Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C17 ⋊ #10372 |
402 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 402 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) = 1088 |
Polycyclic presentation:
2^8,17|a^2=d,b^2=dh,e^2=gh,f^2=g,b^a=bd,c^a=ce,e^a=eh,i^a=i^16,c^b=cf,e^b=eg,d^c=dg,e^c=egh,f^c=fg296 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 72706);