Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C4×C11×AGL(1,ℤ/8) ⋊ C2 |
| Sylow | C11 ⋊ #61156 |
2254 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^8,11|a^2=f,b^2=h,g^2=h,b^a=bf,c^a=cg,e^a=eh,g^a=gh,i^a=i^10,d^b=df,i^b=i^10,g^c=gh,i^d=i^10275 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 1046576);