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Elements of the group are displayed as words in the presentation of the abelian group $\langle a, b, c \mid a^{2}=b^{2}=c^{22}=1 \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 11P
$C_2^2\times C_{22}$ 1A $1$ $1$ $C_2^2\times C_{22}$ 1A 1A $1$
$C_2^2\times C_{22}$ 2A $2$ $1$ $C_2^2\times C_{22}$ 1A 2A $c^{11}$
$C_2^2\times C_{22}$ 2B $2$ $1$ $C_2^2\times C_{22}$ 1A 2B $b$
$C_2^2\times C_{22}$ 2C $2$ $1$ $C_2^2\times C_{22}$ 1A 2C $bc^{11}$
$C_2^2\times C_{22}$ 2D $2$ $1$ $C_2^2\times C_{22}$ 1A 2D $a$
$C_2^2\times C_{22}$ 2E $2$ $1$ $C_2^2\times C_{22}$ 1A 2E $ac^{11}$
$C_2^2\times C_{22}$ 2F $2$ $1$ $C_2^2\times C_{22}$ 1A 2F $ab$
$C_2^2\times C_{22}$ 2G $2$ $1$ $C_2^2\times C_{22}$ 1A 2G $abc^{11}$
$C_2^2\times C_{22}$ 11A1 $11$ $1$ $C_2^2\times C_{22}$ 11A2 11A5 $c^{2}$
$C_2^2\times C_{22}$ 11A-1 $11$ $1$ $C_2^2\times C_{22}$ 11A-2 11A-5 $c^{20}$
$C_2^2\times C_{22}$ 11A2 $11$ $1$ $C_2^2\times C_{22}$ 11A4 11A-1 $c^{4}$
$C_2^2\times C_{22}$ 11A-2 $11$ $1$ $C_2^2\times C_{22}$ 11A-4 11A1 $c^{18}$
$C_2^2\times C_{22}$ 11A3 $11$ $1$ $C_2^2\times C_{22}$ 11A-5 11A4 $c^{6}$
$C_2^2\times C_{22}$ 11A-3 $11$ $1$ $C_2^2\times C_{22}$ 11A5 11A-4 $c^{16}$
$C_2^2\times C_{22}$ 11A4 $11$ $1$ $C_2^2\times C_{22}$ 11A-3 11A-2 $c^{8}$
$C_2^2\times C_{22}$ 11A-4 $11$ $1$ $C_2^2\times C_{22}$ 11A3 11A2 $c^{14}$
$C_2^2\times C_{22}$ 11A5 $11$ $1$ $C_2^2\times C_{22}$ 11A-1 11A3 $c^{10}$
$C_2^2\times C_{22}$ 11A-5 $11$ $1$ $C_2^2\times C_{22}$ 11A1 11A-3 $c^{12}$
$C_2^2\times C_{22}$ 22A1 $22$ $1$ $C_2^2\times C_{22}$ 11A1 22A5 $c$
$C_2^2\times C_{22}$ 22A-1 $22$ $1$ $C_2^2\times C_{22}$ 11A-1 22A-5 $c^{21}$
$C_2^2\times C_{22}$ 22A3 $22$ $1$ $C_2^2\times C_{22}$ 11A3 22A-7 $c^{3}$
$C_2^2\times C_{22}$ 22A-3 $22$ $1$ $C_2^2\times C_{22}$ 11A-3 22A7 $c^{19}$
$C_2^2\times C_{22}$ 22A5 $22$ $1$ $C_2^2\times C_{22}$ 11A5 22A3 $c^{5}$
$C_2^2\times C_{22}$ 22A-5 $22$ $1$ $C_2^2\times C_{22}$ 11A-5 22A-3 $c^{17}$
$C_2^2\times C_{22}$ 22A7 $22$ $1$ $C_2^2\times C_{22}$ 11A-4 22A-9 $c^{7}$
$C_2^2\times C_{22}$ 22A-7 $22$ $1$ $C_2^2\times C_{22}$ 11A4 22A9 $c^{15}$
$C_2^2\times C_{22}$ 22A9 $22$ $1$ $C_2^2\times C_{22}$ 11A-2 22A1 $c^{9}$
$C_2^2\times C_{22}$ 22A-9 $22$ $1$ $C_2^2\times C_{22}$ 11A2 22A-1 $c^{13}$
$C_2^2\times C_{22}$ 22B1 $22$ $1$ $C_2^2\times C_{22}$ 11A2 22B5 $bc^{2}$
$C_2^2\times C_{22}$ 22B-1 $22$ $1$ $C_2^2\times C_{22}$ 11A-2 22B-5 $bc^{20}$
$C_2^2\times C_{22}$ 22B3 $22$ $1$ $C_2^2\times C_{22}$ 11A-5 22B-7 $bc^{6}$
$C_2^2\times C_{22}$ 22B-3 $22$ $1$ $C_2^2\times C_{22}$ 11A5 22B7 $bc^{16}$
$C_2^2\times C_{22}$ 22B5 $22$ $1$ $C_2^2\times C_{22}$ 11A-1 22B3 $bc^{10}$
$C_2^2\times C_{22}$ 22B-5 $22$ $1$ $C_2^2\times C_{22}$ 11A1 22B-3 $bc^{12}$
$C_2^2\times C_{22}$ 22B7 $22$ $1$ $C_2^2\times C_{22}$ 11A3 22B-9 $bc^{14}$
$C_2^2\times C_{22}$ 22B-7 $22$ $1$ $C_2^2\times C_{22}$ 11A-3 22B9 $bc^{8}$
$C_2^2\times C_{22}$ 22B9 $22$ $1$ $C_2^2\times C_{22}$ 11A-4 22B1 $bc^{18}$
$C_2^2\times C_{22}$ 22B-9 $22$ $1$ $C_2^2\times C_{22}$ 11A4 22B-1 $bc^{4}$
$C_2^2\times C_{22}$ 22C1 $22$ $1$ $C_2^2\times C_{22}$ 11A1 22C5 $bc$
$C_2^2\times C_{22}$ 22C-1 $22$ $1$ $C_2^2\times C_{22}$ 11A-1 22C-5 $bc^{21}$
$C_2^2\times C_{22}$ 22C3 $22$ $1$ $C_2^2\times C_{22}$ 11A3 22C-7 $bc^{3}$
$C_2^2\times C_{22}$ 22C-3 $22$ $1$ $C_2^2\times C_{22}$ 11A-3 22C7 $bc^{19}$
$C_2^2\times C_{22}$ 22C5 $22$ $1$ $C_2^2\times C_{22}$ 11A5 22C3 $bc^{5}$
$C_2^2\times C_{22}$ 22C-5 $22$ $1$ $C_2^2\times C_{22}$ 11A-5 22C-3 $bc^{17}$
$C_2^2\times C_{22}$ 22C7 $22$ $1$ $C_2^2\times C_{22}$ 11A-4 22C-9 $bc^{7}$
$C_2^2\times C_{22}$ 22C-7 $22$ $1$ $C_2^2\times C_{22}$ 11A4 22C9 $bc^{15}$
$C_2^2\times C_{22}$ 22C9 $22$ $1$ $C_2^2\times C_{22}$ 11A-2 22C1 $bc^{9}$
$C_2^2\times C_{22}$ 22C-9 $22$ $1$ $C_2^2\times C_{22}$ 11A2 22C-1 $bc^{13}$
$C_2^2\times C_{22}$ 22D1 $22$ $1$ $C_2^2\times C_{22}$ 11A2 22D5 $ac^{2}$
$C_2^2\times C_{22}$ 22D-1 $22$ $1$ $C_2^2\times C_{22}$ 11A-2 22D-5 $ac^{20}$
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