Multiplication table for the binary tetrahedral group


The elements are denoted by the symbols derived in the Quaternionic representation of the binary tetrahedral group.

NOTE: each element has a negative, so the table should be four times as large; but -1 commutes with everything, so the missing products are easy to retrieve.


      1    i    j    k    a    a^2   b    b^2   c    c^2   d    d^2

1     1    i    j    k    a    a^2   b    b^2   c    c^2   d    d^2

i     i   -1    k   -j    d   -c^2   c   -d^2  -b    a^2  -a    b^2

j     j   -k   -1    i    b   -d^2  -a    c^2   d   -b^2  -c    a^2

k     k    j   -i   -1    c   -b^2  -d    a^2  -a    d^2   b   -c^2

a     a    c    d    b   a^2   -1  -c^2    j  -d^2    k   -b^2   i  

a^2  a^2 -d^2 -b^2 -c^2  -1    -a   -k     d   -i     b   -j     c  

b     b    d   -c   -a  -d^2   -j   b^2   -1  -a^2    i   -c^2   -k
  
b^2  b^2 -c^2  a^2  d^2   k     c   -1    -b    j     d   -i     a  

c     c   -a    b   -d  -b^2   -k  -d^2   -i   c^2   -1   -a^2   j   

c^2  c^2  b^2 -d^2  a^2   i     d   -j     a    -1   -c    k     b   

d     d   -b   -a    c  -c^2   -i  -a^2    k  -b^2   -j   d^2   -1  

d^2  d^2  a^2  c^2 -b^2   j     b    i     c    -k    a   -1    -d  



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