Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C17 ⋊ #12804 |
432 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 103 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=f,b^2=d,c^2=h,e^2=h,f^2=h,b^a=bd,c^a=ce,e^a=eg,g^a=gh,c^b=ch,e^c=eh,f^c=fgh,i^c=i^16,f^e=fh290 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 85576);