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Results (33 matches)

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Elements of the group are displayed as words in the presentation $\langle a, b, c \mid a^{2}=b^{2}=c^{24}=[a,b]=1, c^{a}=c^{13}, c^{b}=c^{19} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 3P
$D_8:C_6$ 1A $1$ $1$ $D_8:C_6$ 1A 1A $1$
$D_8:C_6$ 2A $2$ $1$ $D_8:C_6$ 1A 2A $c^{12}$
$D_8:C_6$ 2B $2$ $2$ $C_6\times D_4$ 1A 2B $a$
$D_8:C_6$ 2C $2$ $4$ $C_2^2\times C_6$ 1A 2C $b$
$D_8:C_6$ 2D $2$ $4$ $C_2^2\times C_6$ 1A 2D $ab$
$D_8:C_6$ 2E $2$ $4$ $C_2\times C_{12}$ 1A 2E $abc^{9}$
$D_8:C_6$ 3A1 $3$ $1$ $D_8:C_6$ 3A-1 1A $c^{16}$
$D_8:C_6$ 3A-1 $3$ $1$ $D_8:C_6$ 3A1 1A $c^{8}$
$D_8:C_6$ 4A $4$ $2$ $D_4:C_6$ 2A 4A $ac^{6}$
$D_8:C_6$ 4B $4$ $2$ $C_3\times \OD_{16}$ 2A 4B $c^{6}$
$D_8:C_6$ 4C $4$ $4$ $C_2\times C_{12}$ 2A 4C $bc^{21}$
$D_8:C_6$ 6A1 $6$ $1$ $D_8:C_6$ 3A-1 2A $c^{4}$
$D_8:C_6$ 6A-1 $6$ $1$ $D_8:C_6$ 3A1 2A $c^{20}$
$D_8:C_6$ 6B1 $6$ $2$ $C_6\times D_4$ 3A1 2B $ac^{8}$
$D_8:C_6$ 6B-1 $6$ $2$ $C_6\times D_4$ 3A-1 2B $ac^{4}$
$D_8:C_6$ 6C1 $6$ $4$ $C_2^2\times C_6$ 3A1 2C $bc^{8}$
$D_8:C_6$ 6C-1 $6$ $4$ $C_2^2\times C_6$ 3A-1 2C $bc^{4}$
$D_8:C_6$ 6D1 $6$ $4$ $C_2^2\times C_6$ 3A1 2D $abc^{8}$
$D_8:C_6$ 6D-1 $6$ $4$ $C_2^2\times C_6$ 3A-1 2D $abc^{4}$
$D_8:C_6$ 6E1 $6$ $4$ $C_2\times C_{12}$ 3A-1 2E $abc$
$D_8:C_6$ 6E-1 $6$ $4$ $C_2\times C_{12}$ 3A1 2E $abc^{5}$
$D_8:C_6$ 8A $8$ $4$ $C_{24}$ 4B 8A $c^{3}$
$D_8:C_6$ 8B $8$ $4$ $C_{24}$ 4B 8B $ac^{15}$
$D_8:C_6$ 12A1 $12$ $2$ $D_4:C_6$ 6A1 4A $ac^{2}$
$D_8:C_6$ 12A-1 $12$ $2$ $D_4:C_6$ 6A-1 4A $ac^{10}$
$D_8:C_6$ 12B1 $12$ $2$ $C_3\times \OD_{16}$ 6A1 4B $c^{2}$
$D_8:C_6$ 12B-1 $12$ $2$ $C_3\times \OD_{16}$ 6A-1 4B $c^{22}$
$D_8:C_6$ 12C1 $12$ $4$ $C_2\times C_{12}$ 6A-1 4C $bc$
$D_8:C_6$ 12C-1 $12$ $4$ $C_2\times C_{12}$ 6A1 4C $bc^{5}$
$D_8:C_6$ 24A1 $24$ $4$ $C_{24}$ 12B1 8A $c$
$D_8:C_6$ 24A-1 $24$ $4$ $C_{24}$ 12B-1 8A $c^{5}$
$D_8:C_6$ 24B1 $24$ $4$ $C_{24}$ 12B1 8B $ac$
$D_8:C_6$ 24B-1 $24$ $4$ $C_{24}$ 12B-1 8B $ac^{5}$
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