Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C8 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C2×C3×#431 ⋊ C2 |
| Sylow | C3 ⋊ #60276 |
2306 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^8,3|a^2=g,e^2=f,g^2=h,b^a=bf,d^a=df,c^b=cf,i^c=i^2216 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1034873);