Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C2×C3×#568 ⋊ C2 |
| Sylow | C3 ⋊ #21009 |
1708 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|a^2=g,b^2=eg,d^2=h,e^2=h,b^a=be,c^a=cf,e^a=eh,f^a=fh,i^a=i^2,f^b=fh,e^c=eh,g^c=gh126 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#21009, #72253896, #72253901 |
| maximal normal subgroup of | D3×#21009, #72253896, #72253901 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 171554);