Finite Group DatabasebetaFinite Group Databasebeta| order | 11008 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C43 ⋊ #10606 |
306 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^8,43|a^2=de,b^2=d,c^2=gh,d^2=g,e^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eg,f^a=fg,i^a=i^42,c^b=cf,f^b=fg,d^c=dg,e^c=eh,i^c=i^42835 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11008, 74217);