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Download displayed columns for resultsElements of the group are displayed as words in the presentation $\langle a, b, c \mid a^{6}=b^{4}=c^{4}=[b,c]=1, b^{a}=c, c^{a}=bc \rangle$ .
| Group | Label | Order | Size | Centralizer | Powers | Representative | |
|---|---|---|---|---|---|---|---|
| 2P | 3P | ||||||
| $C_4^2:C_6$ | 1A | $1$ | $1$ | $C_4^2:C_6$ | 1A | 1A | $1$ |
| $C_4^2:C_6$ | 2A | $2$ | $3$ | $C_4^2:C_2$ | 1A | 2A | $c^{2}$ |
| $C_4^2:C_6$ | 2B | $2$ | $4$ | $C_2\times A_4$ | 1A | 2B | $a^{3}b^{2}$ |
| $C_4^2:C_6$ | 3A1 | $3$ | $16$ | $C_6$ | 3A-1 | 1A | $a^{2}b^{3}$ |
| $C_4^2:C_6$ | 3A-1 | $3$ | $16$ | $C_6$ | 3A1 | 1A | $a^{4}b^{2}c^{3}$ |
| $C_4^2:C_6$ | 4A1 | $4$ | $6$ | $C_4^2$ | 2A | 4A-1 | $c$ |
| $C_4^2:C_6$ | 4A-1 | $4$ | $6$ | $C_4^2$ | 2A | 4A1 | $c^{3}$ |
| $C_4^2:C_6$ | 4B | $4$ | $12$ | $C_2\times C_4$ | 2A | 4B | $a^{3}c$ |
| $C_4^2:C_6$ | 6A1 | $6$ | $16$ | $C_6$ | 3A1 | 2B | $ab^{2}c$ |
| $C_4^2:C_6$ | 6A-1 | $6$ | $16$ | $C_6$ | 3A-1 | 2B | $a^{5}bc^{2}$ |