Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26×C4 |
No aliases for this group.
| Fitting | C2×C3×B(4,𝔽2) ⋊ C2 |
| Sylow | C3 ⋊ #23904 |
2032 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|b^2=h,b^a=be,c^a=cf,d^a=deh,c^b=cg,f^b=fh,i^b=i^2,e^c=eh,f^d=fh72 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#23904, #72270620, #72270648, … |
| maximal normal subgroup of | D3×#23904, #72270620, #72270648, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 201184);