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Elements of the group are displayed as words in the presentation $\langle a, b, c, d, e, f \mid b^{4}=c^{18}=d^{18}=e^{9}=f^{9}=[c,e]=[c,f]=[d,e]=[e,f]=1, a^{6}=c^{6}e^{6}f^{6}, b^{a}=b^{3}c^{7}d^{9}e^{5}f^{2}, c^{a}=c^{15}d^{2}e^{3}f^{7}, d^{a}=c^{2}d^{5}e^{5}f^{4}, e^{a}=c^{10}e^{3}f^{7}, f^{a}=f^{5}, c^{b}=c^{12}d^{11}f^{3}, d^{b}=c^{13}d^{2}e^{8}, e^{b}=c^{2}e^{6}f^{5}, f^{b}=d^{10}e^{7}, d^{c}=d^{17}e^{4}f^{4}, f^{d}=f^{8} \rangle$ .
| Group | Label | Order | Size | Centralizer | Powers | Representative | |
|---|---|---|---|---|---|---|---|
| 2P | 3P | ||||||
| $D_9^2\wr C_2.C_3$ | 1A | $1$ | $1$ | not computed | 1A | 1A | $1$ |
| $D_9^2\wr C_2.C_3$ | 2A | $2$ | $18$ | not computed | 1A | 2A | $c^{9}d^{12}e^{3}$ |
| $D_9^2\wr C_2.C_3$ | 2B | $2$ | $18$ | not computed | 1A | 2B | $a^{3}b^{2}c^{4}e^{6}f^{8}$ |
| $D_9^2\wr C_2.C_3$ | 2C | $2$ | $81$ | not computed | 1A | 2C | $b^{2}c^{3}d^{13}e^{6}f^{8}$ |
| $D_9^2\wr C_2.C_3$ | 2D | $2$ | $81$ | not computed | 1A | 2D | $c^{9}d^{11}e^{5}$ |
| $D_9^2\wr C_2.C_3$ | 2E | $2$ | $162$ | not computed | 1A | 2E | $a^{3}c^{14}d^{3}ef$ |
| $D_9^2\wr C_2.C_3$ | 2F | $2$ | $162$ | not computed | 1A | 2F | $a^{3}b^{2}c^{7}d^{6}e^{6}f^{2}$ |
| $D_9^2\wr C_2.C_3$ | 2G | $2$ | $324$ | not computed | 1A | 2G | $a^{3}b^{3}c^{11}d^{12}e^{4}f^{2}$ |
| $D_9^2\wr C_2.C_3$ | 2H | $2$ | $1458$ | not computed | 1A | 2H | $a^{3}c^{6}e^{6}f^{5}$ |
| $D_9^2\wr C_2.C_3$ | 2I | $2$ | $1458$ | not computed | 1A | 2I | $b^{2}c^{14}d^{7}e^{8}f^{3}$ |
| $D_9^2\wr C_2.C_3$ | 2J | $2$ | $6561$ | not computed | 1A | 2J | $b^{2}c^{4}d^{16}e^{3}f^{2}$ |
| $D_9^2\wr C_2.C_3$ | 3A | $3$ | $4$ | not computed | 3A | 1A | $f^{3}$ |
| $D_9^2\wr C_2.C_3$ | 3B | $3$ | $4$ | not computed | 3B | 1A | $e^{3}$ |
| $D_9^2\wr C_2.C_3$ | 3C | $3$ | $4$ | not computed | 3C | 1A | $d^{6}e^{6}f^{3}$ |
| $D_9^2\wr C_2.C_3$ | 3D | $3$ | $4$ | not computed | 3D | 1A | $c^{6}e^{3}f^{6}$ |
| $D_9^2\wr C_2.C_3$ | 3E | $3$ | $8$ | not computed | 3E | 1A | $c^{6}e^{3}$ |
| $D_9^2\wr C_2.C_3$ | 3F | $3$ | $8$ | not computed | 3F | 1A | $c^{6}d^{6}f^{6}$ |
| $D_9^2\wr C_2.C_3$ | 3G | $3$ | $16$ | not computed | 3G | 1A | $d^{6}$ |
| $D_9^2\wr C_2.C_3$ | 3H | $3$ | $16$ | not computed | 3H | 1A | $d^{6}f^{3}$ |
| $D_9^2\wr C_2.C_3$ | 3I | $3$ | $16$ | not computed | 3I | 1A | $c^{6}d^{6}$ |
| $D_9^2\wr C_2.C_3$ | 3J1 | $3$ | $81$ | not computed | 3J-1 | 1A | $a^{4}c^{8}d^{6}e^{5}f^{8}$ |
| $D_9^2\wr C_2.C_3$ | 3J-1 | $3$ | $81$ | not computed | 3J1 | 1A | $a^{2}c^{10}d^{12}e^{4}f$ |
| $D_9^2\wr C_2.C_3$ | 4A | $4$ | $2916$ | not computed | 2D | 4A | $a^{3}b^{3}c^{11}d^{13}e^{4}f^{6}$ |
| $D_9^2\wr C_2.C_3$ | 4B | $4$ | $2916$ | not computed | 2C | 4B | $bc^{9}e^{3}f^{5}$ |
| $D_9^2\wr C_2.C_3$ | 4C | $4$ | $26244$ | not computed | 2J | 4C | $b^{3}c^{7}d^{7}e^{4}f^{2}$ |
| $D_9^2\wr C_2.C_3$ | 6A | $6$ | $36$ | not computed | 3A | 2A | $d^{3}e^{3}$ |
| $D_9^2\wr C_2.C_3$ | 6B | $6$ | $36$ | not computed | 3D | 2A | $c^{3}e^{3}f^{3}$ |
| $D_9^2\wr C_2.C_3$ | 6C | $6$ | $36$ | not computed | 3D | 2A | $c^{3}d^{4}e^{7}f^{3}$ |
| $D_9^2\wr C_2.C_3$ | 6D | $6$ | $36$ | not computed | 3D | 2B | $a^{3}b^{2}e^{2}f^{7}$ |
| $D_9^2\wr C_2.C_3$ | 6E | $6$ | $36$ | not computed | 3A | 2B | $a^{3}b^{2}e^{5}f^{4}$ |
| $D_9^2\wr C_2.C_3$ | 6F | $6$ | $36$ | not computed | 3A | 2B | $a^{3}cd^{13}e^{3}f^{5}$ |
| $D_9^2\wr C_2.C_3$ | 6G | $6$ | $72$ | not computed | 3E | 2A | $c^{3}d^{4}e^{7}$ |
| $D_9^2\wr C_2.C_3$ | 6H | $6$ | $72$ | not computed | 3F | 2A | $c^{3}d^{2}e^{8}$ |
| $D_9^2\wr C_2.C_3$ | 6I | $6$ | $72$ | not computed | 3E | 2B | $a^{3}b^{2}c^{8}ef^{6}$ |
| $D_9^2\wr C_2.C_3$ | 6J | $6$ | $72$ | not computed | 3B | 2A | $c^{3}f^{3}$ |
| $D_9^2\wr C_2.C_3$ | 6K | $6$ | $72$ | not computed | 3C | 2B | $a^{3}b^{2}d^{6}e^{2}f^{4}$ |
| $D_9^2\wr C_2.C_3$ | 6L | $6$ | $72$ | not computed | 3F | 2B | $a^{3}c^{5}d^{13}e^{2}f^{4}$ |
| $D_9^2\wr C_2.C_3$ | 6M | $6$ | $144$ | not computed | 3G | 2A | $d^{3}$ |
| $D_9^2\wr C_2.C_3$ | 6N | $6$ | $144$ | not computed | 3I | 2B | $a^{3}b^{2}c^{16}d^{6}e^{3}f^{8}$ |
| $D_9^2\wr C_2.C_3$ | 6O | $6$ | $324$ | not computed | 3D | 2E | $a^{3}c^{8}d^{3}e^{4}f^{7}$ |
| $D_9^2\wr C_2.C_3$ | 6P | $6$ | $324$ | not computed | 3A | 2C | $b^{2}c^{3}de^{3}f^{8}$ |
| $D_9^2\wr C_2.C_3$ | 6Q | $6$ | $324$ | not computed | 3A | 2E | $a^{3}c^{10}d^{5}ef^{5}$ |
| $D_9^2\wr C_2.C_3$ | 6R | $6$ | $324$ | not computed | 3B | 2D | $c^{9}de^{4}f^{3}$ |
| $D_9^2\wr C_2.C_3$ | 6S | $6$ | $324$ | not computed | 3D | 2D | $c^{15}d^{3}e^{6}f^{3}$ |
| $D_9^2\wr C_2.C_3$ | 6T | $6$ | $324$ | not computed | 3D | 2F | $a^{3}b^{2}cd^{6}e^{3}f^{5}$ |
| $D_9^2\wr C_2.C_3$ | 6U | $6$ | $324$ | not computed | 3C | 2C | $b^{2}c^{15}de^{7}f^{2}$ |
| $D_9^2\wr C_2.C_3$ | 6V | $6$ | $324$ | not computed | 3A | 2F | $a^{3}c^{5}d^{10}e^{5}f^{3}$ |
| $D_9^2\wr C_2.C_3$ | 6W1 | $6$ | $486$ | not computed | 3J1 | 2A | $a^{2}cef$ |
| $D_9^2\wr C_2.C_3$ | 6W-1 | $6$ | $486$ | not computed | 3J-1 | 2A | $a^{4}c^{2}d^{3}e^{2}$ |
| $D_9^2\wr C_2.C_3$ | 6X1 | $6$ | $486$ | not computed | 3J-1 | 2B | $ab^{2}c^{2}e$ |