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Elements of the group are displayed as words in the presentation $\langle a, b \mid a^{2}=b^{47}=1, b^{a}=b^{46} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 47P
$D_{47}$ 1A $1$ $1$ $D_{47}$ 1A 1A $1$
$D_{47}$ 2A $2$ $47$ $C_2$ 1A 2A $ab^{3}$
$D_{47}$ 47A1 $47$ $2$ $C_{47}$ 47A2 47A23 $b$
$D_{47}$ 47A2 $47$ $2$ $C_{47}$ 47A4 47A1 $b^{2}$
$D_{47}$ 47A3 $47$ $2$ $C_{47}$ 47A6 47A22 $b^{3}$
$D_{47}$ 47A4 $47$ $2$ $C_{47}$ 47A8 47A2 $b^{4}$
$D_{47}$ 47A5 $47$ $2$ $C_{47}$ 47A10 47A21 $b^{5}$
$D_{47}$ 47A6 $47$ $2$ $C_{47}$ 47A12 47A3 $b^{6}$
$D_{47}$ 47A7 $47$ $2$ $C_{47}$ 47A14 47A20 $b^{7}$
$D_{47}$ 47A8 $47$ $2$ $C_{47}$ 47A16 47A4 $b^{8}$
$D_{47}$ 47A9 $47$ $2$ $C_{47}$ 47A18 47A19 $b^{9}$
$D_{47}$ 47A10 $47$ $2$ $C_{47}$ 47A20 47A5 $b^{10}$
$D_{47}$ 47A11 $47$ $2$ $C_{47}$ 47A22 47A18 $b^{11}$
$D_{47}$ 47A12 $47$ $2$ $C_{47}$ 47A23 47A6 $b^{12}$
$D_{47}$ 47A13 $47$ $2$ $C_{47}$ 47A21 47A17 $b^{13}$
$D_{47}$ 47A14 $47$ $2$ $C_{47}$ 47A19 47A7 $b^{14}$
$D_{47}$ 47A15 $47$ $2$ $C_{47}$ 47A17 47A16 $b^{15}$
$D_{47}$ 47A16 $47$ $2$ $C_{47}$ 47A15 47A8 $b^{16}$
$D_{47}$ 47A17 $47$ $2$ $C_{47}$ 47A13 47A15 $b^{17}$
$D_{47}$ 47A18 $47$ $2$ $C_{47}$ 47A11 47A9 $b^{18}$
$D_{47}$ 47A19 $47$ $2$ $C_{47}$ 47A9 47A14 $b^{19}$
$D_{47}$ 47A20 $47$ $2$ $C_{47}$ 47A7 47A10 $b^{20}$
$D_{47}$ 47A21 $47$ $2$ $C_{47}$ 47A5 47A13 $b^{21}$
$D_{47}$ 47A22 $47$ $2$ $C_{47}$ 47A3 47A11 $b^{22}$
$D_{47}$ 47A23 $47$ $2$ $C_{47}$ 47A1 47A12 $b^{23}$
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