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Download displayed columns for resultsElements of the group are displayed as words in the presentation of the abelian group $\langle a, b \mid a^{4}=b^{4}=1 \rangle$ .
| Group | Label | Order | Size | Centralizer | Powers | Representative |
|---|---|---|---|---|---|---|
| 2P | ||||||
| $C_4^2$ | 1A | $1$ | $1$ | $C_4^2$ | 1A | $1$ |
| $C_4^2$ | 2A | $2$ | $1$ | $C_4^2$ | 1A | $b^{2}$ |
| $C_4^2$ | 2B | $2$ | $1$ | $C_4^2$ | 1A | $a^{2}$ |
| $C_4^2$ | 2C | $2$ | $1$ | $C_4^2$ | 1A | $a^{2}b^{2}$ |
| $C_4^2$ | 4A1 | $4$ | $1$ | $C_4^2$ | 2A | $b$ |
| $C_4^2$ | 4A-1 | $4$ | $1$ | $C_4^2$ | 2A | $b^{3}$ |
| $C_4^2$ | 4B1 | $4$ | $1$ | $C_4^2$ | 2B | $a$ |
| $C_4^2$ | 4B-1 | $4$ | $1$ | $C_4^2$ | 2B | $a^{3}$ |
| $C_4^2$ | 4C1 | $4$ | $1$ | $C_4^2$ | 2A | $a^{2}b$ |
| $C_4^2$ | 4C-1 | $4$ | $1$ | $C_4^2$ | 2A | $a^{2}b^{3}$ |
| $C_4^2$ | 4D1 | $4$ | $1$ | $C_4^2$ | 2B | $ab^{2}$ |
| $C_4^2$ | 4D-1 | $4$ | $1$ | $C_4^2$ | 2B | $a^{3}b^{2}$ |
| $C_4^2$ | 4E1 | $4$ | $1$ | $C_4^2$ | 2C | $ab$ |
| $C_4^2$ | 4E-1 | $4$ | $1$ | $C_4^2$ | 2C | $a^{3}b^{3}$ |
| $C_4^2$ | 4F1 | $4$ | $1$ | $C_4^2$ | 2C | $ab^{3}$ |
| $C_4^2$ | 4F-1 | $4$ | $1$ | $C_4^2$ | 2C | $a^{3}b$ |