Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C3×#2883 ⋊ C2 |
| Sylow | C3 ⋊ #33359 |
1356 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
Polycyclic presentation:
2^8,3|a^2=f,e^2=h,b^a=be,e^a=eg,g^a=gh,e^b=eh,f^b=fgh,i^b=i^2,d^c=dh,f^e=fh87 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#33359, #72255236, #72255244, … |
| maximal normal subgroup of | D3×#33359, #72255236, #72255244, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 322370);