Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C11×#1371 ⋊ C2 |
| Sylow | C11 ⋊ #12009 |
242 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 242 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) = 1408 |
Polycyclic presentation:
2^8,11|a^2=e,b^2=df,d^2=fh,e^2=g,f^2=h,b^a=bd,d^a=df,f^a=fh,c^b=ch,i^c=i^10284 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 81154);