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Elements of the group are displayed as words in the presentation $\langle a, b, c \mid a^{2}=b^{12}=c^{38}=[a,c]=1, b^{a}=b^{7}, c^{b}=c^{27} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 3P 19P
$C_2\times D_{38}:C_6$ 1A $1$ $1$ $C_2\times D_{38}:C_6$ 1A 1A 1A $1$
$C_2\times D_{38}:C_6$ 2A $2$ $1$ $C_2\times D_{38}:C_6$ 1A 2A 2A $c^{19}$
$C_2\times D_{38}:C_6$ 2B $2$ $1$ $C_2\times D_{38}:C_6$ 1A 2B 2B $b^{6}c^{19}$
$C_2\times D_{38}:C_6$ 2C $2$ $1$ $C_2\times D_{38}:C_6$ 1A 2C 2C $b^{6}$
$C_2\times D_{38}:C_6$ 2D $2$ $2$ $C_2\times C_{38}:C_6$ 1A 2D 2D $a$
$C_2\times D_{38}:C_6$ 2E $2$ $2$ $C_2\times C_{38}:C_6$ 1A 2E 2E $ac^{19}$
$C_2\times D_{38}:C_6$ 2F $2$ $38$ $C_2^2\times C_6$ 1A 2F 2F $ab^{9}c^{30}$
$C_2\times D_{38}:C_6$ 2G $2$ $38$ $C_2^2\times C_6$ 1A 2G 2G $ab^{3}c^{3}$
$C_2\times D_{38}:C_6$ 3A1 $3$ $19$ $C_6\times D_4$ 3A-1 1A 3A1 $b^{8}c^{12}$
$C_2\times D_{38}:C_6$ 3A-1 $3$ $19$ $C_6\times D_4$ 3A1 1A 3A-1 $b^{4}c^{20}$
$C_2\times D_{38}:C_6$ 4A $4$ $38$ $C_2\times C_{12}$ 2C 4A 4A $b^{3}c^{28}$
$C_2\times D_{38}:C_6$ 4B $4$ $38$ $C_2\times C_{12}$ 2C 4B 4B $b^{9}c^{5}$
$C_2\times D_{38}:C_6$ 6A1 $6$ $19$ $C_6\times D_4$ 3A1 2A 6A1 $b^{4}c$
$C_2\times D_{38}:C_6$ 6A-1 $6$ $19$ $C_6\times D_4$ 3A-1 2A 6A-1 $b^{8}c$
$C_2\times D_{38}:C_6$ 6B1 $6$ $19$ $C_6\times D_4$ 3A-1 2B 6B1 $b^{2}c$
$C_2\times D_{38}:C_6$ 6B-1 $6$ $19$ $C_6\times D_4$ 3A1 2B 6B-1 $b^{10}c$
$C_2\times D_{38}:C_6$ 6C1 $6$ $19$ $C_6\times D_4$ 3A-1 2C 6C1 $b^{2}c^{30}$
$C_2\times D_{38}:C_6$ 6C-1 $6$ $19$ $C_6\times D_4$ 3A1 2C 6C-1 $b^{10}c^{12}$
$C_2\times D_{38}:C_6$ 6D1 $6$ $38$ $C_2^2\times C_6$ 3A1 2F 6D1 $abc^{28}$
$C_2\times D_{38}:C_6$ 6D-1 $6$ $38$ $C_2^2\times C_6$ 3A-1 2F 6D-1 $ab^{5}c^{6}$
$C_2\times D_{38}:C_6$ 6E1 $6$ $38$ $C_2^2\times C_6$ 3A-1 2D 6E1 $ab^{8}c^{18}$
$C_2\times D_{38}:C_6$ 6E-1 $6$ $38$ $C_2^2\times C_6$ 3A1 2D 6E-1 $ab^{4}c^{30}$
$C_2\times D_{38}:C_6$ 6F1 $6$ $38$ $C_2^2\times C_6$ 3A-1 2E 6F1 $ab^{8}c^{15}$
$C_2\times D_{38}:C_6$ 6F-1 $6$ $38$ $C_2^2\times C_6$ 3A1 2E 6F-1 $ab^{4}c^{25}$
$C_2\times D_{38}:C_6$ 6G1 $6$ $38$ $C_2^2\times C_6$ 3A1 2G 6G1 $ab^{7}c^{37}$
$C_2\times D_{38}:C_6$ 6G-1 $6$ $38$ $C_2^2\times C_6$ 3A-1 2G 6G-1 $ab^{11}c^{31}$
$C_2\times D_{38}:C_6$ 12A1 $12$ $38$ $C_2\times C_{12}$ 6C1 4A 12A1 $bc^{16}$
$C_2\times D_{38}:C_6$ 12A-1 $12$ $38$ $C_2\times C_{12}$ 6C-1 4A 12A-1 $b^{11}c^{36}$
$C_2\times D_{38}:C_6$ 12B1 $12$ $38$ $C_2\times C_{12}$ 6C-1 4B 12B1 $b^{11}c$
$C_2\times D_{38}:C_6$ 12B-1 $12$ $38$ $C_2\times C_{12}$ 6C1 4B 12B-1 $bc^{11}$
$C_2\times D_{38}:C_6$ 19A1 $19$ $6$ $C_2^2\times C_{38}$ 19A2 19A2 1A $c^{2}$
$C_2\times D_{38}:C_6$ 19A2 $19$ $6$ $C_2^2\times C_{38}$ 19A4 19A4 1A $c^{4}$
$C_2\times D_{38}:C_6$ 19A4 $19$ $6$ $C_2^2\times C_{38}$ 19A1 19A1 1A $c^{8}$
$C_2\times D_{38}:C_6$ 38A1 $38$ $6$ $C_2^2\times C_{38}$ 19A1 38A3 2A $c$
$C_2\times D_{38}:C_6$ 38A3 $38$ $6$ $C_2^2\times C_{38}$ 19A2 38A9 2A $c^{3}$
$C_2\times D_{38}:C_6$ 38A9 $38$ $6$ $C_2^2\times C_{38}$ 19A4 38A1 2A $c^{9}$
$C_2\times D_{38}:C_6$ 38B1 $38$ $6$ $C_2^2\times C_{38}$ 19A2 38B3 2C $b^{6}c^{2}$
$C_2\times D_{38}:C_6$ 38B3 $38$ $6$ $C_2^2\times C_{38}$ 19A4 38B9 2C $b^{6}c^{4}$
$C_2\times D_{38}:C_6$ 38B9 $38$ $6$ $C_2^2\times C_{38}$ 19A1 38B1 2C $b^{6}c^{8}$
$C_2\times D_{38}:C_6$ 38C1 $38$ $6$ $C_2^2\times C_{38}$ 19A1 38C3 2B $b^{6}c$
$C_2\times D_{38}:C_6$ 38C3 $38$ $6$ $C_2^2\times C_{38}$ 19A2 38C9 2B $b^{6}c^{3}$
$C_2\times D_{38}:C_6$ 38C9 $38$ $6$ $C_2^2\times C_{38}$ 19A4 38C1 2B $b^{6}c^{9}$
$C_2\times D_{38}:C_6$ 38D1 $38$ $6$ $C_2^2\times C_{38}$ 19A2 38D3 2D $ac^{2}$
$C_2\times D_{38}:C_6$ 38D-1 $38$ $6$ $C_2^2\times C_{38}$ 19A2 38D-3 2D $ac^{16}$
$C_2\times D_{38}:C_6$ 38D3 $38$ $6$ $C_2^2\times C_{38}$ 19A4 38D9 2D $ac^{4}$
$C_2\times D_{38}:C_6$ 38D-3 $38$ $6$ $C_2^2\times C_{38}$ 19A4 38D-9 2D $ac^{10}$
$C_2\times D_{38}:C_6$ 38D9 $38$ $6$ $C_2^2\times C_{38}$ 19A1 38D-1 2D $ac^{8}$
$C_2\times D_{38}:C_6$ 38D-9 $38$ $6$ $C_2^2\times C_{38}$ 19A1 38D1 2D $ac^{20}$
$C_2\times D_{38}:C_6$ 38E1 $38$ $6$ $C_2^2\times C_{38}$ 19A1 38E3 2E $ac$
$C_2\times D_{38}:C_6$ 38E-1 $38$ $6$ $C_2^2\times C_{38}$ 19A1 38E-3 2E $ac^{27}$
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