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Elements of the group are displayed as words in the presentation $\langle a, b, c \mid a^{6}=b^{4}=c^{4}=[a,b]=1, c^{a}=b^{2}c, c^{b}=c^{3} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 3P
$(C_2^2\times C_{12}):C_2$ 1A $1$ $1$ $(C_2^2\times C_{12}):C_2$ 1A 1A $1$
$(C_2^2\times C_{12}):C_2$ 2A $2$ $1$ $(C_2^2\times C_{12}):C_2$ 1A 2A $b^{2}$
$(C_2^2\times C_{12}):C_2$ 2B $2$ $1$ $(C_2^2\times C_{12}):C_2$ 1A 2B $c^{2}$
$(C_2^2\times C_{12}):C_2$ 2C $2$ $1$ $(C_2^2\times C_{12}):C_2$ 1A 2C $b^{2}c^{2}$
$(C_2^2\times C_{12}):C_2$ 2D $2$ $2$ $C_2^2\times C_{12}$ 1A 2D $a^{3}$
$(C_2^2\times C_{12}):C_2$ 2E $2$ $2$ $C_2^2\times C_{12}$ 1A 2E $a^{3}c^{2}$
$(C_2^2\times C_{12}):C_2$ 2F $2$ $4$ $C_2^2\times C_6$ 1A 2F $a^{3}bc$
$(C_2^2\times C_{12}):C_2$ 3A1 $3$ $1$ $(C_2^2\times C_{12}):C_2$ 3A-1 1A $a^{2}$
$(C_2^2\times C_{12}):C_2$ 3A-1 $3$ $1$ $(C_2^2\times C_{12}):C_2$ 3A1 1A $a^{4}$
$(C_2^2\times C_{12}):C_2$ 4A1 $4$ $2$ $C_2^2\times C_{12}$ 2A 4A-1 $b^{3}$
$(C_2^2\times C_{12}):C_2$ 4A-1 $4$ $2$ $C_2^2\times C_{12}$ 2A 4A1 $b$
$(C_2^2\times C_{12}):C_2$ 4B1 $4$ $2$ $C_2^2\times C_{12}$ 2A 4B-1 $a^{3}b^{3}$
$(C_2^2\times C_{12}):C_2$ 4B-1 $4$ $2$ $C_2^2\times C_{12}$ 2A 4B1 $a^{3}b$
$(C_2^2\times C_{12}):C_2$ 4C $4$ $4$ $C_2\times C_{12}$ 2B 4C $c^{3}$
$(C_2^2\times C_{12}):C_2$ 4D $4$ $4$ $C_2\times C_{12}$ 2C 4D $a^{3}b^{2}c^{3}$
$(C_2^2\times C_{12}):C_2$ 4E $4$ $4$ $C_2\times C_{12}$ 2A 4E $b^{3}c$
$(C_2^2\times C_{12}):C_2$ 6A1 $6$ $1$ $(C_2^2\times C_{12}):C_2$ 3A1 2A $a^{4}b^{2}$
$(C_2^2\times C_{12}):C_2$ 6A-1 $6$ $1$ $(C_2^2\times C_{12}):C_2$ 3A-1 2A $a^{2}b^{2}$
$(C_2^2\times C_{12}):C_2$ 6B1 $6$ $1$ $(C_2^2\times C_{12}):C_2$ 3A1 2B $a^{4}c^{2}$
$(C_2^2\times C_{12}):C_2$ 6B-1 $6$ $1$ $(C_2^2\times C_{12}):C_2$ 3A-1 2B $a^{2}c^{2}$
$(C_2^2\times C_{12}):C_2$ 6C1 $6$ $1$ $(C_2^2\times C_{12}):C_2$ 3A-1 2C $a^{2}b^{2}c^{2}$
$(C_2^2\times C_{12}):C_2$ 6C-1 $6$ $1$ $(C_2^2\times C_{12}):C_2$ 3A1 2C $a^{4}b^{2}c^{2}$
$(C_2^2\times C_{12}):C_2$ 6D1 $6$ $2$ $C_2^2\times C_{12}$ 3A1 2D $a$
$(C_2^2\times C_{12}):C_2$ 6D-1 $6$ $2$ $C_2^2\times C_{12}$ 3A-1 2D $a^{5}$
$(C_2^2\times C_{12}):C_2$ 6E1 $6$ $2$ $C_2^2\times C_{12}$ 3A1 2E $ac^{2}$
$(C_2^2\times C_{12}):C_2$ 6E-1 $6$ $2$ $C_2^2\times C_{12}$ 3A-1 2E $a^{5}c^{2}$
$(C_2^2\times C_{12}):C_2$ 6F1 $6$ $4$ $C_2^2\times C_6$ 3A1 2F $abc$
$(C_2^2\times C_{12}):C_2$ 6F-1 $6$ $4$ $C_2^2\times C_6$ 3A-1 2F $a^{5}bc$
$(C_2^2\times C_{12}):C_2$ 12A1 $12$ $2$ $C_2^2\times C_{12}$ 6A1 4A1 $a^{2}b$
$(C_2^2\times C_{12}):C_2$ 12A-1 $12$ $2$ $C_2^2\times C_{12}$ 6A-1 4A-1 $a^{4}b^{3}$
$(C_2^2\times C_{12}):C_2$ 12A5 $12$ $2$ $C_2^2\times C_{12}$ 6A-1 4A1 $a^{4}b$
$(C_2^2\times C_{12}):C_2$ 12A-5 $12$ $2$ $C_2^2\times C_{12}$ 6A1 4A-1 $a^{2}b^{3}$
$(C_2^2\times C_{12}):C_2$ 12B1 $12$ $2$ $C_2^2\times C_{12}$ 6A-1 4B1 $ab$
$(C_2^2\times C_{12}):C_2$ 12B-1 $12$ $2$ $C_2^2\times C_{12}$ 6A1 4B-1 $a^{5}bc^{2}$
$(C_2^2\times C_{12}):C_2$ 12B5 $12$ $2$ $C_2^2\times C_{12}$ 6A1 4B1 $a^{5}b$
$(C_2^2\times C_{12}):C_2$ 12B-5 $12$ $2$ $C_2^2\times C_{12}$ 6A-1 4B-1 $abc^{2}$
$(C_2^2\times C_{12}):C_2$ 12C1 $12$ $4$ $C_2\times C_{12}$ 6B1 4C $a^{2}c$
$(C_2^2\times C_{12}):C_2$ 12C-1 $12$ $4$ $C_2\times C_{12}$ 6B-1 4C $a^{4}c$
$(C_2^2\times C_{12}):C_2$ 12D1 $12$ $4$ $C_2\times C_{12}$ 6C1 4D $ac$
$(C_2^2\times C_{12}):C_2$ 12D-1 $12$ $4$ $C_2\times C_{12}$ 6C-1 4D $a^{5}c$
$(C_2^2\times C_{12}):C_2$ 12E1 $12$ $4$ $C_2\times C_{12}$ 6A1 4E $a^{2}bc$
$(C_2^2\times C_{12}):C_2$ 12E-1 $12$ $4$ $C_2\times C_{12}$ 6A-1 4E $a^{4}bc$
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