2132 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 81301);