Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C11 ⋊ #10279 |
510 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 139 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2816 |
Polycyclic presentation:
2^8,11|a^2=gh,b^2=g,c^2=gh,d^2=g,e^2=h,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eh,f^a=fg,i^a=i^10,c^b=cf,d^b=dg,f^b=fg,i^b=i^10,d^c=dg,e^c=eh,f^c=fg,i^c=i^10326 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 72194);