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Elements of the group are displayed as words in the presentation $\langle a, b \mid a^{2}=b^{37}=1, b^{a}=b^{36} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 37P
$D_{37}$ 1A $1$ $1$ $D_{37}$ 1A 1A $1$
$D_{37}$ 2A $2$ $37$ $C_2$ 1A 2A $ab^{3}$
$D_{37}$ 37A1 $37$ $2$ $C_{37}$ 37A2 37A3 $b$
$D_{37}$ 37A2 $37$ $2$ $C_{37}$ 37A4 37A6 $b^{2}$
$D_{37}$ 37A3 $37$ $2$ $C_{37}$ 37A6 37A9 $b^{3}$
$D_{37}$ 37A4 $37$ $2$ $C_{37}$ 37A8 37A12 $b^{4}$
$D_{37}$ 37A5 $37$ $2$ $C_{37}$ 37A10 37A15 $b^{5}$
$D_{37}$ 37A6 $37$ $2$ $C_{37}$ 37A12 37A18 $b^{6}$
$D_{37}$ 37A7 $37$ $2$ $C_{37}$ 37A14 37A16 $b^{7}$
$D_{37}$ 37A8 $37$ $2$ $C_{37}$ 37A16 37A13 $b^{8}$
$D_{37}$ 37A9 $37$ $2$ $C_{37}$ 37A18 37A10 $b^{9}$
$D_{37}$ 37A10 $37$ $2$ $C_{37}$ 37A17 37A7 $b^{10}$
$D_{37}$ 37A11 $37$ $2$ $C_{37}$ 37A15 37A4 $b^{11}$
$D_{37}$ 37A12 $37$ $2$ $C_{37}$ 37A13 37A1 $b^{12}$
$D_{37}$ 37A13 $37$ $2$ $C_{37}$ 37A11 37A2 $b^{13}$
$D_{37}$ 37A14 $37$ $2$ $C_{37}$ 37A9 37A5 $b^{14}$
$D_{37}$ 37A15 $37$ $2$ $C_{37}$ 37A7 37A8 $b^{15}$
$D_{37}$ 37A16 $37$ $2$ $C_{37}$ 37A5 37A11 $b^{16}$
$D_{37}$ 37A17 $37$ $2$ $C_{37}$ 37A3 37A14 $b^{17}$
$D_{37}$ 37A18 $37$ $2$ $C_{37}$ 37A1 37A17 $b^{18}$
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