Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C11×#1738 ⋊ C2 |
| Sylow | C11 ⋊ #23439 |
2026 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^8,11|e^2=h,f^2=h,g^2=h,b^a=be,c^a=cf,d^a=dh,e^a=eh,f^a=fh,g^a=gh,i^a=i^10,c^b=cg,e^b=eh,g^b=gh,i^b=i^10,e^c=eh,f^c=fh,g^c=gh,i^c=i^10266 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 196786);