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Elements of the group are displayed as words in the presentation $\langle a, b, c \mid a^{4}=b^{4}=c^{30}=[a,b]=[b,c]=1, c^{a}=b^{2}c^{19} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 3P 5P
$(C_2\times C_{20}):C_{12}$ 1A $1$ $1$ $(C_2\times C_{20}):C_{12}$ 1A 1A 1A $1$
$(C_2\times C_{20}):C_{12}$ 2A $2$ $1$ $(C_2\times C_{20}):C_{12}$ 1A 2A 2A $a^{2}$
$(C_2\times C_{20}):C_{12}$ 2B $2$ $1$ $(C_2\times C_{20}):C_{12}$ 1A 2B 2B $a^{2}b^{2}$
$(C_2\times C_{20}):C_{12}$ 2C $2$ $1$ $(C_2\times C_{20}):C_{12}$ 1A 2C 2C $b^{2}$
$(C_2\times C_{20}):C_{12}$ 2D $2$ $2$ $C_2^2\times C_{60}$ 1A 2D 2D $c^{15}$
$(C_2\times C_{20}):C_{12}$ 2E $2$ $2$ $C_2^2\times C_{60}$ 1A 2E 2E $a^{2}c^{15}$
$(C_2\times C_{20}):C_{12}$ 3A1 $3$ $1$ $(C_2\times C_{20}):C_{12}$ 3A-1 1A 3A-1 $c^{20}$
$(C_2\times C_{20}):C_{12}$ 3A-1 $3$ $1$ $(C_2\times C_{20}):C_{12}$ 3A1 1A 3A1 $c^{10}$
$(C_2\times C_{20}):C_{12}$ 4A1 $4$ $1$ $(C_2\times C_{20}):C_{12}$ 2C 4A-1 4A1 $b^{3}$
$(C_2\times C_{20}):C_{12}$ 4A-1 $4$ $1$ $(C_2\times C_{20}):C_{12}$ 2C 4A1 4A-1 $b$
$(C_2\times C_{20}):C_{12}$ 4B1 $4$ $1$ $(C_2\times C_{20}):C_{12}$ 2C 4B-1 4B1 $a^{2}b^{3}$
$(C_2\times C_{20}):C_{12}$ 4B-1 $4$ $1$ $(C_2\times C_{20}):C_{12}$ 2C 4B1 4B-1 $a^{2}b$
$(C_2\times C_{20}):C_{12}$ 4C $4$ $2$ $C_2^2\times C_{60}$ 2C 4C 4C $b^{3}c^{15}$
$(C_2\times C_{20}):C_{12}$ 4D $4$ $2$ $C_2^2\times C_{60}$ 2C 4D 4D $a^{2}b^{3}c^{15}$
$(C_2\times C_{20}):C_{12}$ 4E1 $4$ $10$ $C_4\times C_{12}$ 2A 4E-1 4E1 $a^{3}c^{12}$
$(C_2\times C_{20}):C_{12}$ 4E-1 $4$ $10$ $C_4\times C_{12}$ 2A 4E1 4E-1 $ac^{12}$
$(C_2\times C_{20}):C_{12}$ 4F1 $4$ $10$ $C_4\times C_{12}$ 2B 4F-1 4F1 $a^{3}b^{2}c^{21}$
$(C_2\times C_{20}):C_{12}$ 4F-1 $4$ $10$ $C_4\times C_{12}$ 2B 4F1 4F-1 $ac^{21}$
$(C_2\times C_{20}):C_{12}$ 4G1 $4$ $10$ $C_4\times C_{12}$ 2B 4G-1 4G1 $a^{3}b^{3}c^{12}$
$(C_2\times C_{20}):C_{12}$ 4G-1 $4$ $10$ $C_4\times C_{12}$ 2B 4G1 4G-1 $abc^{12}$
$(C_2\times C_{20}):C_{12}$ 4H1 $4$ $10$ $C_4\times C_{12}$ 2A 4H-1 4H1 $a^{3}bc^{21}$
$(C_2\times C_{20}):C_{12}$ 4H-1 $4$ $10$ $C_4\times C_{12}$ 2A 4H1 4H-1 $abc^{21}$
$(C_2\times C_{20}):C_{12}$ 5A1 $5$ $2$ $C_2^2\times C_{60}$ 5A2 5A2 1A $c^{12}$
$(C_2\times C_{20}):C_{12}$ 5A2 $5$ $2$ $C_2^2\times C_{60}$ 5A1 5A1 1A $c^{24}$
$(C_2\times C_{20}):C_{12}$ 6A1 $6$ $1$ $(C_2\times C_{20}):C_{12}$ 3A1 2A 6A-1 $a^{2}c^{10}$
$(C_2\times C_{20}):C_{12}$ 6A-1 $6$ $1$ $(C_2\times C_{20}):C_{12}$ 3A-1 2A 6A1 $a^{2}c^{20}$
$(C_2\times C_{20}):C_{12}$ 6B1 $6$ $1$ $(C_2\times C_{20}):C_{12}$ 3A-1 2B 6B-1 $a^{2}b^{2}c^{20}$
$(C_2\times C_{20}):C_{12}$ 6B-1 $6$ $1$ $(C_2\times C_{20}):C_{12}$ 3A1 2B 6B1 $a^{2}b^{2}c^{10}$
$(C_2\times C_{20}):C_{12}$ 6C1 $6$ $1$ $(C_2\times C_{20}):C_{12}$ 3A-1 2C 6C-1 $b^{2}c^{20}$
$(C_2\times C_{20}):C_{12}$ 6C-1 $6$ $1$ $(C_2\times C_{20}):C_{12}$ 3A1 2C 6C1 $b^{2}c^{10}$
$(C_2\times C_{20}):C_{12}$ 6D1 $6$ $2$ $C_2^2\times C_{60}$ 3A-1 2D 6D-1 $c^{5}$
$(C_2\times C_{20}):C_{12}$ 6D-1 $6$ $2$ $C_2^2\times C_{60}$ 3A1 2D 6D1 $c^{25}$
$(C_2\times C_{20}):C_{12}$ 6E1 $6$ $2$ $C_2^2\times C_{60}$ 3A-1 2E 6E-1 $a^{2}c^{5}$
$(C_2\times C_{20}):C_{12}$ 6E-1 $6$ $2$ $C_2^2\times C_{60}$ 3A1 2E 6E1 $a^{2}c^{25}$
$(C_2\times C_{20}):C_{12}$ 10A1 $10$ $2$ $C_2^2\times C_{60}$ 5A1 10A3 2A $a^{2}c^{6}$
$(C_2\times C_{20}):C_{12}$ 10A3 $10$ $2$ $C_2^2\times C_{60}$ 5A2 10A1 2A $a^{2}c^{18}$
$(C_2\times C_{20}):C_{12}$ 10B1 $10$ $2$ $C_2^2\times C_{60}$ 5A1 10B3 2B $a^{2}b^{2}c^{6}$
$(C_2\times C_{20}):C_{12}$ 10B3 $10$ $2$ $C_2^2\times C_{60}$ 5A2 10B1 2B $a^{2}b^{2}c^{18}$
$(C_2\times C_{20}):C_{12}$ 10C1 $10$ $2$ $C_2^2\times C_{60}$ 5A2 10C3 2C $b^{2}c^{12}$
$(C_2\times C_{20}):C_{12}$ 10C3 $10$ $2$ $C_2^2\times C_{60}$ 5A1 10C1 2C $b^{2}c^{6}$
$(C_2\times C_{20}):C_{12}$ 10D1 $10$ $2$ $C_2^2\times C_{60}$ 5A2 10D3 2D $c^{3}$
$(C_2\times C_{20}):C_{12}$ 10D-1 $10$ $2$ $C_2^2\times C_{60}$ 5A2 10D-3 2D $c^{27}$
$(C_2\times C_{20}):C_{12}$ 10D3 $10$ $2$ $C_2^2\times C_{60}$ 5A1 10D-1 2D $c^{9}$
$(C_2\times C_{20}):C_{12}$ 10D-3 $10$ $2$ $C_2^2\times C_{60}$ 5A1 10D1 2D $c^{21}$
$(C_2\times C_{20}):C_{12}$ 10E1 $10$ $2$ $C_2^2\times C_{60}$ 5A2 10E3 2E $a^{2}c^{3}$
$(C_2\times C_{20}):C_{12}$ 10E-1 $10$ $2$ $C_2^2\times C_{60}$ 5A2 10E-3 2E $a^{2}c^{27}$
$(C_2\times C_{20}):C_{12}$ 10E3 $10$ $2$ $C_2^2\times C_{60}$ 5A1 10E-1 2E $a^{2}c^{9}$
$(C_2\times C_{20}):C_{12}$ 10E-3 $10$ $2$ $C_2^2\times C_{60}$ 5A1 10E1 2E $a^{2}c^{21}$
$(C_2\times C_{20}):C_{12}$ 12A1 $12$ $1$ $(C_2\times C_{20}):C_{12}$ 6C1 4A1 12A5 $bc^{10}$
$(C_2\times C_{20}):C_{12}$ 12A-1 $12$ $1$ $(C_2\times C_{20}):C_{12}$ 6C-1 4A-1 12A-5 $b^{3}c^{20}$
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