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Elements of the group are displayed as words in the presentation $\langle a, b, c \mid a^{2}=b^{4}=c^{114}=[a,b]=[b,c]=1, c^{a}=c^{37} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 3P 19P
$C_{12}\times D_{38}$ 1A $1$ $1$ $C_{12}\times D_{38}$ 1A 1A 1A $1$
$C_{12}\times D_{38}$ 2A $2$ $1$ $C_{12}\times D_{38}$ 1A 2A 2A $b^{2}$
$C_{12}\times D_{38}$ 2B $2$ $1$ $C_{12}\times D_{38}$ 1A 2B 2B $c^{57}$
$C_{12}\times D_{38}$ 2C $2$ $1$ $C_{12}\times D_{38}$ 1A 2C 2C $b^{2}c^{57}$
$C_{12}\times D_{38}$ 2D $2$ $19$ $C_2^2\times C_{12}$ 1A 2D 2D $ac^{78}$
$C_{12}\times D_{38}$ 2E $2$ $19$ $C_2^2\times C_{12}$ 1A 2E 2E $ac^{39}$
$C_{12}\times D_{38}$ 2F $2$ $19$ $C_2^2\times C_{12}$ 1A 2F 2F $ab^{2}c^{78}$
$C_{12}\times D_{38}$ 2G $2$ $19$ $C_2^2\times C_{12}$ 1A 2G 2G $ab^{2}c^{39}$
$C_{12}\times D_{38}$ 3A1 $3$ $1$ $C_{12}\times D_{38}$ 3A-1 1A 3A1 $c^{76}$
$C_{12}\times D_{38}$ 3A-1 $3$ $1$ $C_{12}\times D_{38}$ 3A1 1A 3A-1 $c^{38}$
$C_{12}\times D_{38}$ 4A1 $4$ $1$ $C_{12}\times D_{38}$ 2A 4A-1 4A-1 $b$
$C_{12}\times D_{38}$ 4A-1 $4$ $1$ $C_{12}\times D_{38}$ 2A 4A1 4A1 $b^{3}$
$C_{12}\times D_{38}$ 4B1 $4$ $1$ $C_{12}\times D_{38}$ 2A 4B-1 4B-1 $bc^{57}$
$C_{12}\times D_{38}$ 4B-1 $4$ $1$ $C_{12}\times D_{38}$ 2A 4B1 4B1 $b^{3}c^{57}$
$C_{12}\times D_{38}$ 4C1 $4$ $19$ $C_2^2\times C_{12}$ 2A 4C-1 4C-1 $ab^{3}c^{78}$
$C_{12}\times D_{38}$ 4C-1 $4$ $19$ $C_2^2\times C_{12}$ 2A 4C1 4C1 $abc^{78}$
$C_{12}\times D_{38}$ 4D1 $4$ $19$ $C_2^2\times C_{12}$ 2A 4D-1 4D-1 $ab^{3}c^{39}$
$C_{12}\times D_{38}$ 4D-1 $4$ $19$ $C_2^2\times C_{12}$ 2A 4D1 4D1 $abc^{39}$
$C_{12}\times D_{38}$ 6A1 $6$ $1$ $C_{12}\times D_{38}$ 3A-1 2A 6A1 $b^{2}c^{76}$
$C_{12}\times D_{38}$ 6A-1 $6$ $1$ $C_{12}\times D_{38}$ 3A1 2A 6A-1 $b^{2}c^{38}$
$C_{12}\times D_{38}$ 6B1 $6$ $1$ $C_{12}\times D_{38}$ 3A-1 2B 6B1 $c^{19}$
$C_{12}\times D_{38}$ 6B-1 $6$ $1$ $C_{12}\times D_{38}$ 3A1 2B 6B-1 $c^{95}$
$C_{12}\times D_{38}$ 6C1 $6$ $1$ $C_{12}\times D_{38}$ 3A-1 2C 6C1 $b^{2}c^{19}$
$C_{12}\times D_{38}$ 6C-1 $6$ $1$ $C_{12}\times D_{38}$ 3A1 2C 6C-1 $b^{2}c^{95}$
$C_{12}\times D_{38}$ 6D1 $6$ $19$ $C_2^2\times C_{12}$ 3A1 2D 6D1 $ac^{2}$
$C_{12}\times D_{38}$ 6D-1 $6$ $19$ $C_2^2\times C_{12}$ 3A-1 2D 6D-1 $ac^{4}$
$C_{12}\times D_{38}$ 6E1 $6$ $19$ $C_2^2\times C_{12}$ 3A-1 2E 6E1 $ac$
$C_{12}\times D_{38}$ 6E-1 $6$ $19$ $C_2^2\times C_{12}$ 3A1 2E 6E-1 $ac^{5}$
$C_{12}\times D_{38}$ 6F1 $6$ $19$ $C_2^2\times C_{12}$ 3A1 2F 6F1 $ab^{2}c^{2}$
$C_{12}\times D_{38}$ 6F-1 $6$ $19$ $C_2^2\times C_{12}$ 3A-1 2F 6F-1 $ab^{2}c^{4}$
$C_{12}\times D_{38}$ 6G1 $6$ $19$ $C_2^2\times C_{12}$ 3A-1 2G 6G1 $ab^{2}c$
$C_{12}\times D_{38}$ 6G-1 $6$ $19$ $C_2^2\times C_{12}$ 3A1 2G 6G-1 $ab^{2}c^{5}$
$C_{12}\times D_{38}$ 12A1 $12$ $1$ $C_{12}\times D_{38}$ 6A1 4A1 12A-5 $b^{3}c^{38}$
$C_{12}\times D_{38}$ 12A-1 $12$ $1$ $C_{12}\times D_{38}$ 6A-1 4A-1 12A5 $bc^{76}$
$C_{12}\times D_{38}$ 12A5 $12$ $1$ $C_{12}\times D_{38}$ 6A-1 4A1 12A-1 $b^{3}c^{76}$
$C_{12}\times D_{38}$ 12A-5 $12$ $1$ $C_{12}\times D_{38}$ 6A1 4A-1 12A1 $bc^{38}$
$C_{12}\times D_{38}$ 12B1 $12$ $1$ $C_{12}\times D_{38}$ 6A-1 4B1 12B-5 $b^{3}c^{19}$
$C_{12}\times D_{38}$ 12B-1 $12$ $1$ $C_{12}\times D_{38}$ 6A1 4B-1 12B5 $bc^{95}$
$C_{12}\times D_{38}$ 12B5 $12$ $1$ $C_{12}\times D_{38}$ 6A1 4B1 12B-1 $b^{3}c^{95}$
$C_{12}\times D_{38}$ 12B-5 $12$ $1$ $C_{12}\times D_{38}$ 6A-1 4B-1 12B1 $bc^{19}$
$C_{12}\times D_{38}$ 12C1 $12$ $19$ $C_2^2\times C_{12}$ 6A1 4C1 12C-5 $abc^{2}$
$C_{12}\times D_{38}$ 12C-1 $12$ $19$ $C_2^2\times C_{12}$ 6A-1 4C-1 12C5 $ab^{3}c^{4}$
$C_{12}\times D_{38}$ 12C5 $12$ $19$ $C_2^2\times C_{12}$ 6A-1 4C1 12C-1 $abc^{4}$
$C_{12}\times D_{38}$ 12C-5 $12$ $19$ $C_2^2\times C_{12}$ 6A1 4C-1 12C1 $ab^{3}c^{2}$
$C_{12}\times D_{38}$ 12D1 $12$ $19$ $C_2^2\times C_{12}$ 6A-1 4D1 12D-5 $abc$
$C_{12}\times D_{38}$ 12D-1 $12$ $19$ $C_2^2\times C_{12}$ 6A1 4D-1 12D5 $ab^{3}c^{5}$
$C_{12}\times D_{38}$ 12D5 $12$ $19$ $C_2^2\times C_{12}$ 6A1 4D1 12D-1 $abc^{5}$
$C_{12}\times D_{38}$ 12D-5 $12$ $19$ $C_2^2\times C_{12}$ 6A-1 4D-1 12D1 $ab^{3}c$
$C_{12}\times D_{38}$ 19A1 $19$ $2$ $C_2\times C_{228}$ 19A2 19A3 1A $c^{6}$
$C_{12}\times D_{38}$ 19A2 $19$ $2$ $C_2\times C_{228}$ 19A4 19A6 1A $c^{12}$
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