Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C3 ⋊ #7125 |
182 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 67 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=d,b^2=e,c^2=f,d^2=g,f^2=h,b^a=bc,c^a=ce,e^a=eh,i^a=i^2,c^b=cf,d^b=defh,f^b=fh,g^b=gh,d^c=dh72 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 56371);