Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C3×#1986 ⋊ C2 |
| Sylow | C3 ⋊ #24148 |
1102 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|d^2=eh,g^2=h,b^a=be,c^a=cf,d^a=de,g^a=gh,i^a=i^2,c^b=cg,f^b=fh,g^b=gh,i^b=i^2,g^c=gh,i^c=i^281 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 203851);