Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C11 ⋊ #13128 |
328 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 103 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=df,c^2=d,e^2=h,f^2=g,g^2=h,b^a=bd,c^a=ce,d^a=dh,c^b=cg,d^b=dh,f^b=fh,f^c=fh,i^c=i^10272 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 87348);