Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C22×C3×#100 ⋊ C2 |
| Sylow | C3 ⋊ #10989 |
1502 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|a^2=g,d^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dh,e^a=eh,f^a=fh,c^b=cf,d^b=dh,i^b=i^2,d^c=dh,g^c=gh90 conjugacy classes — view the full character table.
| maximal subgroup of | #72253525, D3×#10989, #72253536, … |
| maximal normal subgroup of | #72253525, D3×#10989, #72253536, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 76167);