Finite Group DatabasebetaFinite Group Databasebeta| order | 11008 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C43×#1455 ⋊ C2 |
| Sylow | C43 ⋊ #19754 |
728 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 728 conjugacy classes of subgroups — too many to draw. Only its 179 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=g,b^2=egh,c^2=fg,e^2=g,f^2=h,b^a=be,c^a=cf,e^a=eg,f^a=fh,i^a=i^42,d^b=dg,d^c=dh1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11008, 158905);