Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C11×AΣL(1,𝔽16) ⋊ C2 |
| Sylow | C11 ⋊ #12725 |
846 conjugacy classes of subgroups.
| transitive degree | μt(G) = 176 |
Polycyclic presentation:
2^8,11|a^2=f,c^2=g,b^a=bd,c^a=ce,d^a=dg,g^a=gh,f^b=fg,e^c=eh,i^c=i^10,f^d=fh164 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 85182);