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Download displayed columns for resultsElements of the group are displayed as words in the presentation of the abelian group $\langle a, b, c, d \mid a^{2}=b^{2}=c^{2}=d^{2}=1 \rangle$ .
| Group | Label | Order | Size | Centralizer | Powers | Representative |
|---|---|---|---|---|---|---|
| 2P | ||||||
| $C_2^4$ | 1A | $1$ | $1$ | $C_2^4$ | 1A | $1$ |
| $C_2^4$ | 2A | $2$ | $1$ | $C_2^4$ | 1A | $d$ |
| $C_2^4$ | 2B | $2$ | $1$ | $C_2^4$ | 1A | $c$ |
| $C_2^4$ | 2C | $2$ | $1$ | $C_2^4$ | 1A | $b$ |
| $C_2^4$ | 2D | $2$ | $1$ | $C_2^4$ | 1A | $a$ |
| $C_2^4$ | 2E | $2$ | $1$ | $C_2^4$ | 1A | $cd$ |
| $C_2^4$ | 2F | $2$ | $1$ | $C_2^4$ | 1A | $bd$ |
| $C_2^4$ | 2G | $2$ | $1$ | $C_2^4$ | 1A | $bc$ |
| $C_2^4$ | 2H | $2$ | $1$ | $C_2^4$ | 1A | $ad$ |
| $C_2^4$ | 2I | $2$ | $1$ | $C_2^4$ | 1A | $ac$ |
| $C_2^4$ | 2J | $2$ | $1$ | $C_2^4$ | 1A | $ab$ |
| $C_2^4$ | 2K | $2$ | $1$ | $C_2^4$ | 1A | $bcd$ |
| $C_2^4$ | 2L | $2$ | $1$ | $C_2^4$ | 1A | $acd$ |
| $C_2^4$ | 2M | $2$ | $1$ | $C_2^4$ | 1A | $abd$ |
| $C_2^4$ | 2N | $2$ | $1$ | $C_2^4$ | 1A | $abc$ |
| $C_2^4$ | 2O | $2$ | $1$ | $C_2^4$ | 1A | $abcd$ |