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Download displayed columns for resultsElements of the group are displayed as words in the presentation $\langle a, b \mid a^{2}=b^{12}=1, b^{a}=b^{11} \rangle$ .
| Group | Label | Order | Size | Centralizer | Powers | Representative | |
|---|---|---|---|---|---|---|---|
| 2P | 3P | ||||||
| $D_{12}$ | 1A | $1$ | $1$ | $D_{12}$ | 1A | 1A | $1$ |
| $D_{12}$ | 2A | $2$ | $1$ | $D_{12}$ | 1A | 2A | $b^{6}$ |
| $D_{12}$ | 2B | $2$ | $6$ | $C_2^2$ | 1A | 2B | $ab^{10}$ |
| $D_{12}$ | 2C | $2$ | $6$ | $C_2^2$ | 1A | 2C | $ab^{5}$ |
| $D_{12}$ | 3A | $3$ | $2$ | $C_{12}$ | 3A | 1A | $b^{4}$ |
| $D_{12}$ | 4A | $4$ | $2$ | $C_{12}$ | 2A | 4A | $b^{3}$ |
| $D_{12}$ | 6A | $6$ | $2$ | $C_{12}$ | 3A | 2A | $b^{2}$ |
| $D_{12}$ | 12A1 | $12$ | $2$ | $C_{12}$ | 6A | 4A | $b$ |
| $D_{12}$ | 12A5 | $12$ | $2$ | $C_{12}$ | 6A | 4A | $b^{5}$ |