Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C17 ⋊ #11394 |
1090 conjugacy classes of subgroups; only the 235 normal subgroups are shown.
This group has 1090 conjugacy classes of subgroups — too many to draw. Only its 235 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=g,b^2=f,c^2=f,b^a=bd,c^a=ce,d^a=dh,f^a=fh,i^a=i^16,c^b=cf,d^b=dh,g^b=gh,d^c=dh,e^c=eh398 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 78534);