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Elements of the group are displayed as words in the presentation $\langle a, b, c \mid a^{2}=c^{48}=[a,b]=1, b^{4}=c^{36}, c^{a}=b^{2}c^{23}, c^{b}=c^{25} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 3P
$C_{16}:D_{12}$ 1A $1$ $1$ $C_{16}:D_{12}$ 1A 1A $1$
$C_{16}:D_{12}$ 2A $2$ $1$ $C_{16}:D_{12}$ 1A 2A $c^{24}$
$C_{16}:D_{12}$ 2B $2$ $1$ $C_{16}:D_{12}$ 1A 2B $b^{2}c^{30}$
$C_{16}:D_{12}$ 2C $2$ $1$ $C_{16}:D_{12}$ 1A 2C $b^{2}c^{6}$
$C_{16}:D_{12}$ 2D $2$ $6$ $C_2^2\times C_{16}$ 1A 2D $a$
$C_{16}:D_{12}$ 2E $2$ $6$ $C_2^2\times C_{16}$ 1A 2E $ac^{8}$
$C_{16}:D_{12}$ 2F $2$ $12$ $C_2^2\times C_8$ 1A 2F $abc^{7}$
$C_{16}:D_{12}$ 3A $3$ $2$ $C_{16}:C_{12}$ 3A 1A $c^{16}$
$C_{16}:D_{12}$ 4A1 $4$ $1$ $C_{16}:D_{12}$ 2A 4A-1 $c^{36}$
$C_{16}:D_{12}$ 4A-1 $4$ $1$ $C_{16}:D_{12}$ 2A 4A1 $c^{12}$
$C_{16}:D_{12}$ 4B1 $4$ $1$ $C_{16}:D_{12}$ 2A 4B-1 $b^{2}c^{18}$
$C_{16}:D_{12}$ 4B-1 $4$ $1$ $C_{16}:D_{12}$ 2A 4B1 $b^{2}c^{42}$
$C_{16}:D_{12}$ 4C $4$ $4$ $C_4\times C_{24}$ 2B 4C $bc^{3}$
$C_{16}:D_{12}$ 4D $4$ $4$ $C_4\times C_{24}$ 2C 4D $b^{3}c^{45}$
$C_{16}:D_{12}$ 4E1 $4$ $6$ $C_2^2\times C_{16}$ 2A 4E-1 $ac^{4}$
$C_{16}:D_{12}$ 4E-1 $4$ $6$ $C_2^2\times C_{16}$ 2A 4E1 $ac^{12}$
$C_{16}:D_{12}$ 4F $4$ $12$ $C_2^2\times C_8$ 2A 4F $abc^{3}$
$C_{16}:D_{12}$ 6A $6$ $2$ $C_{16}:C_{12}$ 3A 2B $b^{2}c^{14}$
$C_{16}:D_{12}$ 6B $6$ $2$ $C_{16}:C_{12}$ 3A 2C $b^{2}c^{38}$
$C_{16}:D_{12}$ 6C $6$ $2$ $C_{16}:C_{12}$ 3A 2A $c^{40}$
$C_{16}:D_{12}$ 8A1 $8$ $1$ $C_{16}:D_{12}$ 4A1 8A3 $b^{2}$
$C_{16}:D_{12}$ 8A-1 $8$ $1$ $C_{16}:D_{12}$ 4A-1 8A-3 $b^{2}c^{12}$
$C_{16}:D_{12}$ 8A3 $8$ $1$ $C_{16}:D_{12}$ 4A-1 8A1 $b^{2}c^{36}$
$C_{16}:D_{12}$ 8A-3 $8$ $1$ $C_{16}:D_{12}$ 4A1 8A-1 $b^{2}c^{24}$
$C_{16}:D_{12}$ 8B1 $8$ $1$ $C_{16}:D_{12}$ 4A-1 8B3 $c^{6}$
$C_{16}:D_{12}$ 8B-1 $8$ $1$ $C_{16}:D_{12}$ 4A1 8B-3 $c^{42}$
$C_{16}:D_{12}$ 8B3 $8$ $1$ $C_{16}:D_{12}$ 4A1 8B1 $c^{18}$
$C_{16}:D_{12}$ 8B-3 $8$ $1$ $C_{16}:D_{12}$ 4A-1 8B-1 $c^{30}$
$C_{16}:D_{12}$ 8C1 $8$ $4$ $C_4\times C_{24}$ 4B1 8C-1 $b^{3}c^{27}$
$C_{16}:D_{12}$ 8C-1 $8$ $4$ $C_4\times C_{24}$ 4B-1 8C1 $bc^{9}$
$C_{16}:D_{12}$ 8D1 $8$ $6$ $C_2^2\times C_{16}$ 4A1 8D3 $ac^{2}$
$C_{16}:D_{12}$ 8D-1 $8$ $6$ $C_2^2\times C_{16}$ 4A-1 8D-3 $ab^{2}c^{4}$
$C_{16}:D_{12}$ 8D3 $8$ $6$ $C_2^2\times C_{16}$ 4A-1 8D1 $ac^{6}$
$C_{16}:D_{12}$ 8D-3 $8$ $6$ $C_2^2\times C_{16}$ 4A1 8D-1 $ab^{2}$
$C_{16}:D_{12}$ 8E1 $8$ $12$ $C_2^2\times C_8$ 4A1 8E-1 $abc$
$C_{16}:D_{12}$ 8E-1 $8$ $12$ $C_2^2\times C_8$ 4A-1 8E1 $abc^{5}$
$C_{16}:D_{12}$ 12A1 $12$ $2$ $C_{16}:C_{12}$ 6C 4B1 $b^{2}c^{26}$
$C_{16}:D_{12}$ 12A-1 $12$ $2$ $C_{16}:C_{12}$ 6C 4B-1 $b^{2}c^{34}$
$C_{16}:D_{12}$ 12B1 $12$ $2$ $C_{16}:C_{12}$ 6C 4A-1 $c^{4}$
$C_{16}:D_{12}$ 12B-1 $12$ $2$ $C_{16}:C_{12}$ 6C 4A1 $c^{44}$
$C_{16}:D_{12}$ 12C1 $12$ $4$ $C_4\times C_{24}$ 6A 4C $b^{3}c$
$C_{16}:D_{12}$ 12C5 $12$ $4$ $C_4\times C_{24}$ 6A 4C $bc^{19}$
$C_{16}:D_{12}$ 12D1 $12$ $4$ $C_4\times C_{24}$ 6B 4D $bc^{7}$
$C_{16}:D_{12}$ 12D5 $12$ $4$ $C_4\times C_{24}$ 6B 4D $bc^{23}$
$C_{16}:D_{12}$ 16A1 $16$ $2$ $D_6\times C_{16}$ 8A3 16A3 $b^{3}$
$C_{16}:D_{12}$ 16A-1 $16$ $2$ $D_6\times C_{16}$ 8A-3 16A-3 $bc^{12}$
$C_{16}:D_{12}$ 16A3 $16$ $2$ $D_6\times C_{16}$ 8A1 16A1 $bc^{24}$
$C_{16}:D_{12}$ 16A-3 $16$ $2$ $D_6\times C_{16}$ 8A-1 16A-1 $b^{3}c^{36}$
$C_{16}:D_{12}$ 16B1 $16$ $2$ $D_6\times C_{16}$ 8A1 16B3 $b^{3}c^{6}$
$C_{16}:D_{12}$ 16B-1 $16$ $2$ $D_6\times C_{16}$ 8A-1 16B-3 $bc^{6}$
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