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Elements of the group are displayed as words in the presentation $\langle a, b \mid a^{198}=b^{2189}=1, b^{a}=b^{1651} \rangle$ .
| Group | Label | Order | Size | Centralizer | Powers | Representative | |||
|---|---|---|---|---|---|---|---|---|---|
| 2P | 3P | 11P | 199P | ||||||
| $C_{2189}:C_{198}$ | 1A | $1$ | $1$ | $C_{2189}:C_{198}$ | 1A | 1A | 1A | 1A | $1$ |
| $C_{2189}:C_{198}$ | 2A | $2$ | $199$ | $C_{11}\times C_{198}$ | 1A | 2A | 2A | 2A | $a^{99}$ |
| $C_{2189}:C_{198}$ | 3A1 | $3$ | $1$ | $C_{2189}:C_{198}$ | 3A-1 | 1A | 3A-1 | 3A-1 | $a^{66}$ |
| $C_{2189}:C_{198}$ | 3A-1 | $3$ | $1$ | $C_{2189}:C_{198}$ | 3A1 | 1A | 3A1 | 3A1 | $a^{132}$ |
| $C_{2189}:C_{198}$ | 6A1 | $6$ | $199$ | $C_{11}\times C_{198}$ | 3A1 | 2A | 6A-1 | 6A-1 | $a^{33}$ |
| $C_{2189}:C_{198}$ | 6A-1 | $6$ | $199$ | $C_{11}\times C_{198}$ | 3A-1 | 2A | 6A1 | 6A1 | $a^{165}$ |
| $C_{2189}:C_{198}$ | 9A1 | $9$ | $199$ | $C_{11}\times C_{198}$ | 9A2 | 3A1 | 9A-4 | 9A2 | $a^{22}$ |
| $C_{2189}:C_{198}$ | 9A-1 | $9$ | $199$ | $C_{11}\times C_{198}$ | 9A-2 | 3A-1 | 9A4 | 9A-2 | $a^{176}$ |
| $C_{2189}:C_{198}$ | 9A2 | $9$ | $199$ | $C_{11}\times C_{198}$ | 9A4 | 3A-1 | 9A1 | 9A4 | $a^{44}$ |
| $C_{2189}:C_{198}$ | 9A-2 | $9$ | $199$ | $C_{11}\times C_{198}$ | 9A-4 | 3A1 | 9A-1 | 9A-4 | $a^{154}$ |
| $C_{2189}:C_{198}$ | 9A4 | $9$ | $199$ | $C_{11}\times C_{198}$ | 9A-1 | 3A1 | 9A2 | 9A-1 | $a^{88}$ |
| $C_{2189}:C_{198}$ | 9A-4 | $9$ | $199$ | $C_{11}\times C_{198}$ | 9A1 | 3A-1 | 9A-2 | 9A1 | $a^{110}$ |
| $C_{2189}:C_{198}$ | 11A1 | $11$ | $1$ | $C_{2189}:C_{198}$ | 11A2 | 11A3 | 11A5 | 1A | $b^{1393}$ |
| $C_{2189}:C_{198}$ | 11A-1 | $11$ | $1$ | $C_{2189}:C_{198}$ | 11A-2 | 11A-3 | 11A-5 | 1A | $b^{796}$ |
| $C_{2189}:C_{198}$ | 11A2 | $11$ | $1$ | $C_{2189}:C_{198}$ | 11A4 | 11A-5 | 11A-1 | 1A | $b^{597}$ |
| $C_{2189}:C_{198}$ | 11A-2 | $11$ | $1$ | $C_{2189}:C_{198}$ | 11A-4 | 11A5 | 11A1 | 1A | $b^{1592}$ |
| $C_{2189}:C_{198}$ | 11A3 | $11$ | $1$ | $C_{2189}:C_{198}$ | 11A-5 | 11A-2 | 11A4 | 1A | $b^{1990}$ |
| $C_{2189}:C_{198}$ | 11A-3 | $11$ | $1$ | $C_{2189}:C_{198}$ | 11A5 | 11A2 | 11A-4 | 1A | $b^{199}$ |
| $C_{2189}:C_{198}$ | 11A4 | $11$ | $1$ | $C_{2189}:C_{198}$ | 11A-3 | 11A1 | 11A-2 | 1A | $b^{1194}$ |
| $C_{2189}:C_{198}$ | 11A-4 | $11$ | $1$ | $C_{2189}:C_{198}$ | 11A3 | 11A-1 | 11A2 | 1A | $b^{995}$ |
| $C_{2189}:C_{198}$ | 11A5 | $11$ | $1$ | $C_{2189}:C_{198}$ | 11A-1 | 11A4 | 11A3 | 1A | $b^{398}$ |
| $C_{2189}:C_{198}$ | 11A-5 | $11$ | $1$ | $C_{2189}:C_{198}$ | 11A1 | 11A-4 | 11A-3 | 1A | $b^{1791}$ |
| $C_{2189}:C_{198}$ | 11B1 | $11$ | $199$ | $C_{11}\times C_{198}$ | 11B2 | 11B3 | 11B5 | 1A | $a^{18}$ |
| $C_{2189}:C_{198}$ | 11B-1 | $11$ | $199$ | $C_{11}\times C_{198}$ | 11B-2 | 11B-3 | 11B-5 | 1A | $a^{180}$ |
| $C_{2189}:C_{198}$ | 11B2 | $11$ | $199$ | $C_{11}\times C_{198}$ | 11B4 | 11B-5 | 11B-1 | 1A | $a^{36}$ |
| $C_{2189}:C_{198}$ | 11B-2 | $11$ | $199$ | $C_{11}\times C_{198}$ | 11B-4 | 11B5 | 11B1 | 1A | $a^{162}$ |
| $C_{2189}:C_{198}$ | 11B3 | $11$ | $199$ | $C_{11}\times C_{198}$ | 11B-5 | 11B-2 | 11B4 | 1A | $a^{54}$ |
| $C_{2189}:C_{198}$ | 11B-3 | $11$ | $199$ | $C_{11}\times C_{198}$ | 11B5 | 11B2 | 11B-4 | 1A | $a^{144}$ |
| $C_{2189}:C_{198}$ | 11B4 | $11$ | $199$ | $C_{11}\times C_{198}$ | 11B-3 | 11B1 | 11B-2 | 1A | $a^{72}$ |
| $C_{2189}:C_{198}$ | 11B-4 | $11$ | $199$ | $C_{11}\times C_{198}$ | 11B3 | 11B-1 | 11B2 | 1A | $a^{126}$ |
| $C_{2189}:C_{198}$ | 11B5 | $11$ | $199$ | $C_{11}\times C_{198}$ | 11B-1 | 11B4 | 11B3 | 1A | $a^{90}$ |
| $C_{2189}:C_{198}$ | 11B-5 | $11$ | $199$ | $C_{11}\times C_{198}$ | 11B1 | 11B-4 | 11B-3 | 1A | $a^{108}$ |
| $C_{2189}:C_{198}$ | 11C1 | $11$ | $199$ | $C_{11}\times C_{198}$ | 11C2 | 11C3 | 11C5 | 1A | $a^{18}b^{502}$ |
| $C_{2189}:C_{198}$ | 11C-1 | $11$ | $199$ | $C_{11}\times C_{198}$ | 11C-2 | 11C-3 | 11C-5 | 1A | $a^{180}b^{2061}$ |
| $C_{2189}:C_{198}$ | 11C2 | $11$ | $199$ | $C_{11}\times C_{198}$ | 11C4 | 11C-5 | 11C-1 | 1A | $a^{36}b^{487}$ |
| $C_{2189}:C_{198}$ | 11C-2 | $11$ | $199$ | $C_{11}\times C_{198}$ | 11C-4 | 11C5 | 11C1 | 1A | $a^{162}b^{1383}$ |
| $C_{2189}:C_{198}$ | 11C3 | $11$ | $199$ | $C_{11}\times C_{198}$ | 11C-5 | 11C-2 | 11C4 | 1A | $a^{54}b^{736}$ |
| $C_{2189}:C_{198}$ | 11C-3 | $11$ | $199$ | $C_{11}\times C_{198}$ | 11C5 | 11C2 | 11C-4 | 1A | $a^{144}b^{870}$ |
| $C_{2189}:C_{198}$ | 11C4 | $11$ | $199$ | $C_{11}\times C_{198}$ | 11C-3 | 11C1 | 11C-2 | 1A | $a^{72}b^{105}$ |
| $C_{2189}:C_{198}$ | 11C-4 | $11$ | $199$ | $C_{11}\times C_{198}$ | 11C3 | 11C-1 | 11C2 | 1A | $a^{126}b^{1402}$ |
| $C_{2189}:C_{198}$ | 11C5 | $11$ | $199$ | $C_{11}\times C_{198}$ | 11C-1 | 11C4 | 11C3 | 1A | $a^{90}b^{948}$ |
| $C_{2189}:C_{198}$ | 11C-5 | $11$ | $199$ | $C_{11}\times C_{198}$ | 11C1 | 11C-4 | 11C-3 | 1A | $a^{108}b^{526}$ |
| $C_{2189}:C_{198}$ | 11D1 | $11$ | $199$ | $C_{11}\times C_{198}$ | 11D2 | 11D3 | 11D5 | 1A | $a^{18}b^{1004}$ |
| $C_{2189}:C_{198}$ | 11D-1 | $11$ | $199$ | $C_{11}\times C_{198}$ | 11D-2 | 11D-3 | 11D-5 | 1A | $a^{180}b^{1933}$ |
| $C_{2189}:C_{198}$ | 11D2 | $11$ | $199$ | $C_{11}\times C_{198}$ | 11D4 | 11D-5 | 11D-1 | 1A | $a^{36}b^{974}$ |
| $C_{2189}:C_{198}$ | 11D-2 | $11$ | $199$ | $C_{11}\times C_{198}$ | 11D-4 | 11D5 | 11D1 | 1A | $a^{162}b^{577}$ |
| $C_{2189}:C_{198}$ | 11D3 | $11$ | $199$ | $C_{11}\times C_{198}$ | 11D-5 | 11D-2 | 11D4 | 1A | $a^{54}b^{1472}$ |
| $C_{2189}:C_{198}$ | 11D-3 | $11$ | $199$ | $C_{11}\times C_{198}$ | 11D5 | 11D2 | 11D-4 | 1A | $a^{144}b^{1740}$ |
| $C_{2189}:C_{198}$ | 11D4 | $11$ | $199$ | $C_{11}\times C_{198}$ | 11D-3 | 11D1 | 11D-2 | 1A | $a^{72}b^{210}$ |
| $C_{2189}:C_{198}$ | 11D-4 | $11$ | $199$ | $C_{11}\times C_{198}$ | 11D3 | 11D-1 | 11D2 | 1A | $a^{126}b^{615}$ |