Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×C3×#324 ⋊ C2 |
| Sylow | C3 ⋊ #17351 |
1278 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^8,3|a^2=f,b^2=g,f^2=h,b^a=be,e^a=eg,f^b=fg,d^c=dg,i^d=i^2126 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 135388);