Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C3×#1297 ⋊ C2 |
| Sylow | C3 ⋊ #7396 |
296 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 37 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
Polycyclic presentation:
2^8,3|a^2=d,c^2=fh,e^2=h,f^2=h,b^a=bc,c^a=ce,e^a=eg,c^b=cf,d^b=defh,e^b=eh,f^b=fh,g^b=gh,i^b=i^2,d^c=dgh,e^c=eh69 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 57056);