Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C17 ⋊ #12068 |
204 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
Polycyclic presentation:
2^8,17|a^2=e,c^2=ef,d^2=f,e^2=g,f^2=h,g^2=h,b^a=bd,c^a=cf,d^a=df,f^a=fh,i^a=i^4,d^b=dfh,e^b=eh,f^b=fh,d^c=dh,i^c=i^13,i^e=i^16134 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 1095550);