Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C11 ⋊ #12002 |
220 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 143 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^8,11|a^2=e,b^2=d,d^2=f,e^2=g,f^2=h,g^2=h,b^a=bd,d^a=df,f^a=fh,i^a=i^10,c^b=ch,e^b=eh464 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 81133);