Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C11 ⋊ #12802 |
468 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^8,11|a^2=f,b^2=d,c^2=h,e^2=h,f^2=h,b^a=bd,c^a=ce,e^a=eg,g^a=gh,e^c=eh,f^c=fgh,i^c=i^10,f^e=fh200 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 85568);