Refine search
Results (11 matches)
Download displayed columns for resultsElements of the group are displayed as words in the presentation $\langle a, b, c \mid b^{2}=c^{4}=[b,c]=1, a^{4}=c^{2}, b^{a}=bc^{2}, c^{a}=bc \rangle$ .
| Group | Label | Order | Size | Centralizer | Powers | Representative |
|---|---|---|---|---|---|---|
| 2P | ||||||
| $C_4.D_4$ | 1A | $1$ | $1$ | $C_4.D_4$ | 1A | $1$ |
| $C_4.D_4$ | 2A | $2$ | $1$ | $C_4.D_4$ | 1A | $c^{2}$ |
| $C_4.D_4$ | 2B | $2$ | $2$ | $C_2\times Q_8$ | 1A | $b$ |
| $C_4.D_4$ | 4A | $4$ | $2$ | $\OD_{16}$ | 2A | $a^{2}$ |
| $C_4.D_4$ | 4B | $4$ | $2$ | $\OD_{16}$ | 2A | $a^{2}bc^{2}$ |
| $C_4.D_4$ | 4C | $4$ | $4$ | $C_2\times C_4$ | 2A | $c$ |
| $C_4.D_4$ | 4D | $4$ | $4$ | $C_2\times C_4$ | 2A | $a^{2}c$ |
| $C_4.D_4$ | 8A1 | $8$ | $4$ | $C_8$ | 4A | $a$ |
| $C_4.D_4$ | 8A-1 | $8$ | $4$ | $C_8$ | 4A | $a^{3}$ |
| $C_4.D_4$ | 8B1 | $8$ | $4$ | $C_8$ | 4B | $ac$ |
| $C_4.D_4$ | 8B-1 | $8$ | $4$ | $C_8$ | 4B | $a^{3}c$ |