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Elements of the group are displayed as words in the presentation $\langle a, b \mid a^{2}=b^{128}=1, b^{a}=b^{63} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P
$\SD_{256}$ 1A $1$ $1$ $\SD_{256}$ 1A $1$
$\SD_{256}$ 2A $2$ $1$ $\SD_{256}$ 1A $b^{64}$
$\SD_{256}$ 2B $2$ $64$ $C_2^2$ 1A $ab^{72}$
$\SD_{256}$ 4A $4$ $2$ $C_{128}$ 2A $b^{32}$
$\SD_{256}$ 4B $4$ $64$ $C_4$ 2A $ab^{3}$
$\SD_{256}$ 8A1 $8$ $2$ $C_{128}$ 4A $b^{16}$
$\SD_{256}$ 8A3 $8$ $2$ $C_{128}$ 4A $b^{48}$
$\SD_{256}$ 16A1 $16$ $2$ $C_{128}$ 8A1 $b^{8}$
$\SD_{256}$ 16A3 $16$ $2$ $C_{128}$ 8A3 $b^{24}$
$\SD_{256}$ 16A5 $16$ $2$ $C_{128}$ 8A3 $b^{40}$
$\SD_{256}$ 16A7 $16$ $2$ $C_{128}$ 8A1 $b^{56}$
$\SD_{256}$ 32A1 $32$ $2$ $C_{128}$ 16A1 $b^{4}$
$\SD_{256}$ 32A3 $32$ $2$ $C_{128}$ 16A3 $b^{12}$
$\SD_{256}$ 32A5 $32$ $2$ $C_{128}$ 16A5 $b^{20}$
$\SD_{256}$ 32A7 $32$ $2$ $C_{128}$ 16A7 $b^{28}$
$\SD_{256}$ 32A9 $32$ $2$ $C_{128}$ 16A7 $b^{36}$
$\SD_{256}$ 32A11 $32$ $2$ $C_{128}$ 16A5 $b^{44}$
$\SD_{256}$ 32A13 $32$ $2$ $C_{128}$ 16A3 $b^{52}$
$\SD_{256}$ 32A15 $32$ $2$ $C_{128}$ 16A1 $b^{60}$
$\SD_{256}$ 64A1 $64$ $2$ $C_{128}$ 32A1 $b^{2}$
$\SD_{256}$ 64A3 $64$ $2$ $C_{128}$ 32A3 $b^{6}$
$\SD_{256}$ 64A5 $64$ $2$ $C_{128}$ 32A5 $b^{10}$
$\SD_{256}$ 64A7 $64$ $2$ $C_{128}$ 32A7 $b^{14}$
$\SD_{256}$ 64A9 $64$ $2$ $C_{128}$ 32A9 $b^{18}$
$\SD_{256}$ 64A11 $64$ $2$ $C_{128}$ 32A11 $b^{22}$
$\SD_{256}$ 64A13 $64$ $2$ $C_{128}$ 32A13 $b^{26}$
$\SD_{256}$ 64A15 $64$ $2$ $C_{128}$ 32A15 $b^{30}$
$\SD_{256}$ 64A17 $64$ $2$ $C_{128}$ 32A15 $b^{34}$
$\SD_{256}$ 64A19 $64$ $2$ $C_{128}$ 32A13 $b^{38}$
$\SD_{256}$ 64A21 $64$ $2$ $C_{128}$ 32A11 $b^{42}$
$\SD_{256}$ 64A23 $64$ $2$ $C_{128}$ 32A9 $b^{46}$
$\SD_{256}$ 64A25 $64$ $2$ $C_{128}$ 32A7 $b^{50}$
$\SD_{256}$ 64A27 $64$ $2$ $C_{128}$ 32A5 $b^{54}$
$\SD_{256}$ 64A29 $64$ $2$ $C_{128}$ 32A3 $b^{58}$
$\SD_{256}$ 64A31 $64$ $2$ $C_{128}$ 32A1 $b^{62}$
$\SD_{256}$ 128A1 $128$ $2$ $C_{128}$ 64A1 $b$
$\SD_{256}$ 128A-1 $128$ $2$ $C_{128}$ 64A1 $b^{65}$
$\SD_{256}$ 128A3 $128$ $2$ $C_{128}$ 64A3 $b^{3}$
$\SD_{256}$ 128A-3 $128$ $2$ $C_{128}$ 64A3 $b^{67}$
$\SD_{256}$ 128A5 $128$ $2$ $C_{128}$ 64A5 $b^{5}$
$\SD_{256}$ 128A-5 $128$ $2$ $C_{128}$ 64A5 $b^{69}$
$\SD_{256}$ 128A7 $128$ $2$ $C_{128}$ 64A7 $b^{7}$
$\SD_{256}$ 128A-7 $128$ $2$ $C_{128}$ 64A7 $b^{71}$
$\SD_{256}$ 128A9 $128$ $2$ $C_{128}$ 64A9 $b^{9}$
$\SD_{256}$ 128A-9 $128$ $2$ $C_{128}$ 64A9 $b^{73}$
$\SD_{256}$ 128A11 $128$ $2$ $C_{128}$ 64A11 $b^{11}$
$\SD_{256}$ 128A-11 $128$ $2$ $C_{128}$ 64A11 $b^{75}$
$\SD_{256}$ 128A13 $128$ $2$ $C_{128}$ 64A13 $b^{13}$
$\SD_{256}$ 128A-13 $128$ $2$ $C_{128}$ 64A13 $b^{77}$
$\SD_{256}$ 128A15 $128$ $2$ $C_{128}$ 64A15 $b^{49}$
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