Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C17×#368 ⋊ C4 |
| Sylow | C17 ⋊ #12676 |
306 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 110 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,b^2=f,c^2=deg,d^2=gh,e^2=gh,f^2=h,g^2=h,b^a=bd,c^a=ch,i^a=i^4,d^b=dg,e^b=eg,g^b=gh,i^c=i^13,i^e=i^16152 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 1096316);