Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C3×#1620 ⋊ C2 |
| Sylow | C3 ⋊ #13675 |
408 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 43 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=h,f^2=h,b^a=bd,c^a=ce,f^a=fg,e^b=efgh,g^b=gh,i^b=i^2,d^c=df,f^c=fh,g^c=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, 90288);