Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C3×#1817 ⋊ C2 |
| Sylow | C3 ⋊ #8968 |
600 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^8,3|a^2=f,b^2=dfg,f^2=h,b^a=bd,c^a=ce,e^a=eg,c^b=ch,e^b=eg,d^c=dg,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, 64265);