Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C3×#397 ⋊ C2 |
| Sylow | C3 ⋊ #9918 |
812 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^8,3|b^2=h,d^2=g,b^a=bd,c^a=ce,d^a=dg,f^a=fh,i^a=i^2,c^b=cf,d^b=dg,d^c=dh84 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 69792);