Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C11 ⋊ #13543 |
268 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 89 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=dh,b^2=deg,c^2=d,d^2=h,f^2=g,g^2=h,b^a=bd,c^a=ce,i^a=i^10,c^b=cf,d^b=dh,f^b=fg,g^b=gh,f^c=fg,g^c=gh,i^c=i^10200 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 89721);