Refine search
Elements of the group are displayed as words in the presentation $\langle a, b \mid a^{2}=b^{2618}=1, b^{a}=b^{307} \rangle$ .
| Group | Label | Order | Size | Centralizer | Powers | Representative | |||
|---|---|---|---|---|---|---|---|---|---|
| 2P | 7P | 11P | 17P | ||||||
| $C_{17}\times D_{154}$ | 1A | $1$ | $1$ | $C_{17}\times D_{154}$ | 1A | 1A | 1A | 1A | $1$ |
| $C_{17}\times D_{154}$ | 2A | $2$ | $1$ | $C_{17}\times D_{154}$ | 1A | 2A | 2A | 2A | $b^{1309}$ |
| $C_{17}\times D_{154}$ | 2B | $2$ | $77$ | $C_2\times C_{34}$ | 1A | 2B | 2B | 2B | $ab^{1989}$ |
| $C_{17}\times D_{154}$ | 2C | $2$ | $77$ | $C_2\times C_{34}$ | 1A | 2C | 2C | 2C | $ab^{2142}$ |
| $C_{17}\times D_{154}$ | 7A1 | $7$ | $2$ | $C_{2618}$ | 7A2 | 7A3 | 7A2 | 1A | $b^{374}$ |
| $C_{17}\times D_{154}$ | 7A2 | $7$ | $2$ | $C_{2618}$ | 7A3 | 7A1 | 7A3 | 1A | $b^{748}$ |
| $C_{17}\times D_{154}$ | 7A3 | $7$ | $2$ | $C_{2618}$ | 7A1 | 7A2 | 7A1 | 1A | $b^{1122}$ |
| $C_{17}\times D_{154}$ | 11A1 | $11$ | $2$ | $C_{2618}$ | 11A2 | 11A3 | 11A5 | 11A4 | $b^{238}$ |
| $C_{17}\times D_{154}$ | 11A2 | $11$ | $2$ | $C_{2618}$ | 11A4 | 11A5 | 11A1 | 11A3 | $b^{476}$ |
| $C_{17}\times D_{154}$ | 11A3 | $11$ | $2$ | $C_{2618}$ | 11A5 | 11A2 | 11A4 | 11A1 | $b^{714}$ |
| $C_{17}\times D_{154}$ | 11A4 | $11$ | $2$ | $C_{2618}$ | 11A3 | 11A1 | 11A2 | 11A5 | $b^{952}$ |
| $C_{17}\times D_{154}$ | 11A5 | $11$ | $2$ | $C_{2618}$ | 11A1 | 11A4 | 11A3 | 11A2 | $b^{1190}$ |
| $C_{17}\times D_{154}$ | 14A1 | $14$ | $2$ | $C_{2618}$ | 7A1 | 14A3 | 14A5 | 2A | $b^{187}$ |
| $C_{17}\times D_{154}$ | 14A3 | $14$ | $2$ | $C_{2618}$ | 7A3 | 14A5 | 14A1 | 2A | $b^{561}$ |
| $C_{17}\times D_{154}$ | 14A5 | $14$ | $2$ | $C_{2618}$ | 7A2 | 14A1 | 14A3 | 2A | $b^{935}$ |
| $C_{17}\times D_{154}$ | 17A1 | $17$ | $1$ | $C_{17}\times D_{154}$ | 17A2 | 17A3 | 17A5 | 17A7 | $b^{154}$ |
| $C_{17}\times D_{154}$ | 17A-1 | $17$ | $1$ | $C_{17}\times D_{154}$ | 17A-2 | 17A-3 | 17A-5 | 17A-7 | $b^{2464}$ |
| $C_{17}\times D_{154}$ | 17A2 | $17$ | $1$ | $C_{17}\times D_{154}$ | 17A4 | 17A6 | 17A-7 | 17A-3 | $b^{308}$ |
| $C_{17}\times D_{154}$ | 17A-2 | $17$ | $1$ | $C_{17}\times D_{154}$ | 17A-4 | 17A-6 | 17A7 | 17A3 | $b^{2310}$ |
| $C_{17}\times D_{154}$ | 17A3 | $17$ | $1$ | $C_{17}\times D_{154}$ | 17A6 | 17A-8 | 17A-2 | 17A4 | $b^{462}$ |
| $C_{17}\times D_{154}$ | 17A-3 | $17$ | $1$ | $C_{17}\times D_{154}$ | 17A-6 | 17A8 | 17A2 | 17A-4 | $b^{2156}$ |
| $C_{17}\times D_{154}$ | 17A4 | $17$ | $1$ | $C_{17}\times D_{154}$ | 17A8 | 17A-5 | 17A3 | 17A-6 | $b^{616}$ |
| $C_{17}\times D_{154}$ | 17A-4 | $17$ | $1$ | $C_{17}\times D_{154}$ | 17A-8 | 17A5 | 17A-3 | 17A6 | $b^{2002}$ |
| $C_{17}\times D_{154}$ | 17A5 | $17$ | $1$ | $C_{17}\times D_{154}$ | 17A-7 | 17A-2 | 17A8 | 17A1 | $b^{770}$ |
| $C_{17}\times D_{154}$ | 17A-5 | $17$ | $1$ | $C_{17}\times D_{154}$ | 17A7 | 17A2 | 17A-8 | 17A-1 | $b^{1848}$ |
| $C_{17}\times D_{154}$ | 17A6 | $17$ | $1$ | $C_{17}\times D_{154}$ | 17A-5 | 17A1 | 17A-4 | 17A8 | $b^{924}$ |
| $C_{17}\times D_{154}$ | 17A-6 | $17$ | $1$ | $C_{17}\times D_{154}$ | 17A5 | 17A-1 | 17A4 | 17A-8 | $b^{1694}$ |
| $C_{17}\times D_{154}$ | 17A7 | $17$ | $1$ | $C_{17}\times D_{154}$ | 17A-3 | 17A4 | 17A1 | 17A-2 | $b^{1078}$ |
| $C_{17}\times D_{154}$ | 17A-7 | $17$ | $1$ | $C_{17}\times D_{154}$ | 17A3 | 17A-4 | 17A-1 | 17A2 | $b^{1540}$ |
| $C_{17}\times D_{154}$ | 17A8 | $17$ | $1$ | $C_{17}\times D_{154}$ | 17A-1 | 17A7 | 17A6 | 17A5 | $b^{1232}$ |
| $C_{17}\times D_{154}$ | 17A-8 | $17$ | $1$ | $C_{17}\times D_{154}$ | 17A1 | 17A-7 | 17A-6 | 17A-5 | $b^{1386}$ |
| $C_{17}\times D_{154}$ | 22A1 | $22$ | $2$ | $C_{2618}$ | 11A1 | 22A3 | 22A5 | 22A7 | $b^{119}$ |
| $C_{17}\times D_{154}$ | 22A3 | $22$ | $2$ | $C_{2618}$ | 11A3 | 22A9 | 22A7 | 22A1 | $b^{357}$ |
| $C_{17}\times D_{154}$ | 22A5 | $22$ | $2$ | $C_{2618}$ | 11A5 | 22A7 | 22A3 | 22A9 | $b^{595}$ |
| $C_{17}\times D_{154}$ | 22A7 | $22$ | $2$ | $C_{2618}$ | 11A4 | 22A1 | 22A9 | 22A5 | $b^{833}$ |
| $C_{17}\times D_{154}$ | 22A9 | $22$ | $2$ | $C_{2618}$ | 11A2 | 22A5 | 22A1 | 22A3 | $b^{1071}$ |
| $C_{17}\times D_{154}$ | 34A1 | $34$ | $1$ | $C_{17}\times D_{154}$ | 17A1 | 34A3 | 34A5 | 34A7 | $b^{77}$ |
| $C_{17}\times D_{154}$ | 34A-1 | $34$ | $1$ | $C_{17}\times D_{154}$ | 17A-1 | 34A-3 | 34A-5 | 34A-7 | $b^{2541}$ |
| $C_{17}\times D_{154}$ | 34A3 | $34$ | $1$ | $C_{17}\times D_{154}$ | 17A3 | 34A9 | 34A15 | 34A-13 | $b^{231}$ |
| $C_{17}\times D_{154}$ | 34A-3 | $34$ | $1$ | $C_{17}\times D_{154}$ | 17A-3 | 34A-9 | 34A-15 | 34A13 | $b^{2387}$ |
| $C_{17}\times D_{154}$ | 34A5 | $34$ | $1$ | $C_{17}\times D_{154}$ | 17A5 | 34A15 | 34A-9 | 34A1 | $b^{385}$ |
| $C_{17}\times D_{154}$ | 34A-5 | $34$ | $1$ | $C_{17}\times D_{154}$ | 17A-5 | 34A-15 | 34A9 | 34A-1 | $b^{2233}$ |
| $C_{17}\times D_{154}$ | 34A7 | $34$ | $1$ | $C_{17}\times D_{154}$ | 17A7 | 34A-13 | 34A1 | 34A15 | $b^{539}$ |
| $C_{17}\times D_{154}$ | 34A-7 | $34$ | $1$ | $C_{17}\times D_{154}$ | 17A-7 | 34A13 | 34A-1 | 34A-15 | $b^{2079}$ |
| $C_{17}\times D_{154}$ | 34A9 | $34$ | $1$ | $C_{17}\times D_{154}$ | 17A-8 | 34A-7 | 34A11 | 34A-5 | $b^{693}$ |
| $C_{17}\times D_{154}$ | 34A-9 | $34$ | $1$ | $C_{17}\times D_{154}$ | 17A8 | 34A7 | 34A-11 | 34A5 | $b^{1925}$ |
| $C_{17}\times D_{154}$ | 34A11 | $34$ | $1$ | $C_{17}\times D_{154}$ | 17A-6 | 34A-1 | 34A-13 | 34A9 | $b^{847}$ |
| $C_{17}\times D_{154}$ | 34A-11 | $34$ | $1$ | $C_{17}\times D_{154}$ | 17A6 | 34A1 | 34A13 | 34A-9 | $b^{1771}$ |
| $C_{17}\times D_{154}$ | 34A13 | $34$ | $1$ | $C_{17}\times D_{154}$ | 17A-4 | 34A5 | 34A-3 | 34A-11 | $b^{1001}$ |
| $C_{17}\times D_{154}$ | 34A-13 | $34$ | $1$ | $C_{17}\times D_{154}$ | 17A4 | 34A-5 | 34A3 | 34A11 | $b^{1617}$ |