Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C3×#1273 ⋊ C2 |
| Sylow | C3 ⋊ #10305 |
802 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
Polycyclic presentation:
2^8,3|a^2=g,d^2=g,e^2=h,f^2=gh,b^a=bd,c^a=ce,d^a=dg,e^a=eh,f^a=fgh,i^a=i^2,c^b=cf,d^b=dg,e^b=eh,f^b=fgh,i^b=i^2,d^c=dg,e^c=eh,f^c=fgh,i^c=i^2132 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 72344);