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Results (16 matches)
Download displayed columns for resultsElements of the group are displayed as words in the presentation of the abelian group $\langle a, b, c \mid a^{2}=b^{2}=c^{4}=1 \rangle$ .
| Group | Label | Order | Size | Centralizer | Powers | Representative |
|---|---|---|---|---|---|---|
| 2P | ||||||
| $C_2^2\times C_4$ | 1A | $1$ | $1$ | $C_2^2\times C_4$ | 1A | $1$ |
| $C_2^2\times C_4$ | 2A | $2$ | $1$ | $C_2^2\times C_4$ | 1A | $b$ |
| $C_2^2\times C_4$ | 2B | $2$ | $1$ | $C_2^2\times C_4$ | 1A | $a$ |
| $C_2^2\times C_4$ | 2C | $2$ | $1$ | $C_2^2\times C_4$ | 1A | $bc^{2}$ |
| $C_2^2\times C_4$ | 2D | $2$ | $1$ | $C_2^2\times C_4$ | 1A | $ac^{2}$ |
| $C_2^2\times C_4$ | 2E | $2$ | $1$ | $C_2^2\times C_4$ | 1A | $ab$ |
| $C_2^2\times C_4$ | 2F | $2$ | $1$ | $C_2^2\times C_4$ | 1A | $abc^{2}$ |
| $C_2^2\times C_4$ | 2G | $2$ | $1$ | $C_2^2\times C_4$ | 1A | $c^{2}$ |
| $C_2^2\times C_4$ | 4A1 | $4$ | $1$ | $C_2^2\times C_4$ | 2G | $c$ |
| $C_2^2\times C_4$ | 4A-1 | $4$ | $1$ | $C_2^2\times C_4$ | 2G | $c^{3}$ |
| $C_2^2\times C_4$ | 4B1 | $4$ | $1$ | $C_2^2\times C_4$ | 2G | $bc$ |
| $C_2^2\times C_4$ | 4B-1 | $4$ | $1$ | $C_2^2\times C_4$ | 2G | $bc^{3}$ |
| $C_2^2\times C_4$ | 4C1 | $4$ | $1$ | $C_2^2\times C_4$ | 2G | $ac$ |
| $C_2^2\times C_4$ | 4C-1 | $4$ | $1$ | $C_2^2\times C_4$ | 2G | $ac^{3}$ |
| $C_2^2\times C_4$ | 4D1 | $4$ | $1$ | $C_2^2\times C_4$ | 2G | $abc$ |
| $C_2^2\times C_4$ | 4D-1 | $4$ | $1$ | $C_2^2\times C_4$ | 2G | $abc^{3}$ |