Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| automorphism | ? |
| homology | Abelianization (H1) = C43 · Schur multiplier (H2) = C22×C8 |
No aliases for this group.
| Fitting | C17×#322 ⋊ C4 |
| Sylow | C17 ⋊ #7844 |
518 conjugacy classes of subgroups; only the 212 normal subgroups are shown.
This group has 518 conjugacy classes of subgroups — too many to draw. Only its 212 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=d,b^2=e,c^2=f,d^2=g,e^2=h,c^a=ch,i^a=i^4,c^b=cg,i^b=i^4,i^c=i^13,i^d=i^16,i^e=i^16,i^f=i^16272 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 1085530);