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R summary

Dear all
i use R only a few days and don't understand the difference between
fivenum(x) und summary(x).
[1] 20.77 22.56 22.71 22.99 26.39 27.08 27.32 27.33 27.57 27.81 28.69 29.36
[13] 30.25 31.89 32.88 33.23 33.28 33.40 33.52 33.83 33.95 34.82
[1] 20.770 27.080 29.025 33.280 34.820
Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  20.77   27.14   29.03   29.17   33.27   34.82 

And why is the 1st Qu. 27.14 although
qL=x(1/4*(n+1))=x(23/4)=x(5 3/4)
x(5)=26.39
x(6)=27.08
why is ql in summary between x(6) und x(7)??

I have learned that 1st Qu. = q(0.25)... so i am a little confused.

Thanks a lot
Matze