Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C17 ⋊ #9969 |
658 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 658 conjugacy classes of subgroups — too many to draw. Only its 111 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=g,b^2=h,d^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,f^a=fh,i^a=i^16,c^b=cf,d^b=dg,f^b=fg,i^b=i^16,d^c=dh,f^c=fg344 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 70141);