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Elements of the group are displayed as words in the presentation $\langle a, b \mid a^{2}=b^{44}=1, b^{a}=b^{43} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 11P
$D_{44}$ 1A $1$ $1$ $D_{44}$ 1A 1A $1$
$D_{44}$ 2A $2$ $1$ $D_{44}$ 1A 2A $b^{22}$
$D_{44}$ 2B $2$ $22$ $C_2^2$ 1A 2B $ab^{40}$
$D_{44}$ 2C $2$ $22$ $C_2^2$ 1A 2C $ab^{3}$
$D_{44}$ 4A $4$ $2$ $C_{44}$ 2A 4A $b^{11}$
$D_{44}$ 11A1 $11$ $2$ $C_{44}$ 11A2 11A5 $b^{4}$
$D_{44}$ 11A2 $11$ $2$ $C_{44}$ 11A4 11A1 $b^{8}$
$D_{44}$ 11A3 $11$ $2$ $C_{44}$ 11A5 11A4 $b^{12}$
$D_{44}$ 11A4 $11$ $2$ $C_{44}$ 11A3 11A2 $b^{16}$
$D_{44}$ 11A5 $11$ $2$ $C_{44}$ 11A1 11A3 $b^{20}$
$D_{44}$ 22A1 $22$ $2$ $C_{44}$ 11A1 22A5 $b^{2}$
$D_{44}$ 22A3 $22$ $2$ $C_{44}$ 11A3 22A7 $b^{6}$
$D_{44}$ 22A5 $22$ $2$ $C_{44}$ 11A5 22A3 $b^{10}$
$D_{44}$ 22A7 $22$ $2$ $C_{44}$ 11A4 22A9 $b^{14}$
$D_{44}$ 22A9 $22$ $2$ $C_{44}$ 11A2 22A1 $b^{18}$
$D_{44}$ 44A1 $44$ $2$ $C_{44}$ 22A1 44A5 $b$
$D_{44}$ 44A3 $44$ $2$ $C_{44}$ 22A3 44A15 $b^{3}$
$D_{44}$ 44A5 $44$ $2$ $C_{44}$ 22A5 44A19 $b^{5}$
$D_{44}$ 44A7 $44$ $2$ $C_{44}$ 22A7 44A9 $b^{37}$
$D_{44}$ 44A9 $44$ $2$ $C_{44}$ 22A9 44A1 $b^{9}$
$D_{44}$ 44A13 $44$ $2$ $C_{44}$ 22A9 44A21 $b^{13}$
$D_{44}$ 44A15 $44$ $2$ $C_{44}$ 22A7 44A13 $b^{29}$
$D_{44}$ 44A17 $44$ $2$ $C_{44}$ 22A5 44A3 $b^{17}$
$D_{44}$ 44A19 $44$ $2$ $C_{44}$ 22A3 44A7 $b^{25}$
$D_{44}$ 44A21 $44$ $2$ $C_{44}$ 22A1 44A17 $b^{21}$
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