Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C3×#3484 ⋊ 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,c^b=ch,d^b=df,f^b=fh,i^b=i^2,f^d=fh96 conjugacy classes — view the full character table.
| maximal subgroup of | #72253922, D3×#61059, #72253935 |
| maximal normal subgroup of | #72253922, D3×#61059, #72253935 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1045047);