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Elements of the group are displayed as words in the presentation $\langle a, b \mid a^{12}=b^{579}=1, b^{a}=b^{85} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 3P 193P
$C_{579}:C_{12}$ 1A $1$ $1$ $C_{579}:C_{12}$ 1A 1A 1A $1$
$C_{579}:C_{12}$ 2A $2$ $1$ $C_{579}:C_{12}$ 1A 2A 2A $a^{6}$
$C_{579}:C_{12}$ 3A1 $3$ $1$ $C_{579}:C_{12}$ 3A-1 1A 3A1 $b^{386}$
$C_{579}:C_{12}$ 3A-1 $3$ $1$ $C_{579}:C_{12}$ 3A1 1A 3A-1 $b^{193}$
$C_{579}:C_{12}$ 3B1 $3$ $193$ $C_3\times C_{12}$ 3B-1 1A 3B1 $a^{4}b^{5}$
$C_{579}:C_{12}$ 3B-1 $3$ $193$ $C_3\times C_{12}$ 3B1 1A 3B-1 $a^{8}b^{352}$
$C_{579}:C_{12}$ 3C1 $3$ $193$ $C_3\times C_{12}$ 3C-1 1A 3C1 $a^{8}b^{126}$
$C_{579}:C_{12}$ 3C-1 $3$ $193$ $C_3\times C_{12}$ 3C1 1A 3C-1 $a^{4}b^{288}$
$C_{579}:C_{12}$ 3D1 $3$ $193$ $C_3\times C_{12}$ 3D-1 1A 3D1 $a^{4}b^{400}$
$C_{579}:C_{12}$ 3D-1 $3$ $193$ $C_3\times C_{12}$ 3D1 1A 3D-1 $a^{8}b^{368}$
$C_{579}:C_{12}$ 4A1 $4$ $193$ $C_3\times C_{12}$ 2A 4A-1 4A1 $a^{9}b^{45}$
$C_{579}:C_{12}$ 4A-1 $4$ $193$ $C_3\times C_{12}$ 2A 4A1 4A-1 $a^{3}b^{45}$
$C_{579}:C_{12}$ 6A1 $6$ $1$ $C_{579}:C_{12}$ 3A1 2A 6A1 $a^{6}b^{193}$
$C_{579}:C_{12}$ 6A-1 $6$ $1$ $C_{579}:C_{12}$ 3A-1 2A 6A-1 $a^{6}b^{386}$
$C_{579}:C_{12}$ 6B1 $6$ $193$ $C_3\times C_{12}$ 3B1 2A 6B1 $a^{2}b^{352}$
$C_{579}:C_{12}$ 6B-1 $6$ $193$ $C_3\times C_{12}$ 3B-1 2A 6B-1 $a^{10}b^{5}$
$C_{579}:C_{12}$ 6C1 $6$ $193$ $C_3\times C_{12}$ 3C1 2A 6C1 $a^{10}b^{288}$
$C_{579}:C_{12}$ 6C-1 $6$ $193$ $C_3\times C_{12}$ 3C-1 2A 6C-1 $a^{2}b^{126}$
$C_{579}:C_{12}$ 6D1 $6$ $193$ $C_3\times C_{12}$ 3D1 2A 6D1 $a^{2}b^{368}$
$C_{579}:C_{12}$ 6D-1 $6$ $193$ $C_3\times C_{12}$ 3D-1 2A 6D-1 $a^{10}b^{400}$
$C_{579}:C_{12}$ 12A1 $12$ $193$ $C_3\times C_{12}$ 6B1 4A1 12A1 $a^{7}b^{233}$
$C_{579}:C_{12}$ 12A-1 $12$ $193$ $C_3\times C_{12}$ 6B-1 4A-1 12A-1 $a^{5}b^{79}$
$C_{579}:C_{12}$ 12A5 $12$ $193$ $C_3\times C_{12}$ 6B-1 4A1 12A5 $a^{11}b^{79}$
$C_{579}:C_{12}$ 12A-5 $12$ $193$ $C_3\times C_{12}$ 6B1 4A-1 12A-5 $ab^{233}$
$C_{579}:C_{12}$ 12B1 $12$ $193$ $C_3\times C_{12}$ 6C1 4A1 12B1 $a^{11}b^{150}$
$C_{579}:C_{12}$ 12B-1 $12$ $193$ $C_3\times C_{12}$ 6C-1 4A-1 12B-1 $ab^{567}$
$C_{579}:C_{12}$ 12B5 $12$ $193$ $C_3\times C_{12}$ 6C-1 4A1 12B5 $a^{7}b^{567}$
$C_{579}:C_{12}$ 12B-5 $12$ $193$ $C_3\times C_{12}$ 6C1 4A-1 12B-5 $a^{5}b^{150}$
$C_{579}:C_{12}$ 12C1 $12$ $193$ $C_3\times C_{12}$ 6A-1 4A-1 12C1 $a^{9}b^{559}$
$C_{579}:C_{12}$ 12C-1 $12$ $193$ $C_3\times C_{12}$ 6A1 4A1 12C-1 $a^{3}b^{173}$
$C_{579}:C_{12}$ 12C5 $12$ $193$ $C_3\times C_{12}$ 6A1 4A-1 12C5 $a^{9}b^{173}$
$C_{579}:C_{12}$ 12C-5 $12$ $193$ $C_3\times C_{12}$ 6A-1 4A1 12C-5 $a^{3}b^{559}$
$C_{579}:C_{12}$ 12D1 $12$ $193$ $C_3\times C_{12}$ 6D1 4A1 12D1 $a^{7}b^{112}$
$C_{579}:C_{12}$ 12D-1 $12$ $193$ $C_3\times C_{12}$ 6D-1 4A-1 12D-1 $a^{5}b^{530}$
$C_{579}:C_{12}$ 12D5 $12$ $193$ $C_3\times C_{12}$ 6D-1 4A1 12D5 $a^{11}b^{530}$
$C_{579}:C_{12}$ 12D-5 $12$ $193$ $C_3\times C_{12}$ 6D1 4A-1 12D-5 $ab^{112}$
$C_{579}:C_{12}$ 193A1 $193$ $6$ $C_{1158}$ 193A2 193A3 1A $b^{6}$
$C_{579}:C_{12}$ 193A2 $193$ $6$ $C_{1158}$ 193A4 193A6 1A $b^{12}$
$C_{579}:C_{12}$ 193A3 $193$ $6$ $C_{1158}$ 193A6 193A7 1A $b^{18}$
$C_{579}:C_{12}$ 193A4 $193$ $6$ $C_{1158}$ 193A8 193A12 1A $b^{24}$
$C_{579}:C_{12}$ 193A5 $193$ $6$ $C_{1158}$ 193A10 193A15 1A $b^{30}$
$C_{579}:C_{12}$ 193A6 $193$ $6$ $C_{1158}$ 193A12 193A14 1A $b^{36}$
$C_{579}:C_{12}$ 193A7 $193$ $6$ $C_{1158}$ 193A14 193A21 1A $b^{42}$
$C_{579}:C_{12}$ 193A8 $193$ $6$ $C_{1158}$ 193A7 193A24 1A $b^{48}$
$C_{579}:C_{12}$ 193A10 $193$ $6$ $C_{1158}$ 193A20 193A11 1A $b^{60}$
$C_{579}:C_{12}$ 193A11 $193$ $6$ $C_{1158}$ 193A22 193A33 1A $b^{66}$
$C_{579}:C_{12}$ 193A12 $193$ $6$ $C_{1158}$ 193A24 193A28 1A $b^{72}$
$C_{579}:C_{12}$ 193A13 $193$ $6$ $C_{1158}$ 193A26 193A5 1A $b^{78}$
$C_{579}:C_{12}$ 193A14 $193$ $6$ $C_{1158}$ 193A28 193A42 1A $b^{84}$
$C_{579}:C_{12}$ 193A15 $193$ $6$ $C_{1158}$ 193A11 193A35 1A $b^{90}$
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