Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23×C4 |
| unambiguous semidirect product | #595⋊#323 |
| Fitting | C2×C22⋊C4×C17 ⋊ C8 |
| Sylow | C17 ⋊ C4×#323 |
946 conjugacy classes of subgroups.
| transitive degree | μt(G) = 272 |
Polycyclic presentation:
2^8,17|a^2=e,b^2=f,c^2=e,f^2=h,b^a=bd,f^a=fg,i^a=i^4,d^b=dg,i^b=i^9,i^c=i^4,i^e=i^16,i^f=i^13,i^h=i^16128 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 1116845);