Refine search
Results (19 matches)
Download displayed columns for resultsElements of the group are displayed as words in the presentation $\langle a, b, c \mid b^{4}=c^{8}=[a,b]=1, a^{2}=c^{4}, c^{a}=b^{2}c, c^{b}=c^{3} \rangle$ .
| Group | Label | Order | Size | Centralizer | Powers | Representative |
|---|---|---|---|---|---|---|
| 2P | ||||||
| $C_2^3.D_4$ | 1A | $1$ | $1$ | $C_2^3.D_4$ | 1A | $1$ |
| $C_2^3.D_4$ | 2A | $2$ | $1$ | $C_2^3.D_4$ | 1A | $c^{4}$ |
| $C_2^3.D_4$ | 2B | $2$ | $1$ | $C_2^3.D_4$ | 1A | $b^{2}$ |
| $C_2^3.D_4$ | 2C | $2$ | $1$ | $C_2^3.D_4$ | 1A | $b^{2}c^{4}$ |
| $C_2^3.D_4$ | 2D | $2$ | $4$ | $C_2^2\times C_4$ | 1A | $ac^{2}$ |
| $C_2^3.D_4$ | 2E | $2$ | $8$ | $C_2^3$ | 1A | $abc$ |
| $C_2^3.D_4$ | 4A | $4$ | $2$ | $C_2^2:C_8$ | 2A | $c^{2}$ |
| $C_2^3.D_4$ | 4B | $4$ | $2$ | $C_2^2:C_8$ | 2A | $b^{2}c^{6}$ |
| $C_2^3.D_4$ | 4C1 | $4$ | $2$ | $C_4^2:C_2$ | 2A | $a$ |
| $C_2^3.D_4$ | 4C-1 | $4$ | $2$ | $C_4^2:C_2$ | 2A | $ac^{4}$ |
| $C_2^3.D_4$ | 4D1 | $4$ | $4$ | $C_4^2$ | 2B | $b$ |
| $C_2^3.D_4$ | 4D-1 | $4$ | $4$ | $C_4^2$ | 2B | $b^{3}$ |
| $C_2^3.D_4$ | 4E1 | $4$ | $4$ | $C_4^2$ | 2C | $ab$ |
| $C_2^3.D_4$ | 4E-1 | $4$ | $4$ | $C_4^2$ | 2C | $abc^{2}$ |
| $C_2^3.D_4$ | 4F | $4$ | $8$ | $C_2\times C_4$ | 2C | $bc$ |
| $C_2^3.D_4$ | 8A1 | $8$ | $4$ | $C_2\times C_8$ | 4A | $c$ |
| $C_2^3.D_4$ | 8A-1 | $8$ | $4$ | $C_2\times C_8$ | 4A | $c^{5}$ |
| $C_2^3.D_4$ | 8B1 | $8$ | $4$ | $C_2\times C_8$ | 4B | $ac$ |
| $C_2^3.D_4$ | 8B3 | $8$ | $4$ | $C_2\times C_8$ | 4B | $ac^{5}$ |