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$\begingroup$

Could you help me to find a set of normal forms for the group $\langle a,b,c| a^2=b^2=c^2=1, (ab)^2=(ac)^4=1\rangle$?

EDIT: how can I draw a cayley graph for this group?

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    $a$ and $c$ generate a dihedral group of order $8$; $a$ and $b$ generate a Klein $4$-group. $b$ and $c$ generate a $C_2*C_2$.2012-03-22
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    In particular, this is an amalgamated product of $D_4$ and $D_8$, with some reflection ($a$) amalgamated.2012-03-22

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