Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C3×#338 ⋊ C2 |
| Sylow | C3 ⋊ #11058 |
970 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|a^2=g,b^2=d,f^2=h,g^2=h,b^a=bd,c^a=ce,e^a=eh,i^a=i^2,c^b=cf,f^b=fh,i^b=i^2,f^c=fh,g^c=gh,i^c=i^290 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#11058, #72253365, #72253373, … |
| maximal normal subgroup of | D3×#11058, #72253365, #72253373, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 76572);