Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C11×#1842 ⋊ C2 |
| Sylow | C11 ⋊ #23375 |
696 conjugacy classes of subgroups; only the 255 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 255 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=g,c^2=e,d^2=f,g^2=h,b^a=be,c^a=cf,d^a=def,i^a=i^10,c^b=cef,d^b=de,i^b=i^10356 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 196266);