Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C17×#1726 ⋊ C2 |
| Sylow | C17 ⋊ #20508 |
1206 conjugacy classes of subgroups; only the 403 normal subgroups are shown.
This group has 1206 conjugacy classes of subgroups — too many to draw. Only its 403 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2176 |
Polycyclic presentation:
2^8,17|a^2=f,b^2=g,c^2=g,d^2=fh,e^2=h,b^a=be,c^a=ch,d^a=dh,e^a=eh,i^a=i^16,e^b=eh,i^b=i^16,d^c=dh728 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 168117);