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Elements of the group are displayed as words in the presentation $\langle a, b \mid a^{2}=b^{805}=1, b^{a}=b^{804} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 5P 7P 23P
$D_{805}$ 1A $1$ $1$ $D_{805}$ 1A 1A 1A 1A $1$
$D_{805}$ 2A $2$ $805$ $C_2$ 1A 2A 2A 2A $ab^{770}$
$D_{805}$ 5A1 $5$ $2$ $C_{805}$ 5A2 5A2 1A 5A2 $b^{161}$
$D_{805}$ 5A2 $5$ $2$ $C_{805}$ 5A1 5A1 1A 5A1 $b^{322}$
$D_{805}$ 7A1 $7$ $2$ $C_{805}$ 7A2 7A3 7A2 1A $b^{115}$
$D_{805}$ 7A2 $7$ $2$ $C_{805}$ 7A3 7A1 7A3 1A $b^{230}$
$D_{805}$ 7A3 $7$ $2$ $C_{805}$ 7A1 7A2 7A1 1A $b^{345}$
$D_{805}$ 23A1 $23$ $2$ $C_{805}$ 23A2 23A3 23A5 23A7 $b^{35}$
$D_{805}$ 23A2 $23$ $2$ $C_{805}$ 23A4 23A6 23A10 23A9 $b^{70}$
$D_{805}$ 23A3 $23$ $2$ $C_{805}$ 23A6 23A9 23A8 23A2 $b^{105}$
$D_{805}$ 23A4 $23$ $2$ $C_{805}$ 23A8 23A11 23A3 23A5 $b^{140}$
$D_{805}$ 23A5 $23$ $2$ $C_{805}$ 23A10 23A8 23A2 23A11 $b^{175}$
$D_{805}$ 23A6 $23$ $2$ $C_{805}$ 23A11 23A5 23A7 23A4 $b^{210}$
$D_{805}$ 23A7 $23$ $2$ $C_{805}$ 23A9 23A2 23A11 23A3 $b^{245}$
$D_{805}$ 23A8 $23$ $2$ $C_{805}$ 23A7 23A1 23A6 23A10 $b^{280}$
$D_{805}$ 23A9 $23$ $2$ $C_{805}$ 23A5 23A4 23A1 23A6 $b^{315}$
$D_{805}$ 23A10 $23$ $2$ $C_{805}$ 23A3 23A7 23A4 23A1 $b^{350}$
$D_{805}$ 23A11 $23$ $2$ $C_{805}$ 23A1 23A10 23A9 23A8 $b^{385}$
$D_{805}$ 35A1 $35$ $2$ $C_{805}$ 35A2 35A3 7A1 5A1 $b^{23}$
$D_{805}$ 35A2 $35$ $2$ $C_{805}$ 35A4 35A6 7A2 5A2 $b^{46}$
$D_{805}$ 35A3 $35$ $2$ $C_{805}$ 35A6 35A9 7A3 5A2 $b^{69}$
$D_{805}$ 35A4 $35$ $2$ $C_{805}$ 35A8 35A12 7A3 5A1 $b^{92}$
$D_{805}$ 35A6 $35$ $2$ $C_{805}$ 35A12 35A17 7A1 5A1 $b^{138}$
$D_{805}$ 35A8 $35$ $2$ $C_{805}$ 35A16 35A11 7A1 5A2 $b^{184}$
$D_{805}$ 35A9 $35$ $2$ $C_{805}$ 35A17 35A8 7A2 5A1 $b^{207}$
$D_{805}$ 35A11 $35$ $2$ $C_{805}$ 35A13 35A2 7A3 5A1 $b^{253}$
$D_{805}$ 35A12 $35$ $2$ $C_{805}$ 35A11 35A1 7A2 5A2 $b^{276}$
$D_{805}$ 35A13 $35$ $2$ $C_{805}$ 35A9 35A4 7A1 5A2 $b^{299}$
$D_{805}$ 35A16 $35$ $2$ $C_{805}$ 35A3 35A13 7A2 5A1 $b^{368}$
$D_{805}$ 35A17 $35$ $2$ $C_{805}$ 35A1 35A16 7A3 5A2 $b^{391}$
$D_{805}$ 115A1 $115$ $2$ $C_{805}$ 115A2 115A3 23A1 115A7 $b^{7}$
$D_{805}$ 115A2 $115$ $2$ $C_{805}$ 115A4 115A6 23A2 115A14 $b^{14}$
$D_{805}$ 115A3 $115$ $2$ $C_{805}$ 115A6 115A9 23A3 115A21 $b^{21}$
$D_{805}$ 115A4 $115$ $2$ $C_{805}$ 115A8 115A12 23A4 115A28 $b^{28}$
$D_{805}$ 115A6 $115$ $2$ $C_{805}$ 115A12 115A18 23A6 115A42 $b^{42}$
$D_{805}$ 115A7 $115$ $2$ $C_{805}$ 115A14 115A21 23A7 115A49 $b^{49}$
$D_{805}$ 115A8 $115$ $2$ $C_{805}$ 115A16 115A24 23A8 115A56 $b^{56}$
$D_{805}$ 115A9 $115$ $2$ $C_{805}$ 115A18 115A27 23A9 115A52 $b^{63}$
$D_{805}$ 115A11 $115$ $2$ $C_{805}$ 115A22 115A33 23A11 115A38 $b^{77}$
$D_{805}$ 115A12 $115$ $2$ $C_{805}$ 115A24 115A36 23A11 115A31 $b^{84}$
$D_{805}$ 115A13 $115$ $2$ $C_{805}$ 115A26 115A39 23A10 115A24 $b^{91}$
$D_{805}$ 115A14 $115$ $2$ $C_{805}$ 115A28 115A42 23A9 115A17 $b^{98}$
$D_{805}$ 115A16 $115$ $2$ $C_{805}$ 115A32 115A48 23A7 115A3 $b^{112}$
$D_{805}$ 115A17 $115$ $2$ $C_{805}$ 115A34 115A51 23A6 115A4 $b^{119}$
$D_{805}$ 115A18 $115$ $2$ $C_{805}$ 115A36 115A54 23A5 115A11 $b^{126}$
$D_{805}$ 115A19 $115$ $2$ $C_{805}$ 115A38 115A57 23A4 115A18 $b^{133}$
$D_{805}$ 115A21 $115$ $2$ $C_{805}$ 115A42 115A52 23A2 115A32 $b^{147}$
$D_{805}$ 115A22 $115$ $2$ $C_{805}$ 115A44 115A49 23A1 115A39 $b^{154}$
$D_{805}$ 115A24 $115$ $2$ $C_{805}$ 115A48 115A43 23A1 115A53 $b^{168}$
$D_{805}$ 115A26 $115$ $2$ $C_{805}$ 115A52 115A37 23A3 115A48 $b^{182}$
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