Finite Group DatabasebetaFinite Group Databasebeta| order | 11008 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C43×#1451 ⋊ C2 |
| Sylow | C43 ⋊ #9790 |
384 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 103 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=f,b^2=df,c^2=e,d^2=gh,e^2=gh,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=egh,i^a=i^42,c^b=cg,d^b=dh,f^b=fh1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11008, 69128);