Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C17×#2642 ⋊ C2 |
| Sylow | C17 ⋊ #25691 |
920 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 920 conjugacy classes of subgroups — too many to draw. Only its 175 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^8,17|a^2=eh,c^2=f,d^2=e,f^2=h,g^2=h,b^a=be,c^a=cf,d^a=de,f^a=fh,i^a=i^16,c^b=cg,g^b=gh,i^b=i^16,d^c=dh,g^c=gh,i^c=i^16296 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 224049);