Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C3×#1379 ⋊ C2 |
| Sylow | C3 ⋊ #12554 |
586 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^8,3|a^2=e,b^2=f,d^2=h,e^2=g,g^2=h,b^a=bd,c^a=ch,d^b=dh,e^b=eh,i^c=i^2144 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 84439);