Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C8 |
No aliases for this group.
| Fitting | C11×#1715 ⋊ C2 |
| Sylow | C11 ⋊ #19745 |
994 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 994 conjugacy classes of subgroups — too many to draw. Only its 167 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|b^2=e,c^2=f,e^2=g,f^2=h,b^a=be,c^a=cf,e^a=eg,f^a=fh,i^a=i^10,d^b=dg,d^c=dh,i^c=i^10,i^d=i^10170 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#19745, #72254738, #72269632 |
| maximal normal subgroup of | D11×#19745, #72254738, #72269632 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 158812);