Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C11×#338 ⋊ C2 |
| Sylow | C11 ⋊ #23723 |
972 conjugacy classes of subgroups; only the 271 normal subgroups are shown.
This group has 972 conjugacy classes of subgroups — too many to draw. Only its 271 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=ef,e^2=h,b^a=be,c^a=cf,g^a=gh,c^b=cg,e^b=eh,f^b=fh,i^b=i^10,d^c=dh,i^c=i^10266 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 199320);