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Elements of the group are displayed as words in the presentation of the abelian group $\langle a, b \mid a^{5}=b^{5}=1 \rangle$ .

Group Label Order Size Centralizer Powers Representative
5P
$C_5^2$ 1A $1$ $1$ $C_5^2$ 1A $1$
$C_5^2$ 5A1 $5$ $1$ $C_5^2$ 5A2 $b$
$C_5^2$ 5A-1 $5$ $1$ $C_5^2$ 5A-2 $b^{4}$
$C_5^2$ 5A2 $5$ $1$ $C_5^2$ 5A-1 $b^{2}$
$C_5^2$ 5A-2 $5$ $1$ $C_5^2$ 5A1 $b^{3}$
$C_5^2$ 5B1 $5$ $1$ $C_5^2$ 5B2 $a$
$C_5^2$ 5B-1 $5$ $1$ $C_5^2$ 5B-2 $a^{4}$
$C_5^2$ 5B2 $5$ $1$ $C_5^2$ 5B-1 $a^{2}$
$C_5^2$ 5B-2 $5$ $1$ $C_5^2$ 5B1 $a^{3}$
$C_5^2$ 5C1 $5$ $1$ $C_5^2$ 5C2 $ab$
$C_5^2$ 5C-1 $5$ $1$ $C_5^2$ 5C-2 $a^{4}b^{4}$
$C_5^2$ 5C2 $5$ $1$ $C_5^2$ 5C-1 $a^{2}b^{2}$
$C_5^2$ 5C-2 $5$ $1$ $C_5^2$ 5C1 $a^{3}b^{3}$
$C_5^2$ 5D1 $5$ $1$ $C_5^2$ 5D2 $ab^{2}$
$C_5^2$ 5D-1 $5$ $1$ $C_5^2$ 5D-2 $a^{4}b^{3}$
$C_5^2$ 5D2 $5$ $1$ $C_5^2$ 5D-1 $a^{2}b^{4}$
$C_5^2$ 5D-2 $5$ $1$ $C_5^2$ 5D1 $a^{3}b$
$C_5^2$ 5E1 $5$ $1$ $C_5^2$ 5E2 $a^{2}b$
$C_5^2$ 5E-1 $5$ $1$ $C_5^2$ 5E-2 $a^{3}b^{4}$
$C_5^2$ 5E2 $5$ $1$ $C_5^2$ 5E-1 $a^{4}b^{2}$
$C_5^2$ 5E-2 $5$ $1$ $C_5^2$ 5E1 $ab^{3}$
$C_5^2$ 5F1 $5$ $1$ $C_5^2$ 5F2 $ab^{4}$
$C_5^2$ 5F-1 $5$ $1$ $C_5^2$ 5F-2 $a^{4}b$
$C_5^2$ 5F2 $5$ $1$ $C_5^2$ 5F-1 $a^{2}b^{3}$
$C_5^2$ 5F-2 $5$ $1$ $C_5^2$ 5F1 $a^{3}b^{2}$
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