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Elements of the group are displayed as words in the presentation $\langle a \mid a^{715}=1 \rangle$ .
| Group | Label | Order | Size | Centralizer | Powers | Representative | ||
|---|---|---|---|---|---|---|---|---|
| 5P | 11P | 13P | ||||||
| $C_{715}$ | 1A | $1$ | $1$ | $C_{715}$ | 1A | 1A | 1A | $1$ |
| $C_{715}$ | 5A1 | $5$ | $1$ | $C_{715}$ | 5A2 | 5A-2 | 1A | $a^{143}$ |
| $C_{715}$ | 5A-1 | $5$ | $1$ | $C_{715}$ | 5A-2 | 5A2 | 1A | $a^{572}$ |
| $C_{715}$ | 5A2 | $5$ | $1$ | $C_{715}$ | 5A-1 | 5A1 | 1A | $a^{286}$ |
| $C_{715}$ | 5A-2 | $5$ | $1$ | $C_{715}$ | 5A1 | 5A-1 | 1A | $a^{429}$ |
| $C_{715}$ | 11A1 | $11$ | $1$ | $C_{715}$ | 11A2 | 11A3 | 11A5 | $a^{65}$ |
| $C_{715}$ | 11A-1 | $11$ | $1$ | $C_{715}$ | 11A-2 | 11A-3 | 11A-5 | $a^{650}$ |
| $C_{715}$ | 11A2 | $11$ | $1$ | $C_{715}$ | 11A4 | 11A-5 | 11A-1 | $a^{130}$ |
| $C_{715}$ | 11A-2 | $11$ | $1$ | $C_{715}$ | 11A-4 | 11A5 | 11A1 | $a^{585}$ |
| $C_{715}$ | 11A3 | $11$ | $1$ | $C_{715}$ | 11A-5 | 11A-2 | 11A4 | $a^{195}$ |
| $C_{715}$ | 11A-3 | $11$ | $1$ | $C_{715}$ | 11A5 | 11A2 | 11A-4 | $a^{520}$ |
| $C_{715}$ | 11A4 | $11$ | $1$ | $C_{715}$ | 11A-3 | 11A1 | 11A-2 | $a^{260}$ |
| $C_{715}$ | 11A-4 | $11$ | $1$ | $C_{715}$ | 11A3 | 11A-1 | 11A2 | $a^{455}$ |
| $C_{715}$ | 11A5 | $11$ | $1$ | $C_{715}$ | 11A-1 | 11A4 | 11A3 | $a^{325}$ |
| $C_{715}$ | 11A-5 | $11$ | $1$ | $C_{715}$ | 11A1 | 11A-4 | 11A-3 | $a^{390}$ |
| $C_{715}$ | 13A1 | $13$ | $1$ | $C_{715}$ | 13A2 | 13A3 | 13A5 | $a^{55}$ |
| $C_{715}$ | 13A-1 | $13$ | $1$ | $C_{715}$ | 13A-2 | 13A-3 | 13A-5 | $a^{660}$ |
| $C_{715}$ | 13A2 | $13$ | $1$ | $C_{715}$ | 13A4 | 13A6 | 13A-3 | $a^{110}$ |
| $C_{715}$ | 13A-2 | $13$ | $1$ | $C_{715}$ | 13A-4 | 13A-6 | 13A3 | $a^{605}$ |
| $C_{715}$ | 13A3 | $13$ | $1$ | $C_{715}$ | 13A6 | 13A-4 | 13A2 | $a^{165}$ |
| $C_{715}$ | 13A-3 | $13$ | $1$ | $C_{715}$ | 13A-6 | 13A4 | 13A-2 | $a^{550}$ |
| $C_{715}$ | 13A4 | $13$ | $1$ | $C_{715}$ | 13A-5 | 13A-1 | 13A-6 | $a^{220}$ |
| $C_{715}$ | 13A-4 | $13$ | $1$ | $C_{715}$ | 13A5 | 13A1 | 13A6 | $a^{495}$ |
| $C_{715}$ | 13A5 | $13$ | $1$ | $C_{715}$ | 13A-3 | 13A2 | 13A-1 | $a^{275}$ |
| $C_{715}$ | 13A-5 | $13$ | $1$ | $C_{715}$ | 13A3 | 13A-2 | 13A1 | $a^{440}$ |
| $C_{715}$ | 13A6 | $13$ | $1$ | $C_{715}$ | 13A-1 | 13A5 | 13A4 | $a^{330}$ |
| $C_{715}$ | 13A-6 | $13$ | $1$ | $C_{715}$ | 13A1 | 13A-5 | 13A-4 | $a^{385}$ |
| $C_{715}$ | 55A1 | $55$ | $1$ | $C_{715}$ | 55A2 | 55A3 | 11A1 | $a^{13}$ |
| $C_{715}$ | 55A-1 | $55$ | $1$ | $C_{715}$ | 55A-2 | 55A-3 | 11A-1 | $a^{702}$ |
| $C_{715}$ | 55A2 | $55$ | $1$ | $C_{715}$ | 55A4 | 55A6 | 11A2 | $a^{26}$ |
| $C_{715}$ | 55A-2 | $55$ | $1$ | $C_{715}$ | 55A-4 | 55A-6 | 11A-2 | $a^{689}$ |
| $C_{715}$ | 55A3 | $55$ | $1$ | $C_{715}$ | 55A6 | 55A9 | 11A3 | $a^{39}$ |
| $C_{715}$ | 55A-3 | $55$ | $1$ | $C_{715}$ | 55A-6 | 55A-9 | 11A-3 | $a^{676}$ |
| $C_{715}$ | 55A4 | $55$ | $1$ | $C_{715}$ | 55A8 | 55A12 | 11A4 | $a^{52}$ |
| $C_{715}$ | 55A-4 | $55$ | $1$ | $C_{715}$ | 55A-8 | 55A-12 | 11A-4 | $a^{663}$ |
| $C_{715}$ | 55A6 | $55$ | $1$ | $C_{715}$ | 55A12 | 55A18 | 11A-5 | $a^{78}$ |
| $C_{715}$ | 55A-6 | $55$ | $1$ | $C_{715}$ | 55A-12 | 55A-18 | 11A5 | $a^{637}$ |
| $C_{715}$ | 55A7 | $55$ | $1$ | $C_{715}$ | 55A14 | 55A21 | 11A-4 | $a^{91}$ |
| $C_{715}$ | 55A-7 | $55$ | $1$ | $C_{715}$ | 55A-14 | 55A-21 | 11A4 | $a^{624}$ |
| $C_{715}$ | 55A8 | $55$ | $1$ | $C_{715}$ | 55A16 | 55A24 | 11A-3 | $a^{104}$ |
| $C_{715}$ | 55A-8 | $55$ | $1$ | $C_{715}$ | 55A-16 | 55A-24 | 11A3 | $a^{611}$ |
| $C_{715}$ | 55A9 | $55$ | $1$ | $C_{715}$ | 55A18 | 55A27 | 11A-2 | $a^{117}$ |
| $C_{715}$ | 55A-9 | $55$ | $1$ | $C_{715}$ | 55A-18 | 55A-27 | 11A2 | $a^{598}$ |
| $C_{715}$ | 55A12 | $55$ | $1$ | $C_{715}$ | 55A24 | 55A-19 | 11A1 | $a^{156}$ |
| $C_{715}$ | 55A-12 | $55$ | $1$ | $C_{715}$ | 55A-24 | 55A19 | 11A-1 | $a^{559}$ |
| $C_{715}$ | 55A13 | $55$ | $1$ | $C_{715}$ | 55A26 | 55A-16 | 11A2 | $a^{169}$ |
| $C_{715}$ | 55A-13 | $55$ | $1$ | $C_{715}$ | 55A-26 | 55A16 | 11A-2 | $a^{546}$ |
| $C_{715}$ | 55A14 | $55$ | $1$ | $C_{715}$ | 55A-27 | 55A-13 | 11A3 | $a^{182}$ |
| $C_{715}$ | 55A-14 | $55$ | $1$ | $C_{715}$ | 55A27 | 55A13 | 11A-3 | $a^{533}$ |
| $C_{715}$ | 55A16 | $55$ | $1$ | $C_{715}$ | 55A-23 | 55A-7 | 11A5 | $a^{208}$ |