Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C17 ⋊ #7191 |
342 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 272 |
Polycyclic presentation:
2^8,17|a^2=d,b^2=e,d^2=g,g^2=h,b^a=bc,c^a=cf,f^a=fh,i^a=i^9,d^b=df,i^b=i^4,d^c=dh,i^d=i^13,i^e=i^16,i^g=i^1692 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 1116538);