Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C27×C4 |
No aliases for this group.
| Fitting | C2×C3×#535 ⋊ C2 |
| Sylow | C3 ⋊ #60806 |
2222 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|b^2=f,g^2=h,b^a=bf,c^a=cg,d^a=df,e^a=eh,g^a=gh,i^a=i^2,c^b=cf,d^b=dh,g^c=gh90 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1041087);