Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C3 ⋊ #29131 |
742 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
Polycyclic presentation:
2^8,3|a^2=fg,b^2=gh,d^2=eh,f^2=h,b^a=be,c^a=cf,d^a=deh,i^a=i^2,c^b=cg,f^c=fh102 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 269311);