Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C3×#1831 ⋊ C2 |
| Sylow | C3 ⋊ #7574 |
520 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
Polycyclic presentation:
2^8,3|a^2=e,c^2=f,d^2=g,e^2=h,b^a=bd,c^a=cf,d^a=df,i^a=i^2,d^b=dg,e^b=efg,i^b=i^2120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 57563);