Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C3×#2140 ⋊ C2 |
| Sylow | C3 ⋊ #12741 |
930 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|a^2=f,d^2=gh,g^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eh,g^a=gh,d^b=dg,g^b=gh,f^c=fh,i^c=i^272 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#12741, #72269973, #72269978, … |
| maximal normal subgroup of | D3×#12741, #72269973, #72269978, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 85252);