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Elements of the group are displayed as words in the presentation $\langle a, b \mid a^{2}=b^{1161}=1, b^{a}=b^{431} \rangle$ .
| Group | Label | Order | Size | Centralizer | Powers | Representative | ||
|---|---|---|---|---|---|---|---|---|
| 2P | 3P | 43P | ||||||
| $C_{43}\times D_{27}$ | 1A | $1$ | $1$ | $C_{43}\times D_{27}$ | 1A | 1A | 1A | $1$ |
| $C_{43}\times D_{27}$ | 2A | $2$ | $27$ | $C_{86}$ | 1A | 2A | 2A | $a$ |
| $C_{43}\times D_{27}$ | 3A | $3$ | $2$ | $C_{1161}$ | 3A | 1A | 3A | $b^{387}$ |
| $C_{43}\times D_{27}$ | 9A1 | $9$ | $2$ | $C_{1161}$ | 9A2 | 3A | 9A2 | $b^{129}$ |
| $C_{43}\times D_{27}$ | 9A2 | $9$ | $2$ | $C_{1161}$ | 9A4 | 3A | 9A4 | $b^{258}$ |
| $C_{43}\times D_{27}$ | 9A4 | $9$ | $2$ | $C_{1161}$ | 9A1 | 3A | 9A1 | $b^{516}$ |
| $C_{43}\times D_{27}$ | 27A1 | $27$ | $2$ | $C_{1161}$ | 27A2 | 9A1 | 27A7 | $b^{43}$ |
| $C_{43}\times D_{27}$ | 27A2 | $27$ | $2$ | $C_{1161}$ | 27A4 | 9A2 | 27A13 | $b^{86}$ |
| $C_{43}\times D_{27}$ | 27A4 | $27$ | $2$ | $C_{1161}$ | 27A8 | 9A4 | 27A1 | $b^{172}$ |
| $C_{43}\times D_{27}$ | 27A5 | $27$ | $2$ | $C_{1161}$ | 27A10 | 9A4 | 27A8 | $b^{215}$ |
| $C_{43}\times D_{27}$ | 27A7 | $27$ | $2$ | $C_{1161}$ | 27A13 | 9A2 | 27A5 | $b^{301}$ |
| $C_{43}\times D_{27}$ | 27A8 | $27$ | $2$ | $C_{1161}$ | 27A11 | 9A1 | 27A2 | $b^{344}$ |
| $C_{43}\times D_{27}$ | 27A10 | $27$ | $2$ | $C_{1161}$ | 27A7 | 9A1 | 27A11 | $b^{430}$ |
| $C_{43}\times D_{27}$ | 27A11 | $27$ | $2$ | $C_{1161}$ | 27A5 | 9A2 | 27A4 | $b^{473}$ |
| $C_{43}\times D_{27}$ | 27A13 | $27$ | $2$ | $C_{1161}$ | 27A1 | 9A4 | 27A10 | $b^{559}$ |
| $C_{43}\times D_{27}$ | 43A1 | $43$ | $1$ | $C_{43}\times D_{27}$ | 43A2 | 43A3 | 43A7 | $b^{54}$ |
| $C_{43}\times D_{27}$ | 43A-1 | $43$ | $1$ | $C_{43}\times D_{27}$ | 43A-2 | 43A-3 | 43A-7 | $b^{1107}$ |
| $C_{43}\times D_{27}$ | 43A2 | $43$ | $1$ | $C_{43}\times D_{27}$ | 43A4 | 43A6 | 43A14 | $b^{108}$ |
| $C_{43}\times D_{27}$ | 43A-2 | $43$ | $1$ | $C_{43}\times D_{27}$ | 43A-4 | 43A-6 | 43A-14 | $b^{1053}$ |
| $C_{43}\times D_{27}$ | 43A3 | $43$ | $1$ | $C_{43}\times D_{27}$ | 43A6 | 43A9 | 43A21 | $b^{162}$ |
| $C_{43}\times D_{27}$ | 43A-3 | $43$ | $1$ | $C_{43}\times D_{27}$ | 43A-6 | 43A-9 | 43A-21 | $b^{999}$ |
| $C_{43}\times D_{27}$ | 43A4 | $43$ | $1$ | $C_{43}\times D_{27}$ | 43A8 | 43A12 | 43A-15 | $b^{216}$ |
| $C_{43}\times D_{27}$ | 43A-4 | $43$ | $1$ | $C_{43}\times D_{27}$ | 43A-8 | 43A-12 | 43A15 | $b^{945}$ |
| $C_{43}\times D_{27}$ | 43A5 | $43$ | $1$ | $C_{43}\times D_{27}$ | 43A10 | 43A15 | 43A-8 | $b^{270}$ |
| $C_{43}\times D_{27}$ | 43A-5 | $43$ | $1$ | $C_{43}\times D_{27}$ | 43A-10 | 43A-15 | 43A8 | $b^{891}$ |
| $C_{43}\times D_{27}$ | 43A6 | $43$ | $1$ | $C_{43}\times D_{27}$ | 43A12 | 43A18 | 43A-1 | $b^{324}$ |
| $C_{43}\times D_{27}$ | 43A-6 | $43$ | $1$ | $C_{43}\times D_{27}$ | 43A-12 | 43A-18 | 43A1 | $b^{837}$ |
| $C_{43}\times D_{27}$ | 43A7 | $43$ | $1$ | $C_{43}\times D_{27}$ | 43A14 | 43A21 | 43A6 | $b^{378}$ |
| $C_{43}\times D_{27}$ | 43A-7 | $43$ | $1$ | $C_{43}\times D_{27}$ | 43A-14 | 43A-21 | 43A-6 | $b^{783}$ |
| $C_{43}\times D_{27}$ | 43A8 | $43$ | $1$ | $C_{43}\times D_{27}$ | 43A16 | 43A-19 | 43A13 | $b^{432}$ |
| $C_{43}\times D_{27}$ | 43A-8 | $43$ | $1$ | $C_{43}\times D_{27}$ | 43A-16 | 43A19 | 43A-13 | $b^{729}$ |
| $C_{43}\times D_{27}$ | 43A9 | $43$ | $1$ | $C_{43}\times D_{27}$ | 43A18 | 43A-16 | 43A20 | $b^{486}$ |
| $C_{43}\times D_{27}$ | 43A-9 | $43$ | $1$ | $C_{43}\times D_{27}$ | 43A-18 | 43A16 | 43A-20 | $b^{675}$ |
| $C_{43}\times D_{27}$ | 43A10 | $43$ | $1$ | $C_{43}\times D_{27}$ | 43A20 | 43A-13 | 43A-16 | $b^{540}$ |
| $C_{43}\times D_{27}$ | 43A-10 | $43$ | $1$ | $C_{43}\times D_{27}$ | 43A-20 | 43A13 | 43A16 | $b^{621}$ |
| $C_{43}\times D_{27}$ | 43A11 | $43$ | $1$ | $C_{43}\times D_{27}$ | 43A-21 | 43A-10 | 43A-9 | $b^{594}$ |
| $C_{43}\times D_{27}$ | 43A-11 | $43$ | $1$ | $C_{43}\times D_{27}$ | 43A21 | 43A10 | 43A9 | $b^{567}$ |
| $C_{43}\times D_{27}$ | 43A12 | $43$ | $1$ | $C_{43}\times D_{27}$ | 43A-19 | 43A-7 | 43A-2 | $b^{648}$ |
| $C_{43}\times D_{27}$ | 43A-12 | $43$ | $1$ | $C_{43}\times D_{27}$ | 43A19 | 43A7 | 43A2 | $b^{513}$ |
| $C_{43}\times D_{27}$ | 43A13 | $43$ | $1$ | $C_{43}\times D_{27}$ | 43A-17 | 43A-4 | 43A5 | $b^{702}$ |
| $C_{43}\times D_{27}$ | 43A-13 | $43$ | $1$ | $C_{43}\times D_{27}$ | 43A17 | 43A4 | 43A-5 | $b^{459}$ |
| $C_{43}\times D_{27}$ | 43A14 | $43$ | $1$ | $C_{43}\times D_{27}$ | 43A-15 | 43A-1 | 43A12 | $b^{756}$ |
| $C_{43}\times D_{27}$ | 43A-14 | $43$ | $1$ | $C_{43}\times D_{27}$ | 43A15 | 43A1 | 43A-12 | $b^{405}$ |
| $C_{43}\times D_{27}$ | 43A15 | $43$ | $1$ | $C_{43}\times D_{27}$ | 43A-13 | 43A2 | 43A19 | $b^{810}$ |
| $C_{43}\times D_{27}$ | 43A-15 | $43$ | $1$ | $C_{43}\times D_{27}$ | 43A13 | 43A-2 | 43A-19 | $b^{351}$ |
| $C_{43}\times D_{27}$ | 43A16 | $43$ | $1$ | $C_{43}\times D_{27}$ | 43A-11 | 43A5 | 43A-17 | $b^{864}$ |
| $C_{43}\times D_{27}$ | 43A-16 | $43$ | $1$ | $C_{43}\times D_{27}$ | 43A11 | 43A-5 | 43A17 | $b^{297}$ |
| $C_{43}\times D_{27}$ | 43A17 | $43$ | $1$ | $C_{43}\times D_{27}$ | 43A-9 | 43A8 | 43A-10 | $b^{918}$ |
| $C_{43}\times D_{27}$ | 43A-17 | $43$ | $1$ | $C_{43}\times D_{27}$ | 43A9 | 43A-8 | 43A10 | $b^{243}$ |
| $C_{43}\times D_{27}$ | 43A18 | $43$ | $1$ | $C_{43}\times D_{27}$ | 43A-7 | 43A11 | 43A-3 | $b^{972}$ |