Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C17 ⋊ #12025 |
224 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 119 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2176 |
Polycyclic presentation:
2^8,17|a^2=e,b^2=df,d^2=fh,e^2=g,f^2=h,b^a=bd,c^a=cg,d^a=df,f^a=fh,i^a=i^16,c^b=ch692 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 81221);