Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C22×C3×AGL(1,ℤ/8) ⋊ C2 |
| Sylow | C3 ⋊ #61059 |
2878 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|b^2=h,f^2=h,b^a=bf,c^a=cg,e^a=eh,f^a=fh,i^a=i^2,c^b=ch,d^b=df,f^b=fh,f^d=fh96 conjugacy classes — view the full character table.
| maximal subgroup of | #72253918, D3×#61059, #72253957 |
| maximal normal subgroup of | #72253918, D3×#61059, #72253957 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1045051);