Conjugacy class search results

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Elements of the group are displayed as words in the presentation $\langle a, b \mid a^{2}=b^{45}=1, b^{a}=b^{44} \rangle$ .

Group	Label	Order	Size	Centralizer	Powers			Representative
					2P	3P	5P
$D_{45}$	1A	$1$	$1$	$D_{45}$	1A	1A	1A	$1$
$D_{45}$	2A	$2$	$45$	$C_2$	1A	2A	2A	$ab^{36}$
$D_{45}$	3A	$3$	$2$	$C_{45}$	3A	1A	3A	$b^{15}$
$D_{45}$	5A1	$5$	$2$	$C_{45}$	5A2	5A2	1A	$b^{9}$
$D_{45}$	5A2	$5$	$2$	$C_{45}$	5A1	5A1	1A	$b^{18}$
$D_{45}$	9A1	$9$	$2$	$C_{45}$	9A2	3A	9A4	$b^{5}$
$D_{45}$	9A2	$9$	$2$	$C_{45}$	9A4	3A	9A1	$b^{10}$
$D_{45}$	9A4	$9$	$2$	$C_{45}$	9A1	3A	9A2	$b^{20}$
$D_{45}$	15A1	$15$	$2$	$C_{45}$	15A2	5A1	3A	$b^{3}$
$D_{45}$	15A2	$15$	$2$	$C_{45}$	15A4	5A2	3A	$b^{6}$
$D_{45}$	15A4	$15$	$2$	$C_{45}$	15A7	5A1	3A	$b^{12}$
$D_{45}$	15A7	$15$	$2$	$C_{45}$	15A1	5A2	3A	$b^{21}$
$D_{45}$	45A1	$45$	$2$	$C_{45}$	45A2	15A1	9A1	$b$
$D_{45}$	45A2	$45$	$2$	$C_{45}$	45A4	15A2	9A2	$b^{2}$
$D_{45}$	45A4	$45$	$2$	$C_{45}$	45A8	15A4	9A4	$b^{4}$
$D_{45}$	45A7	$45$	$2$	$C_{45}$	45A14	15A7	9A2	$b^{7}$
$D_{45}$	45A8	$45$	$2$	$C_{45}$	45A16	15A7	9A1	$b^{8}$
$D_{45}$	45A11	$45$	$2$	$C_{45}$	45A22	15A4	9A2	$b^{11}$
$D_{45}$	45A13	$45$	$2$	$C_{45}$	45A19	15A2	9A4	$b^{13}$
$D_{45}$	45A14	$45$	$2$	$C_{45}$	45A17	15A1	9A4	$b^{14}$
$D_{45}$	45A16	$45$	$2$	$C_{45}$	45A13	15A1	9A2	$b^{29}$
$D_{45}$	45A17	$45$	$2$	$C_{45}$	45A11	15A2	9A1	$b^{28}$
$D_{45}$	45A19	$45$	$2$	$C_{45}$	45A7	15A4	9A1	$b^{19}$
$D_{45}$	45A22	$45$	$2$	$C_{45}$	45A1	15A7	9A4	$b^{22}$

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