Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C11×#2226 ⋊ C2 |
| Sylow | C11 ⋊ #12375 |
350 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 69 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1408 |
Polycyclic presentation:
2^8,11|a^2=gh,b^2=h,c^2=h,d^2=fh,e^2=g,f^2=h,b^a=bd,c^a=ce,d^a=df,e^a=eg,f^a=fh,d^b=df,e^b=eg,f^b=fh,i^b=i^10,d^c=dg,e^c=eg,i^c=i^10185 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 83396);