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