Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28×C4 |
No aliases for this group.
| Fitting | C2×C3×#532 ⋊ C2 |
| Sylow | C3 ⋊ #60639 |
3314 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^8,3|b^2=f,c^2=g,e^2=h,f^2=h,b^a=bf,c^a=cg,f^a=fh,d^b=dh,i^b=i^2120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1039039);