Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×C17×#359 ⋊ C2 |
| Sylow | C17 ⋊ #13392 |
386 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 89 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|c^2=d,d^2=h,e^2=gh,g^2=h,b^a=bd,c^a=ce,d^a=dh,e^a=eg,f^a=fh,g^a=gh,c^b=cf,d^b=dh,e^b=eh,i^b=i^16,e^c=egh,f^c=fh,g^c=gh,i^c=i^16392 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 88806);