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Elements of the group are displayed as words in the presentation of the abelian group $\langle a, b \mid a^{6}=b^{192}=1 \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 3P
$C_6\times C_{192}$ 1A $1$ $1$ $C_6\times C_{192}$ 1A 1A $1$
$C_6\times C_{192}$ 2A $2$ $1$ $C_6\times C_{192}$ 1A 2A $a^{3}$
$C_6\times C_{192}$ 2B $2$ $1$ $C_6\times C_{192}$ 1A 2B $a^{3}b^{96}$
$C_6\times C_{192}$ 2C $2$ $1$ $C_6\times C_{192}$ 1A 2C $b^{96}$
$C_6\times C_{192}$ 3A1 $3$ $1$ $C_6\times C_{192}$ 3A-1 1A $a^{2}$
$C_6\times C_{192}$ 3A-1 $3$ $1$ $C_6\times C_{192}$ 3A1 1A $a^{4}$
$C_6\times C_{192}$ 3B1 $3$ $1$ $C_6\times C_{192}$ 3B-1 1A $a^{2}b^{128}$
$C_6\times C_{192}$ 3B-1 $3$ $1$ $C_6\times C_{192}$ 3B1 1A $a^{4}b^{64}$
$C_6\times C_{192}$ 3C1 $3$ $1$ $C_6\times C_{192}$ 3C-1 1A $a^{2}b^{64}$
$C_6\times C_{192}$ 3C-1 $3$ $1$ $C_6\times C_{192}$ 3C1 1A $a^{4}b^{128}$
$C_6\times C_{192}$ 3D1 $3$ $1$ $C_6\times C_{192}$ 3D-1 1A $b^{128}$
$C_6\times C_{192}$ 3D-1 $3$ $1$ $C_6\times C_{192}$ 3D1 1A $b^{64}$
$C_6\times C_{192}$ 4A1 $4$ $1$ $C_6\times C_{192}$ 2C 4A-1 $a^{3}b^{48}$
$C_6\times C_{192}$ 4A-1 $4$ $1$ $C_6\times C_{192}$ 2C 4A1 $a^{3}b^{144}$
$C_6\times C_{192}$ 4B1 $4$ $1$ $C_6\times C_{192}$ 2C 4B-1 $b^{48}$
$C_6\times C_{192}$ 4B-1 $4$ $1$ $C_6\times C_{192}$ 2C 4B1 $b^{144}$
$C_6\times C_{192}$ 6A1 $6$ $1$ $C_6\times C_{192}$ 3A1 2A $a$
$C_6\times C_{192}$ 6A-1 $6$ $1$ $C_6\times C_{192}$ 3A-1 2A $a^{5}$
$C_6\times C_{192}$ 6B1 $6$ $1$ $C_6\times C_{192}$ 3B1 2A $ab^{64}$
$C_6\times C_{192}$ 6B-1 $6$ $1$ $C_6\times C_{192}$ 3B-1 2A $a^{5}b^{128}$
$C_6\times C_{192}$ 6C1 $6$ $1$ $C_6\times C_{192}$ 3C1 2B $ab^{32}$
$C_6\times C_{192}$ 6C-1 $6$ $1$ $C_6\times C_{192}$ 3C-1 2B $a^{5}b^{160}$
$C_6\times C_{192}$ 6D1 $6$ $1$ $C_6\times C_{192}$ 3C1 2A $ab^{128}$
$C_6\times C_{192}$ 6D-1 $6$ $1$ $C_6\times C_{192}$ 3C-1 2A $a^{5}b^{64}$
$C_6\times C_{192}$ 6E1 $6$ $1$ $C_6\times C_{192}$ 3A1 2B $ab^{96}$
$C_6\times C_{192}$ 6E-1 $6$ $1$ $C_6\times C_{192}$ 3A-1 2B $a^{5}b^{96}$
$C_6\times C_{192}$ 6F1 $6$ $1$ $C_6\times C_{192}$ 3D1 2A $a^{3}b^{64}$
$C_6\times C_{192}$ 6F-1 $6$ $1$ $C_6\times C_{192}$ 3D-1 2A $a^{3}b^{128}$
$C_6\times C_{192}$ 6G1 $6$ $1$ $C_6\times C_{192}$ 3D-1 2B $a^{3}b^{32}$
$C_6\times C_{192}$ 6G-1 $6$ $1$ $C_6\times C_{192}$ 3D1 2B $a^{3}b^{160}$
$C_6\times C_{192}$ 6H1 $6$ $1$ $C_6\times C_{192}$ 3B1 2B $ab^{160}$
$C_6\times C_{192}$ 6H-1 $6$ $1$ $C_6\times C_{192}$ 3B-1 2B $a^{5}b^{32}$
$C_6\times C_{192}$ 6I1 $6$ $1$ $C_6\times C_{192}$ 3B-1 2C $a^{2}b^{32}$
$C_6\times C_{192}$ 6I-1 $6$ $1$ $C_6\times C_{192}$ 3B1 2C $a^{4}b^{160}$
$C_6\times C_{192}$ 6J1 $6$ $1$ $C_6\times C_{192}$ 3C-1 2C $a^{2}b^{160}$
$C_6\times C_{192}$ 6J-1 $6$ $1$ $C_6\times C_{192}$ 3C1 2C $a^{4}b^{32}$
$C_6\times C_{192}$ 6K1 $6$ $1$ $C_6\times C_{192}$ 3A-1 2C $a^{2}b^{96}$
$C_6\times C_{192}$ 6K-1 $6$ $1$ $C_6\times C_{192}$ 3A1 2C $a^{4}b^{96}$
$C_6\times C_{192}$ 6L1 $6$ $1$ $C_6\times C_{192}$ 3D-1 2C $b^{32}$
$C_6\times C_{192}$ 6L-1 $6$ $1$ $C_6\times C_{192}$ 3D1 2C $b^{160}$
$C_6\times C_{192}$ 8A1 $8$ $1$ $C_6\times C_{192}$ 4B1 8A3 $a^{3}b^{24}$
$C_6\times C_{192}$ 8A-1 $8$ $1$ $C_6\times C_{192}$ 4B-1 8A-3 $a^{3}b^{168}$
$C_6\times C_{192}$ 8A3 $8$ $1$ $C_6\times C_{192}$ 4B-1 8A1 $a^{3}b^{72}$
$C_6\times C_{192}$ 8A-3 $8$ $1$ $C_6\times C_{192}$ 4B1 8A-1 $a^{3}b^{120}$
$C_6\times C_{192}$ 8B1 $8$ $1$ $C_6\times C_{192}$ 4B1 8B3 $b^{24}$
$C_6\times C_{192}$ 8B-1 $8$ $1$ $C_6\times C_{192}$ 4B-1 8B-3 $b^{168}$
$C_6\times C_{192}$ 8B3 $8$ $1$ $C_6\times C_{192}$ 4B-1 8B1 $b^{72}$
$C_6\times C_{192}$ 8B-3 $8$ $1$ $C_6\times C_{192}$ 4B1 8B-1 $b^{120}$
$C_6\times C_{192}$ 12A1 $12$ $1$ $C_6\times C_{192}$ 6I1 4A1 $ab^{16}$
$C_6\times C_{192}$ 12A-1 $12$ $1$ $C_6\times C_{192}$ 6I-1 4A-1 $a^{5}b^{176}$
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