Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28×C4 |
No aliases for this group.
| Fitting | C2×C3×#535 ⋊ C2 |
| Sylow | C3 ⋊ #60644 |
3350 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|b^2=f,c^2=g,f^2=h,b^a=bf,c^a=cg,f^a=fh,e^b=eh,i^b=i^2,d^c=dh102 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#60644, #72249227, #72249228, … |
| maximal normal subgroup of | D3×#60644, #72249227, #72249228, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1039085);