A5 is (5, 2, 3) & A4 is (3, 3, 2)

It comes from 有限群导引（上）-徐明曜.pdf, page 45.

(i) If $abab=1$, then

• $b=aba{b}^2$
• $b^2=aba$
• $a=a^{2}bab$
• $a^2=bab$
• $ab=a^{2}ba{b}^2$
• $a{b}^2=a^{2}ba$
• $a^{2}b=ba{b}^2$
• $a^2{b}^2=ba$
• $b^{2}a=ab{a}^2$
• $b{a}^2=b^{2}ab$
• $b^2{a}^2=ab$
• $a{b}^{2}a=a^{2}b{a}^2$ aba, a2ba, ab2a, aba2,
• $a{b}^{2}ab=a^{2}baab=a^{2}b{a}^{2}b$

1+4+8+16+32=61