Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C3×#1282 ⋊ C2 |
| Sylow | C3 ⋊ #9260 |
594 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^8,3|a^2=f,b^2=dfh,c^2=g,d^2=gh,e^2=gh,f^2=gh,b^a=bd,c^a=ce,d^a=dg,d^b=dh,e^b=egh,f^b=fh,i^b=i^2,d^c=dgh,e^c=egh,f^c=fgh,i^c=i^287 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 66021);