Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C2×C3×#331 ⋊ C2 |
| Sylow | C3 ⋊ #9706 |
850 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
Polycyclic presentation:
2^8,3|a^2=f,b^2=dfgh,c^2=eg,d^2=gh,f^2=h,b^a=bd,c^a=ce,d^a=dg,c^b=cg,d^b=dh,f^b=fh,i^c=i^284 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 68664);