Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Sylow | C11 ⋊ #20936 |
1850 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^8,11|a^2=g,b^2=egh,c^2=h,e^2=h,f^2=h,g^2=h,b^a=be,c^a=cf,d^a=dh,i^a=i^10,d^b=dh,e^b=eh,f^b=fh,g^b=gh,i^b=i^10,e^c=eh,f^c=fh,g^c=gh,i^c=i^10284 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 171026);