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Elements of the group are displayed as words in the presentation of the abelian group $\langle a, b \mid a^{2}=b^{44}=1 \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 11P
$C_2\times C_{44}$ 1A $1$ $1$ $C_2\times C_{44}$ 1A 1A $1$
$C_2\times C_{44}$ 2A $2$ $1$ $C_2\times C_{44}$ 1A 2A $a$
$C_2\times C_{44}$ 2B $2$ $1$ $C_2\times C_{44}$ 1A 2B $ab^{22}$
$C_2\times C_{44}$ 2C $2$ $1$ $C_2\times C_{44}$ 1A 2C $b^{22}$
$C_2\times C_{44}$ 4A1 $4$ $1$ $C_2\times C_{44}$ 2C 4A1 $b^{11}$
$C_2\times C_{44}$ 4A-1 $4$ $1$ $C_2\times C_{44}$ 2C 4A-1 $b^{33}$
$C_2\times C_{44}$ 4B1 $4$ $1$ $C_2\times C_{44}$ 2C 4B1 $ab^{11}$
$C_2\times C_{44}$ 4B-1 $4$ $1$ $C_2\times C_{44}$ 2C 4B-1 $ab^{33}$
$C_2\times C_{44}$ 11A1 $11$ $1$ $C_2\times C_{44}$ 11A2 11A5 $b^{8}$
$C_2\times C_{44}$ 11A-1 $11$ $1$ $C_2\times C_{44}$ 11A-2 11A-5 $b^{36}$
$C_2\times C_{44}$ 11A2 $11$ $1$ $C_2\times C_{44}$ 11A4 11A-1 $b^{16}$
$C_2\times C_{44}$ 11A-2 $11$ $1$ $C_2\times C_{44}$ 11A-4 11A1 $b^{28}$
$C_2\times C_{44}$ 11A3 $11$ $1$ $C_2\times C_{44}$ 11A-5 11A4 $b^{24}$
$C_2\times C_{44}$ 11A-3 $11$ $1$ $C_2\times C_{44}$ 11A5 11A-4 $b^{20}$
$C_2\times C_{44}$ 11A4 $11$ $1$ $C_2\times C_{44}$ 11A-3 11A-2 $b^{32}$
$C_2\times C_{44}$ 11A-4 $11$ $1$ $C_2\times C_{44}$ 11A3 11A2 $b^{12}$
$C_2\times C_{44}$ 11A5 $11$ $1$ $C_2\times C_{44}$ 11A-1 11A3 $b^{40}$
$C_2\times C_{44}$ 11A-5 $11$ $1$ $C_2\times C_{44}$ 11A1 11A-3 $b^{4}$
$C_2\times C_{44}$ 22A1 $22$ $1$ $C_2\times C_{44}$ 11A1 22A5 $ab^{4}$
$C_2\times C_{44}$ 22A-1 $22$ $1$ $C_2\times C_{44}$ 11A-1 22A-5 $ab^{40}$
$C_2\times C_{44}$ 22A3 $22$ $1$ $C_2\times C_{44}$ 11A3 22A-7 $ab^{12}$
$C_2\times C_{44}$ 22A-3 $22$ $1$ $C_2\times C_{44}$ 11A-3 22A7 $ab^{32}$
$C_2\times C_{44}$ 22A5 $22$ $1$ $C_2\times C_{44}$ 11A5 22A3 $ab^{20}$
$C_2\times C_{44}$ 22A-5 $22$ $1$ $C_2\times C_{44}$ 11A-5 22A-3 $ab^{24}$
$C_2\times C_{44}$ 22A7 $22$ $1$ $C_2\times C_{44}$ 11A-4 22A-9 $ab^{28}$
$C_2\times C_{44}$ 22A-7 $22$ $1$ $C_2\times C_{44}$ 11A4 22A9 $ab^{16}$
$C_2\times C_{44}$ 22A9 $22$ $1$ $C_2\times C_{44}$ 11A-2 22A1 $ab^{36}$
$C_2\times C_{44}$ 22A-9 $22$ $1$ $C_2\times C_{44}$ 11A2 22A-1 $ab^{8}$
$C_2\times C_{44}$ 22B1 $22$ $1$ $C_2\times C_{44}$ 11A-5 22B5 $ab^{2}$
$C_2\times C_{44}$ 22B-1 $22$ $1$ $C_2\times C_{44}$ 11A5 22B-5 $ab^{42}$
$C_2\times C_{44}$ 22B3 $22$ $1$ $C_2\times C_{44}$ 11A-4 22B-7 $ab^{6}$
$C_2\times C_{44}$ 22B-3 $22$ $1$ $C_2\times C_{44}$ 11A4 22B7 $ab^{38}$
$C_2\times C_{44}$ 22B5 $22$ $1$ $C_2\times C_{44}$ 11A-3 22B3 $ab^{10}$
$C_2\times C_{44}$ 22B-5 $22$ $1$ $C_2\times C_{44}$ 11A3 22B-3 $ab^{34}$
$C_2\times C_{44}$ 22B7 $22$ $1$ $C_2\times C_{44}$ 11A-2 22B-9 $ab^{14}$
$C_2\times C_{44}$ 22B-7 $22$ $1$ $C_2\times C_{44}$ 11A2 22B9 $ab^{30}$
$C_2\times C_{44}$ 22B9 $22$ $1$ $C_2\times C_{44}$ 11A-1 22B1 $ab^{18}$
$C_2\times C_{44}$ 22B-9 $22$ $1$ $C_2\times C_{44}$ 11A1 22B-1 $ab^{26}$
$C_2\times C_{44}$ 22C1 $22$ $1$ $C_2\times C_{44}$ 11A-5 22C5 $b^{2}$
$C_2\times C_{44}$ 22C-1 $22$ $1$ $C_2\times C_{44}$ 11A5 22C-5 $b^{42}$
$C_2\times C_{44}$ 22C3 $22$ $1$ $C_2\times C_{44}$ 11A-4 22C-7 $b^{6}$
$C_2\times C_{44}$ 22C-3 $22$ $1$ $C_2\times C_{44}$ 11A4 22C7 $b^{38}$
$C_2\times C_{44}$ 22C5 $22$ $1$ $C_2\times C_{44}$ 11A-3 22C3 $b^{10}$
$C_2\times C_{44}$ 22C-5 $22$ $1$ $C_2\times C_{44}$ 11A3 22C-3 $b^{34}$
$C_2\times C_{44}$ 22C7 $22$ $1$ $C_2\times C_{44}$ 11A-2 22C-9 $b^{14}$
$C_2\times C_{44}$ 22C-7 $22$ $1$ $C_2\times C_{44}$ 11A2 22C9 $b^{30}$
$C_2\times C_{44}$ 22C9 $22$ $1$ $C_2\times C_{44}$ 11A-1 22C1 $b^{18}$
$C_2\times C_{44}$ 22C-9 $22$ $1$ $C_2\times C_{44}$ 11A1 22C-1 $b^{26}$
$C_2\times C_{44}$ 44A1 $44$ $1$ $C_2\times C_{44}$ 22C1 44A5 $b$
$C_2\times C_{44}$ 44A-1 $44$ $1$ $C_2\times C_{44}$ 22C-1 44A-5 $b^{43}$
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