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Elements of the group are displayed as words in the presentation $\langle a, b, c \mid b^{24}=c^{36}=1, a^{2}=b^{12}c^{18}, b^{a}=b^{17}, c^{a}=b^{12}c^{19}, c^{b}=c^{35} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 3P
$C_{12}^2.D_6$ 1A $1$ $1$ $C_{12}^2.D_6$ 1A 1A $1$
$C_{12}^2.D_6$ 2A $2$ $1$ $C_{12}^2.D_6$ 1A 2A $b^{12}$
$C_{12}^2.D_6$ 2B $2$ $1$ $C_{12}^2.D_6$ 1A 2B $c^{18}$
$C_{12}^2.D_6$ 2C $2$ $1$ $C_{12}^2.D_6$ 1A 2C $b^{12}c^{18}$
$C_{12}^2.D_6$ 3A $3$ $2$ $C_{36}:C_{24}$ 3A 1A $b^{8}$
$C_{12}^2.D_6$ 3B $3$ $2$ $C_{12}^2.C_6$ 3B 1A $c^{12}$
$C_{12}^2.D_6$ 3C $3$ $4$ $C_{12}\times C_{36}$ 3C 1A $b^{8}c^{12}$
$C_{12}^2.D_6$ 4A1 $4$ $1$ $C_{12}^2.D_6$ 2A 4A-1 $b^{6}c^{18}$
$C_{12}^2.D_6$ 4A-1 $4$ $1$ $C_{12}^2.D_6$ 2A 4A1 $b^{18}c^{18}$
$C_{12}^2.D_6$ 4B1 $4$ $1$ $C_{12}^2.D_6$ 2A 4B-1 $b^{6}$
$C_{12}^2.D_6$ 4B-1 $4$ $1$ $C_{12}^2.D_6$ 2A 4B1 $b^{18}$
$C_{12}^2.D_6$ 4C $4$ $4$ $C_{12}\times C_{36}$ 2B 4C $c^{27}$
$C_{12}^2.D_6$ 4D $4$ $4$ $C_{12}\times C_{36}$ 2C 4D $b^{6}c^{27}$
$C_{12}^2.D_6$ 4E $4$ $6$ $C_{36}:C_8$ 2C 4E $a$
$C_{12}^2.D_6$ 4F $4$ $6$ $C_{36}:C_8$ 2C 4F $ac^{18}$
$C_{12}^2.D_6$ 4G1 $4$ $6$ $C_{36}:C_8$ 2B 4G-1 $ab^{2}$
$C_{12}^2.D_6$ 4G-1 $4$ $6$ $C_{36}:C_8$ 2B 4G1 $ab^{2}c^{18}$
$C_{12}^2.D_6$ 4H $4$ $12$ $C_4\times C_{36}$ 2B 4H $ac^{9}$
$C_{12}^2.D_6$ 4I $4$ $12$ $C_4\times C_{36}$ 2C 4I $ab^{2}c^{9}$
$C_{12}^2.D_6$ 6A $6$ $2$ $C_{36}:C_{24}$ 3A 2A $b^{4}$
$C_{12}^2.D_6$ 6B $6$ $2$ $C_{36}:C_{24}$ 3A 2B $b^{16}c^{18}$
$C_{12}^2.D_6$ 6C $6$ $2$ $C_{36}:C_{24}$ 3A 2C $b^{4}c^{18}$
$C_{12}^2.D_6$ 6D $6$ $2$ $C_{12}^2.C_6$ 3B 2A $b^{12}c^{24}$
$C_{12}^2.D_6$ 6E $6$ $2$ $C_{12}^2.C_6$ 3B 2B $c^{6}$
$C_{12}^2.D_6$ 6F $6$ $2$ $C_{12}^2.C_6$ 3B 2C $b^{12}c^{6}$
$C_{12}^2.D_6$ 6G $6$ $4$ $C_{12}\times C_{36}$ 3C 2A $b^{4}c^{24}$
$C_{12}^2.D_6$ 6H $6$ $4$ $C_{12}\times C_{36}$ 3C 2B $b^{16}c^{6}$
$C_{12}^2.D_6$ 6I $6$ $4$ $C_{12}\times C_{36}$ 3C 2C $b^{4}c^{6}$
$C_{12}^2.D_6$ 8A1 $8$ $18$ $C_{24}:C_4$ 4B1 8A3 $b^{3}$
$C_{12}^2.D_6$ 8A-1 $8$ $18$ $C_{24}:C_4$ 4B-1 8A-3 $b^{21}$
$C_{12}^2.D_6$ 8A3 $8$ $18$ $C_{24}:C_4$ 4B-1 8A1 $b^{9}$
$C_{12}^2.D_6$ 8A-3 $8$ $18$ $C_{24}:C_4$ 4B1 8A-1 $b^{15}$
$C_{12}^2.D_6$ 8B1 $8$ $36$ $C_2\times C_{24}$ 4B1 8B-1 $b^{3}c$
$C_{12}^2.D_6$ 8B-1 $8$ $36$ $C_2\times C_{24}$ 4B-1 8B1 $b^{21}c$
$C_{12}^2.D_6$ 8C1 $8$ $54$ $C_4\times C_8$ 4A1 8C-1 $abc^{10}$
$C_{12}^2.D_6$ 8C-1 $8$ $54$ $C_4\times C_8$ 4A-1 8C1 $ab^{19}c^{28}$
$C_{12}^2.D_6$ 8D1 $8$ $54$ $C_4\times C_8$ 4A1 8D-1 $ab^{9}c^{12}$
$C_{12}^2.D_6$ 8D-1 $8$ $54$ $C_4\times C_8$ 4A-1 8D1 $ab^{3}c^{30}$
$C_{12}^2.D_6$ 8E1 $8$ $108$ $C_2\times C_8$ 4B1 8E-1 $ab^{19}c$
$C_{12}^2.D_6$ 8E-1 $8$ $108$ $C_2\times C_8$ 4B-1 8E1 $ab^{13}c$
$C_{12}^2.D_6$ 9A1 $9$ $2$ $C_{12}^2.C_6$ 9A2 3B $c^{16}$
$C_{12}^2.D_6$ 9A2 $9$ $2$ $C_{12}^2.C_6$ 9A4 3B $c^{32}$
$C_{12}^2.D_6$ 9A4 $9$ $2$ $C_{12}^2.C_6$ 9A1 3B $c^{28}$
$C_{12}^2.D_6$ 9B1 $9$ $4$ $C_{12}\times C_{36}$ 9B2 3B $b^{8}c^{16}$
$C_{12}^2.D_6$ 9B2 $9$ $4$ $C_{12}\times C_{36}$ 9B4 3B $b^{16}c^{32}$
$C_{12}^2.D_6$ 9B4 $9$ $4$ $C_{12}\times C_{36}$ 9B1 3B $b^{8}c^{28}$
$C_{12}^2.D_6$ 12A1 $12$ $2$ $C_{36}:C_{24}$ 6A 4A1 $b^{2}c^{18}$
$C_{12}^2.D_6$ 12A-1 $12$ $2$ $C_{36}:C_{24}$ 6A 4A-1 $b^{14}c^{18}$
$C_{12}^2.D_6$ 12B1 $12$ $2$ $C_{36}:C_{24}$ 6A 4B1 $b^{2}$
$C_{12}^2.D_6$ 12B-1 $12$ $2$ $C_{36}:C_{24}$ 6A 4B-1 $b^{22}$
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