Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C3×#2153 ⋊ C2 |
| Sylow | C3 ⋊ #33426 |
520 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|a^2=f,c^2=e,f^2=g,g^2=h,b^a=be,c^a=cg,e^a=eh,d^b=dh,f^b=fh,i^b=i^2,f^c=fh,i^c=i^2102 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#33426, #72269978, #72269991, … |
| maximal normal subgroup of | D3×#33426, #72269978, #72269991, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 322700);