Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C17×#341 ⋊ C4 |
| Sylow | C17 ⋊ #11332 |
662 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 662 conjugacy classes of subgroups — too many to draw. Only its 156 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=g,b^2=d,c^2=e,d^2=h,e^2=h,f^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dh,e^a=eh,f^a=fh,i^a=i^13,c^b=cf,i^b=i^16,d^c=dh,f^c=fh,i^g=i^16164 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 1093139);