Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C3×#2896 ⋊ C2 |
| Sylow | C3 ⋊ #60168 |
2882 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|a^2=g,c^2=g,f^2=h,b^a=bf,e^a=eh,f^a=fh,i^a=i^2,f^b=fh,i^b=i^2,d^c=dh,i^c=i^2126 conjugacy classes — view the full character table.
| maximal subgroup of | #72248864, #72248898, #72248905, … |
| maximal normal subgroup of | #72248864, #72248898, #72248905, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1033756);