Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25×C4 |
No aliases for this group.
| Fitting | C3×#1460 ⋊ C2 |
| Sylow | C3 ⋊ #17349 |
1314 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^8,3|a^2=f,c^2=h,d^2=g,f^2=h,b^a=be,e^a=eg,f^b=fg,i^c=i^2,i^d=i^2132 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 135378);