Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×C3×Q8⋊C8 ⋊ C2 |
| Sylow | C3 ⋊ #9098 |
488 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
Polycyclic presentation:
2^8,3|a^2=f,b^2=dfg,e^2=g,f^2=h,b^a=bd,c^a=ce,d^a=dg,i^a=i^2,c^b=ch,d^b=dg,e^b=eg,f^b=fg,i^b=i^2,d^c=dg,e^c=eg,f^c=fg,i^c=i^2108 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 65059);