Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C3×#1887 ⋊ C2 |
| Sylow | C3 ⋊ #21782 |
1382 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
Polycyclic presentation:
2^8,3|a^2=g,f^2=h,b^a=be,c^a=cf,d^a=de,e^a=eh,c^b=ce,f^b=fh,g^b=gh,i^b=i^2,f^c=fh,g^c=gh,i^c=i^2,g^d=gh,i^d=i^278 conjugacy classes — view the full character table.
| maximal subgroup of | #72257991, D3×#21782, #72271895, … |
| maximal normal subgroup of | #72257991, D3×#21782, #72271895, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 178757);