Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C3×#1800 ⋊ C2 |
| Sylow | C3 ⋊ #29682 |
1152 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|d^2=eh,f^2=h,b^a=be,c^a=cf,f^a=fh,g^a=gh,i^a=i^2,c^b=cg,f^b=fh,d^c=de,f^c=fh,i^c=i^269 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 275698);