Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C3 ⋊ #7187 |
678 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^8,3|a^2=d,b^2=e,d^2=g,b^a=bc,c^a=cf,f^a=fh,d^b=df,i^b=i^2,d^c=dh96 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 56526);