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Elements of the group are displayed as words in the presentation $\langle a \mid a^{25}=1 \rangle$ .

Group Label Order Size Centralizer Powers Representative
5P
$C_{25}$ 1A $1$ $1$ $C_{25}$ 1A $1$
$C_{25}$ 5A1 $5$ $1$ $C_{25}$ 5A2 $a^{5}$
$C_{25}$ 5A-1 $5$ $1$ $C_{25}$ 5A-2 $a^{20}$
$C_{25}$ 5A2 $5$ $1$ $C_{25}$ 5A-1 $a^{10}$
$C_{25}$ 5A-2 $5$ $1$ $C_{25}$ 5A1 $a^{15}$
$C_{25}$ 25A1 $25$ $1$ $C_{25}$ 25A2 $a$
$C_{25}$ 25A-1 $25$ $1$ $C_{25}$ 25A-2 $a^{24}$
$C_{25}$ 25A2 $25$ $1$ $C_{25}$ 25A4 $a^{2}$
$C_{25}$ 25A-2 $25$ $1$ $C_{25}$ 25A-4 $a^{23}$
$C_{25}$ 25A3 $25$ $1$ $C_{25}$ 25A6 $a^{3}$
$C_{25}$ 25A-3 $25$ $1$ $C_{25}$ 25A-6 $a^{22}$
$C_{25}$ 25A4 $25$ $1$ $C_{25}$ 25A8 $a^{4}$
$C_{25}$ 25A-4 $25$ $1$ $C_{25}$ 25A-8 $a^{21}$
$C_{25}$ 25A6 $25$ $1$ $C_{25}$ 25A12 $a^{6}$
$C_{25}$ 25A-6 $25$ $1$ $C_{25}$ 25A-12 $a^{19}$
$C_{25}$ 25A7 $25$ $1$ $C_{25}$ 25A-11 $a^{7}$
$C_{25}$ 25A-7 $25$ $1$ $C_{25}$ 25A11 $a^{18}$
$C_{25}$ 25A8 $25$ $1$ $C_{25}$ 25A-9 $a^{8}$
$C_{25}$ 25A-8 $25$ $1$ $C_{25}$ 25A9 $a^{17}$
$C_{25}$ 25A9 $25$ $1$ $C_{25}$ 25A-7 $a^{9}$
$C_{25}$ 25A-9 $25$ $1$ $C_{25}$ 25A7 $a^{16}$
$C_{25}$ 25A11 $25$ $1$ $C_{25}$ 25A-3 $a^{11}$
$C_{25}$ 25A-11 $25$ $1$ $C_{25}$ 25A3 $a^{14}$
$C_{25}$ 25A12 $25$ $1$ $C_{25}$ 25A-1 $a^{12}$
$C_{25}$ 25A-12 $25$ $1$ $C_{25}$ 25A1 $a^{13}$
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