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Elements of the group are displayed as words in the presentation $\langle a, b \mid b^{256}=1, a^{2}=b^{128}, b^{a}=b^{127} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P
$\SD_{512}$ 1A $1$ $1$ $\SD_{512}$ 1A $1$
$\SD_{512}$ 2A $2$ $1$ $\SD_{512}$ 1A $b^{128}$
$\SD_{512}$ 2B $2$ $128$ $C_2^2$ 1A $ab^{131}$
$\SD_{512}$ 4A $4$ $2$ $C_{256}$ 2A $b^{64}$
$\SD_{512}$ 4B $4$ $128$ $C_4$ 2A $ab^{136}$
$\SD_{512}$ 8A1 $8$ $2$ $C_{256}$ 4A $b^{32}$
$\SD_{512}$ 8A3 $8$ $2$ $C_{256}$ 4A $b^{96}$
$\SD_{512}$ 16A1 $16$ $2$ $C_{256}$ 8A1 $b^{16}$
$\SD_{512}$ 16A3 $16$ $2$ $C_{256}$ 8A3 $b^{48}$
$\SD_{512}$ 16A5 $16$ $2$ $C_{256}$ 8A3 $b^{80}$
$\SD_{512}$ 16A7 $16$ $2$ $C_{256}$ 8A1 $b^{112}$
$\SD_{512}$ 32A1 $32$ $2$ $C_{256}$ 16A1 $b^{8}$
$\SD_{512}$ 32A3 $32$ $2$ $C_{256}$ 16A3 $b^{24}$
$\SD_{512}$ 32A5 $32$ $2$ $C_{256}$ 16A5 $b^{40}$
$\SD_{512}$ 32A7 $32$ $2$ $C_{256}$ 16A7 $b^{56}$
$\SD_{512}$ 32A9 $32$ $2$ $C_{256}$ 16A7 $b^{72}$
$\SD_{512}$ 32A11 $32$ $2$ $C_{256}$ 16A5 $b^{88}$
$\SD_{512}$ 32A13 $32$ $2$ $C_{256}$ 16A3 $b^{104}$
$\SD_{512}$ 32A15 $32$ $2$ $C_{256}$ 16A1 $b^{120}$
$\SD_{512}$ 64A1 $64$ $2$ $C_{256}$ 32A1 $b^{4}$
$\SD_{512}$ 64A3 $64$ $2$ $C_{256}$ 32A3 $b^{12}$
$\SD_{512}$ 64A5 $64$ $2$ $C_{256}$ 32A5 $b^{20}$
$\SD_{512}$ 64A7 $64$ $2$ $C_{256}$ 32A7 $b^{28}$
$\SD_{512}$ 64A9 $64$ $2$ $C_{256}$ 32A9 $b^{36}$
$\SD_{512}$ 64A11 $64$ $2$ $C_{256}$ 32A11 $b^{44}$
$\SD_{512}$ 64A13 $64$ $2$ $C_{256}$ 32A13 $b^{52}$
$\SD_{512}$ 64A15 $64$ $2$ $C_{256}$ 32A15 $b^{60}$
$\SD_{512}$ 64A17 $64$ $2$ $C_{256}$ 32A15 $b^{68}$
$\SD_{512}$ 64A19 $64$ $2$ $C_{256}$ 32A13 $b^{76}$
$\SD_{512}$ 64A21 $64$ $2$ $C_{256}$ 32A11 $b^{84}$
$\SD_{512}$ 64A23 $64$ $2$ $C_{256}$ 32A9 $b^{92}$
$\SD_{512}$ 64A25 $64$ $2$ $C_{256}$ 32A7 $b^{100}$
$\SD_{512}$ 64A27 $64$ $2$ $C_{256}$ 32A5 $b^{108}$
$\SD_{512}$ 64A29 $64$ $2$ $C_{256}$ 32A3 $b^{116}$
$\SD_{512}$ 64A31 $64$ $2$ $C_{256}$ 32A1 $b^{124}$
$\SD_{512}$ 128A1 $128$ $2$ $C_{256}$ 64A1 $b^{2}$
$\SD_{512}$ 128A3 $128$ $2$ $C_{256}$ 64A3 $b^{6}$
$\SD_{512}$ 128A5 $128$ $2$ $C_{256}$ 64A5 $b^{10}$
$\SD_{512}$ 128A7 $128$ $2$ $C_{256}$ 64A7 $b^{14}$
$\SD_{512}$ 128A9 $128$ $2$ $C_{256}$ 64A9 $b^{18}$
$\SD_{512}$ 128A11 $128$ $2$ $C_{256}$ 64A11 $b^{22}$
$\SD_{512}$ 128A13 $128$ $2$ $C_{256}$ 64A13 $b^{26}$
$\SD_{512}$ 128A15 $128$ $2$ $C_{256}$ 64A15 $b^{30}$
$\SD_{512}$ 128A17 $128$ $2$ $C_{256}$ 64A17 $b^{34}$
$\SD_{512}$ 128A19 $128$ $2$ $C_{256}$ 64A19 $b^{38}$
$\SD_{512}$ 128A21 $128$ $2$ $C_{256}$ 64A21 $b^{42}$
$\SD_{512}$ 128A23 $128$ $2$ $C_{256}$ 64A23 $b^{46}$
$\SD_{512}$ 128A25 $128$ $2$ $C_{256}$ 64A25 $b^{50}$
$\SD_{512}$ 128A27 $128$ $2$ $C_{256}$ 64A27 $b^{54}$
$\SD_{512}$ 128A29 $128$ $2$ $C_{256}$ 64A29 $b^{58}$
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