Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
No aliases for this group.
| Fitting | C3×#3006 ⋊ C2 |
| Sylow | C3 ⋊ #60369 |
4938 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|e^2=h,f^2=h,b^a=bf,c^a=cg,e^a=eh,f^a=fh,f^b=fh,d^c=dh,i^d=i^290 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#60369, #72253889, #72253892 |
| maximal normal subgroup of | D3×#60369, #72253889, #72253892 |
| maximal quotient of | #72269938, #72269976 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1036069);