Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C3×#2170 ⋊ C2 |
| Sylow | C3 ⋊ #33443 |
648 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|a^2=f,c^2=f,e^2=h,f^2=g,g^2=h,b^a=be,d^a=dh,e^a=eh,e^b=eh,d^c=dh,i^d=i^2144 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#33443, #72226250, #72226252 |
| maximal normal subgroup of | D3×#33443, #72226250, #72226252 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 322818);