Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C3×#1527 ⋊ C2 |
| Sylow | C3 ⋊ #17666 |
1306 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|a^2=f,e^2=h,f^2=g,b^a=be,c^a=ch,d^a=dg,e^a=eg,e^b=eh,f^b=fgh,i^c=i^284 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 137634);