Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C17 ⋊ #11783 |
514 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 514 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 544 |
Polycyclic presentation:
2^8,17|a^2=e,c^2=gh,d^2=g,e^2=h,b^a=bd,d^a=df,f^a=fh,i^a=i^16,c^b=cfh,d^b=dg,e^b=efg,d^c=dh,e^d=eh341 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 80168);