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Elements of the group are displayed as words in the presentation $\langle a, b \mid a^{9}=b^{597}=1, b^{a}=b^{43} \rangle$ .

Group Label Order Size Centralizer Powers Representative
3P 199P
$C_{597}:C_9$ 1A $1$ $1$ $C_{597}:C_9$ 1A 1A $1$
$C_{597}:C_9$ 3A1 $3$ $1$ $C_{597}:C_9$ 3A-1 1A $b^{199}$
$C_{597}:C_9$ 3A-1 $3$ $1$ $C_{597}:C_9$ 3A1 1A $b^{398}$
$C_{597}:C_9$ 3B1 $3$ $199$ $C_3\times C_9$ 3B-1 1A $a^{6}b^{33}$
$C_{597}:C_9$ 3B-1 $3$ $199$ $C_3\times C_9$ 3B1 1A $a^{3}b^{84}$
$C_{597}:C_9$ 3C1 $3$ $199$ $C_3\times C_9$ 3C-1 1A $a^{3}b^{175}$
$C_{597}:C_9$ 3C-1 $3$ $199$ $C_3\times C_9$ 3C1 1A $a^{6}b^{218}$
$C_{597}:C_9$ 3D1 $3$ $199$ $C_3\times C_9$ 3D-1 1A $a^{3}b^{194}$
$C_{597}:C_9$ 3D-1 $3$ $199$ $C_3\times C_9$ 3D1 1A $a^{6}b^{460}$
$C_{597}:C_9$ 9A1 $9$ $199$ $C_3\times C_9$ 9A2 3B1 $a^{2}b^{364}$
$C_{597}:C_9$ 9A-1 $9$ $199$ $C_3\times C_9$ 9A-2 3B-1 $a^{7}b^{179}$
$C_{597}:C_9$ 9A2 $9$ $199$ $C_3\times C_9$ 9A4 3B-1 $a^{4}b^{581}$
$C_{597}:C_9$ 9A-2 $9$ $199$ $C_3\times C_9$ 9A-4 3B1 $a^{5}b^{460}$
$C_{597}:C_9$ 9A4 $9$ $199$ $C_3\times C_9$ 9A-1 3B1 $a^{8}b^{487}$
$C_{597}:C_9$ 9A-4 $9$ $199$ $C_3\times C_9$ 9A1 3B-1 $ab^{551}$
$C_{597}:C_9$ 9B1 $9$ $199$ $C_3\times C_9$ 9B2 3B-1 $a^{7}b^{175}$
$C_{597}:C_9$ 9B-1 $9$ $199$ $C_3\times C_9$ 9B-2 3B1 $a^{2}b^{596}$
$C_{597}:C_9$ 9B2 $9$ $199$ $C_3\times C_9$ 9B4 3B1 $a^{5}b^{353}$
$C_{597}:C_9$ 9B-2 $9$ $199$ $C_3\times C_9$ 9B-4 3B-1 $a^{4}b^{538}$
$C_{597}:C_9$ 9B4 $9$ $199$ $C_3\times C_9$ 9B-1 3B-1 $ab^{502}$
$C_{597}:C_9$ 9B-4 $9$ $199$ $C_3\times C_9$ 9B1 3B1 $a^{8}b^{266}$
$C_{597}:C_9$ 9C1 $9$ $199$ $C_3\times C_9$ 9C2 3B-1 $a^{7}b^{9}$
$C_{597}:C_9$ 9C-1 $9$ $199$ $C_3\times C_9$ 9C-2 3B1 $a^{2}b^{75}$
$C_{597}:C_9$ 9C2 $9$ $199$ $C_3\times C_9$ 9C4 3B1 $a^{5}b^{390}$
$C_{597}:C_9$ 9C-2 $9$ $199$ $C_3\times C_9$ 9C-4 3B-1 $a^{4}b^{246}$
$C_{597}:C_9$ 9C4 $9$ $199$ $C_3\times C_9$ 9C-1 3B-1 $ab^{558}$
$C_{597}:C_9$ 9C-4 $9$ $199$ $C_3\times C_9$ 9C1 3B1 $a^{8}b^{348}$
$C_{597}:C_9$ 199A1 $199$ $9$ $C_{597}$ 199A2 199A3 $b^{3}$
$C_{597}:C_9$ 199A-1 $199$ $9$ $C_{597}$ 199A-2 199A-3 $b^{594}$
$C_{597}:C_9$ 199A2 $199$ $9$ $C_{597}$ 199A4 199A6 $b^{6}$
$C_{597}:C_9$ 199A-2 $199$ $9$ $C_{597}$ 199A-4 199A-6 $b^{591}$
$C_{597}:C_9$ 199A3 $199$ $9$ $C_{597}$ 199A6 199A9 $b^{9}$
$C_{597}:C_9$ 199A-3 $199$ $9$ $C_{597}$ 199A-6 199A-9 $b^{588}$
$C_{597}:C_9$ 199A4 $199$ $9$ $C_{597}$ 199A7 199A12 $b^{12}$
$C_{597}:C_9$ 199A-4 $199$ $9$ $C_{597}$ 199A-7 199A-12 $b^{585}$
$C_{597}:C_9$ 199A5 $199$ $9$ $C_{597}$ 199A9 199A-2 $b^{15}$
$C_{597}:C_9$ 199A-5 $199$ $9$ $C_{597}$ 199A-9 199A2 $b^{582}$
$C_{597}:C_9$ 199A6 $199$ $9$ $C_{597}$ 199A12 199A18 $b^{18}$
$C_{597}:C_9$ 199A-6 $199$ $9$ $C_{597}$ 199A-12 199A-18 $b^{579}$
$C_{597}:C_9$ 199A7 $199$ $9$ $C_{597}$ 199A5 199A-1 $b^{21}$
$C_{597}:C_9$ 199A-7 $199$ $9$ $C_{597}$ 199A-5 199A1 $b^{576}$
$C_{597}:C_9$ 199A9 $199$ $9$ $C_{597}$ 199A18 199A-4 $b^{27}$
$C_{597}:C_9$ 199A-9 $199$ $9$ $C_{597}$ 199A-18 199A4 $b^{570}$
$C_{597}:C_9$ 199A12 $199$ $9$ $C_{597}$ 199A-1 199A35 $b^{36}$
$C_{597}:C_9$ 199A-12 $199$ $9$ $C_{597}$ 199A1 199A-35 $b^{561}$
$C_{597}:C_9$ 199A18 $199$ $9$ $C_{597}$ 199A35 199A-7 $b^{54}$
$C_{597}:C_9$ 199A-18 $199$ $9$ $C_{597}$ 199A-35 199A7 $b^{543}$
$C_{597}:C_9$ 199A35 $199$ $9$ $C_{597}$ 199A-3 199A-5 $b^{105}$
$C_{597}:C_9$ 199A-35 $199$ $9$ $C_{597}$ 199A3 199A5 $b^{492}$
$C_{597}:C_9$ 597A1 $597$ $9$ $C_{597}$ 597A2 199A1 $b$
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