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Elements of the group are displayed as words in the presentation $\langle a, b \mid a^{126}=b^{63}=1, b^{a}=b^{62} \rangle$ .
| Group | Label | Order | Size | Centralizer | Powers | Representative | ||
|---|---|---|---|---|---|---|---|---|
| 2P | 3P | 7P | ||||||
| $C_{63}\times D_{63}$ | 1A | $1$ | $1$ | $C_{63}\times D_{63}$ | 1A | 1A | 1A | $1$ |
| $C_{63}\times D_{63}$ | 2A | $2$ | $63$ | $C_{126}$ | 1A | 2A | 2A | $a^{63}$ |
| $C_{63}\times D_{63}$ | 3A1 | $3$ | $1$ | $C_{63}\times D_{63}$ | 3A-1 | 1A | 3A1 | $a^{42}$ |
| $C_{63}\times D_{63}$ | 3A-1 | $3$ | $1$ | $C_{63}\times D_{63}$ | 3A1 | 1A | 3A-1 | $a^{84}$ |
| $C_{63}\times D_{63}$ | 3B | $3$ | $2$ | $C_{63}^2$ | 3B | 1A | 3B | $b^{21}$ |
| $C_{63}\times D_{63}$ | 3C1 | $3$ | $2$ | $C_{63}^2$ | 3C-1 | 1A | 3C1 | $a^{42}b^{21}$ |
| $C_{63}\times D_{63}$ | 3C-1 | $3$ | $2$ | $C_{63}^2$ | 3C1 | 1A | 3C-1 | $a^{84}b^{42}$ |
| $C_{63}\times D_{63}$ | 6A1 | $6$ | $63$ | $C_{126}$ | 3A1 | 2A | 6A1 | $a^{21}$ |
| $C_{63}\times D_{63}$ | 6A-1 | $6$ | $63$ | $C_{126}$ | 3A-1 | 2A | 6A-1 | $a^{105}$ |
| $C_{63}\times D_{63}$ | 7A1 | $7$ | $1$ | $C_{63}\times D_{63}$ | 7A2 | 7A3 | 1A | $a^{36}$ |
| $C_{63}\times D_{63}$ | 7A-1 | $7$ | $1$ | $C_{63}\times D_{63}$ | 7A-2 | 7A-3 | 1A | $a^{90}$ |
| $C_{63}\times D_{63}$ | 7A2 | $7$ | $1$ | $C_{63}\times D_{63}$ | 7A-3 | 7A-1 | 1A | $a^{72}$ |
| $C_{63}\times D_{63}$ | 7A-2 | $7$ | $1$ | $C_{63}\times D_{63}$ | 7A3 | 7A1 | 1A | $a^{54}$ |
| $C_{63}\times D_{63}$ | 7A3 | $7$ | $1$ | $C_{63}\times D_{63}$ | 7A-1 | 7A2 | 1A | $a^{108}$ |
| $C_{63}\times D_{63}$ | 7A-3 | $7$ | $1$ | $C_{63}\times D_{63}$ | 7A1 | 7A-2 | 1A | $a^{18}$ |
| $C_{63}\times D_{63}$ | 7B1 | $7$ | $2$ | $C_{63}^2$ | 7B2 | 7B3 | 1A | $b^{9}$ |
| $C_{63}\times D_{63}$ | 7B2 | $7$ | $2$ | $C_{63}^2$ | 7B3 | 7B1 | 1A | $b^{18}$ |
| $C_{63}\times D_{63}$ | 7B3 | $7$ | $2$ | $C_{63}^2$ | 7B1 | 7B2 | 1A | $b^{27}$ |
| $C_{63}\times D_{63}$ | 7C1 | $7$ | $2$ | $C_{63}^2$ | 7C2 | 7C3 | 1A | $a^{36}b^{9}$ |
| $C_{63}\times D_{63}$ | 7C-1 | $7$ | $2$ | $C_{63}^2$ | 7C-2 | 7C-3 | 1A | $a^{90}b^{54}$ |
| $C_{63}\times D_{63}$ | 7C2 | $7$ | $2$ | $C_{63}^2$ | 7C-3 | 7C-1 | 1A | $a^{72}b^{18}$ |
| $C_{63}\times D_{63}$ | 7C-2 | $7$ | $2$ | $C_{63}^2$ | 7C3 | 7C1 | 1A | $a^{54}b^{45}$ |
| $C_{63}\times D_{63}$ | 7C3 | $7$ | $2$ | $C_{63}^2$ | 7C-1 | 7C2 | 1A | $a^{108}b^{27}$ |
| $C_{63}\times D_{63}$ | 7C-3 | $7$ | $2$ | $C_{63}^2$ | 7C1 | 7C-2 | 1A | $a^{18}b^{36}$ |
| $C_{63}\times D_{63}$ | 7D1 | $7$ | $2$ | $C_{63}^2$ | 7D2 | 7D3 | 1A | $a^{54}b^{9}$ |
| $C_{63}\times D_{63}$ | 7D-1 | $7$ | $2$ | $C_{63}^2$ | 7D-2 | 7D-3 | 1A | $a^{72}b^{54}$ |
| $C_{63}\times D_{63}$ | 7D2 | $7$ | $2$ | $C_{63}^2$ | 7D-3 | 7D-1 | 1A | $a^{108}b^{18}$ |
| $C_{63}\times D_{63}$ | 7D-2 | $7$ | $2$ | $C_{63}^2$ | 7D3 | 7D1 | 1A | $a^{18}b^{45}$ |
| $C_{63}\times D_{63}$ | 7D3 | $7$ | $2$ | $C_{63}^2$ | 7D-1 | 7D2 | 1A | $a^{36}b^{27}$ |
| $C_{63}\times D_{63}$ | 7D-3 | $7$ | $2$ | $C_{63}^2$ | 7D1 | 7D-2 | 1A | $a^{90}b^{36}$ |
| $C_{63}\times D_{63}$ | 7E1 | $7$ | $2$ | $C_{63}^2$ | 7E2 | 7E3 | 1A | $a^{18}b^{9}$ |
| $C_{63}\times D_{63}$ | 7E-1 | $7$ | $2$ | $C_{63}^2$ | 7E-2 | 7E-3 | 1A | $a^{108}b^{54}$ |
| $C_{63}\times D_{63}$ | 7E2 | $7$ | $2$ | $C_{63}^2$ | 7E-3 | 7E-1 | 1A | $a^{36}b^{18}$ |
| $C_{63}\times D_{63}$ | 7E-2 | $7$ | $2$ | $C_{63}^2$ | 7E3 | 7E1 | 1A | $a^{90}b^{45}$ |
| $C_{63}\times D_{63}$ | 7E3 | $7$ | $2$ | $C_{63}^2$ | 7E-1 | 7E2 | 1A | $a^{54}b^{27}$ |
| $C_{63}\times D_{63}$ | 7E-3 | $7$ | $2$ | $C_{63}^2$ | 7E1 | 7E-2 | 1A | $a^{72}b^{36}$ |
| $C_{63}\times D_{63}$ | 9A1 | $9$ | $1$ | $C_{63}\times D_{63}$ | 9A2 | 3A1 | 9A-2 | $a^{98}$ |
| $C_{63}\times D_{63}$ | 9A-1 | $9$ | $1$ | $C_{63}\times D_{63}$ | 9A-2 | 3A-1 | 9A2 | $a^{28}$ |
| $C_{63}\times D_{63}$ | 9A2 | $9$ | $1$ | $C_{63}\times D_{63}$ | 9A4 | 3A-1 | 9A-4 | $a^{70}$ |
| $C_{63}\times D_{63}$ | 9A-2 | $9$ | $1$ | $C_{63}\times D_{63}$ | 9A-4 | 3A1 | 9A4 | $a^{56}$ |
| $C_{63}\times D_{63}$ | 9A4 | $9$ | $1$ | $C_{63}\times D_{63}$ | 9A-1 | 3A1 | 9A1 | $a^{14}$ |
| $C_{63}\times D_{63}$ | 9A-4 | $9$ | $1$ | $C_{63}\times D_{63}$ | 9A1 | 3A-1 | 9A-1 | $a^{112}$ |
| $C_{63}\times D_{63}$ | 9B1 | $9$ | $2$ | $C_{63}^2$ | 9B2 | 3B | 9B2 | $b^{7}$ |
| $C_{63}\times D_{63}$ | 9B2 | $9$ | $2$ | $C_{63}^2$ | 9B4 | 3B | 9B4 | $b^{14}$ |
| $C_{63}\times D_{63}$ | 9B4 | $9$ | $2$ | $C_{63}^2$ | 9B1 | 3B | 9B1 | $b^{28}$ |
| $C_{63}\times D_{63}$ | 9C1 | $9$ | $2$ | $C_{63}^2$ | 9C2 | 3B | 9C-2 | $a^{42}b^{7}$ |
| $C_{63}\times D_{63}$ | 9C-1 | $9$ | $2$ | $C_{63}^2$ | 9C-2 | 3B | 9C2 | $a^{84}b^{56}$ |
| $C_{63}\times D_{63}$ | 9C2 | $9$ | $2$ | $C_{63}^2$ | 9C4 | 3B | 9C-4 | $a^{84}b^{14}$ |
| $C_{63}\times D_{63}$ | 9C-2 | $9$ | $2$ | $C_{63}^2$ | 9C-4 | 3B | 9C4 | $a^{42}b^{49}$ |
| $C_{63}\times D_{63}$ | 9C4 | $9$ | $2$ | $C_{63}^2$ | 9C-1 | 3B | 9C1 | $a^{42}b^{28}$ |