Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C11 ⋊ #7454 |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^8,11|a^2=d,b^2=eg,c^2=fgh,d^2=efgh,e^2=h,f^2=gh,g^2=h,b^a=bc,c^a=ce,e^a=eh,f^a=fh,c^b=cf,d^b=def,e^b=eh,f^b=fg,g^b=gh,i^b=i^10317 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 57230);