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Elements of the group are displayed as words in the presentation $\langle a, b \mid a^{2}=b^{5}=1, b^{a}=b^{4} \rangle$ .

Group	Label	Order	Size	Centralizer	Powers		Representative
					2P	5P
$D_5$	1A	$1$	$1$	$D_5$	1A	1A	$1$
$D_5$	2A	$2$	$5$	$C_2$	1A	2A	$ab^{3}$
$D_5$	5A1	$5$	$2$	$C_5$	5A2	1A	$b$
$D_5$	5A2	$5$	$2$	$C_5$	5A1	1A	$b^{2}$

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