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Elements of the group are displayed as words in the presentation $\langle a, b \mid a^{198}=b^{597}=1, b^{a}=b^{436} \rangle$ .
| Group | Label | Order | Size | Centralizer | Powers | Representative | |||
|---|---|---|---|---|---|---|---|---|---|
| 2P | 3P | 11P | 199P | ||||||
| $C_3\times F_{199}$ | 1A | $1$ | $1$ | $C_3\times F_{199}$ | 1A | 1A | 1A | 1A | $1$ |
| $C_3\times F_{199}$ | 2A | $2$ | $199$ | $C_3\times C_{198}$ | 1A | 2A | 2A | 2A | $a^{99}b^{567}$ |
| $C_3\times F_{199}$ | 3A1 | $3$ | $1$ | $C_3\times F_{199}$ | 3A-1 | 1A | 3A-1 | 3A-1 | $b^{199}$ |
| $C_3\times F_{199}$ | 3A-1 | $3$ | $1$ | $C_3\times F_{199}$ | 3A1 | 1A | 3A1 | 3A1 | $b^{398}$ |
| $C_3\times F_{199}$ | 3B1 | $3$ | $199$ | $C_3\times C_{198}$ | 3B-1 | 1A | 3B-1 | 3B-1 | $a^{66}b^{370}$ |
| $C_3\times F_{199}$ | 3B-1 | $3$ | $199$ | $C_3\times C_{198}$ | 3B1 | 1A | 3B1 | 3B1 | $a^{132}b^{182}$ |
| $C_3\times F_{199}$ | 3C1 | $3$ | $199$ | $C_3\times C_{198}$ | 3C-1 | 1A | 3C-1 | 3C-1 | $a^{66}b^{143}$ |
| $C_3\times F_{199}$ | 3C-1 | $3$ | $199$ | $C_3\times C_{198}$ | 3C1 | 1A | 3C1 | 3C1 | $a^{132}b^{364}$ |
| $C_3\times F_{199}$ | 3D1 | $3$ | $199$ | $C_3\times C_{198}$ | 3D-1 | 1A | 3D-1 | 3D-1 | $a^{66}$ |
| $C_3\times F_{199}$ | 3D-1 | $3$ | $199$ | $C_3\times C_{198}$ | 3D1 | 1A | 3D1 | 3D1 | $a^{132}$ |
| $C_3\times F_{199}$ | 6A1 | $6$ | $199$ | $C_3\times C_{198}$ | 3B1 | 2A | 6A-1 | 6A-1 | $a^{33}b^{584}$ |
| $C_3\times F_{199}$ | 6A-1 | $6$ | $199$ | $C_3\times C_{198}$ | 3B-1 | 2A | 6A1 | 6A1 | $a^{165}b^{595}$ |
| $C_3\times F_{199}$ | 6B1 | $6$ | $199$ | $C_3\times C_{198}$ | 3C1 | 2A | 6B-1 | 6B-1 | $a^{33}b^{571}$ |
| $C_3\times F_{199}$ | 6B-1 | $6$ | $199$ | $C_3\times C_{198}$ | 3C-1 | 2A | 6B1 | 6B1 | $a^{165}b^{593}$ |
| $C_3\times F_{199}$ | 6C1 | $6$ | $199$ | $C_3\times C_{198}$ | 3A1 | 2A | 6C-1 | 6C-1 | $a^{99}b^{488}$ |
| $C_3\times F_{199}$ | 6C-1 | $6$ | $199$ | $C_3\times C_{198}$ | 3A-1 | 2A | 6C1 | 6C1 | $a^{99}b^{289}$ |
| $C_3\times F_{199}$ | 6D1 | $6$ | $199$ | $C_3\times C_{198}$ | 3D1 | 2A | 6D-1 | 6D-1 | $a^{33}$ |
| $C_3\times F_{199}$ | 6D-1 | $6$ | $199$ | $C_3\times C_{198}$ | 3D-1 | 2A | 6D1 | 6D1 | $a^{165}$ |
| $C_3\times F_{199}$ | 9A1 | $9$ | $199$ | $C_3\times C_{198}$ | 9A2 | 3D1 | 9A-4 | 9A2 | $a^{22}$ |
| $C_3\times F_{199}$ | 9A-1 | $9$ | $199$ | $C_3\times C_{198}$ | 9A-2 | 3D-1 | 9A4 | 9A-2 | $a^{176}$ |
| $C_3\times F_{199}$ | 9A2 | $9$ | $199$ | $C_3\times C_{198}$ | 9A4 | 3D-1 | 9A1 | 9A4 | $a^{44}$ |
| $C_3\times F_{199}$ | 9A-2 | $9$ | $199$ | $C_3\times C_{198}$ | 9A-4 | 3D1 | 9A-1 | 9A-4 | $a^{154}$ |
| $C_3\times F_{199}$ | 9A4 | $9$ | $199$ | $C_3\times C_{198}$ | 9A-1 | 3D1 | 9A2 | 9A-1 | $a^{88}$ |
| $C_3\times F_{199}$ | 9A-4 | $9$ | $199$ | $C_3\times C_{198}$ | 9A1 | 3D-1 | 9A-2 | 9A1 | $a^{110}$ |
| $C_3\times F_{199}$ | 9B1 | $9$ | $199$ | $C_3\times C_{198}$ | 9B2 | 3D1 | 9B-4 | 9B2 | $a^{22}b^{136}$ |
| $C_3\times F_{199}$ | 9B-1 | $9$ | $199$ | $C_3\times C_{198}$ | 9B-2 | 3D-1 | 9B4 | 9B-2 | $a^{176}b^{80}$ |
| $C_3\times F_{199}$ | 9B2 | $9$ | $199$ | $C_3\times C_{198}$ | 9B4 | 3D-1 | 9B1 | 9B4 | $a^{44}b^{263}$ |
| $C_3\times F_{199}$ | 9B-2 | $9$ | $199$ | $C_3\times C_{198}$ | 9B-4 | 3D1 | 9B-1 | 9B-4 | $a^{154}b^{349}$ |
| $C_3\times F_{199}$ | 9B4 | $9$ | $199$ | $C_3\times C_{198}$ | 9B-1 | 3D1 | 9B2 | 9B-1 | $a^{88}b^{241}$ |
| $C_3\times F_{199}$ | 9B-4 | $9$ | $199$ | $C_3\times C_{198}$ | 9B1 | 3D-1 | 9B-2 | 9B1 | $a^{110}b^{383}$ |
| $C_3\times F_{199}$ | 9C1 | $9$ | $199$ | $C_3\times C_{198}$ | 9C2 | 3D1 | 9C-4 | 9C2 | $a^{22}b^{272}$ |
| $C_3\times F_{199}$ | 9C-1 | $9$ | $199$ | $C_3\times C_{198}$ | 9C-2 | 3D-1 | 9C4 | 9C-2 | $a^{176}b^{160}$ |
| $C_3\times F_{199}$ | 9C2 | $9$ | $199$ | $C_3\times C_{198}$ | 9C4 | 3D-1 | 9C1 | 9C4 | $a^{44}b^{526}$ |
| $C_3\times F_{199}$ | 9C-2 | $9$ | $199$ | $C_3\times C_{198}$ | 9C-4 | 3D1 | 9C-1 | 9C-4 | $a^{154}b^{101}$ |
| $C_3\times F_{199}$ | 9C4 | $9$ | $199$ | $C_3\times C_{198}$ | 9C-1 | 3D1 | 9C2 | 9C-1 | $a^{88}b^{482}$ |
| $C_3\times F_{199}$ | 9C-4 | $9$ | $199$ | $C_3\times C_{198}$ | 9C1 | 3D-1 | 9C-2 | 9C1 | $a^{110}b^{169}$ |
| $C_3\times F_{199}$ | 11A1 | $11$ | $199$ | $C_3\times C_{198}$ | 11A2 | 11A3 | 11A5 | 1A | $a^{18}b^{303}$ |
| $C_3\times F_{199}$ | 11A-1 | $11$ | $199$ | $C_3\times C_{198}$ | 11A-2 | 11A-3 | 11A-5 | 1A | $a^{180}b^{318}$ |
| $C_3\times F_{199}$ | 11A2 | $11$ | $199$ | $C_3\times C_{198}$ | 11A4 | 11A-5 | 11A-1 | 1A | $a^{36}b^{279}$ |
| $C_3\times F_{199}$ | 11A-2 | $11$ | $199$ | $C_3\times C_{198}$ | 11A-4 | 11A5 | 11A1 | 1A | $a^{162}b^{333}$ |
| $C_3\times F_{199}$ | 11A3 | $11$ | $199$ | $C_3\times C_{198}$ | 11A-5 | 11A-2 | 11A4 | 1A | $a^{54}b^{9}$ |
| $C_3\times F_{199}$ | 11A-3 | $11$ | $199$ | $C_3\times C_{198}$ | 11A5 | 11A2 | 11A-4 | 1A | $a^{144}b^{69}$ |
| $C_3\times F_{199}$ | 11A4 | $11$ | $199$ | $C_3\times C_{198}$ | 11A-3 | 11A1 | 11A-2 | 1A | $a^{72}b^{255}$ |
| $C_3\times F_{199}$ | 11A-4 | $11$ | $199$ | $C_3\times C_{198}$ | 11A3 | 11A-1 | 11A2 | 1A | $a^{126}b^{417}$ |
| $C_3\times F_{199}$ | 11A5 | $11$ | $199$ | $C_3\times C_{198}$ | 11A-1 | 11A4 | 11A3 | 1A | $a^{90}b^{336}$ |
| $C_3\times F_{199}$ | 11A-5 | $11$ | $199$ | $C_3\times C_{198}$ | 11A1 | 11A-4 | 11A-3 | 1A | $a^{108}b^{501}$ |
| $C_3\times F_{199}$ | 18A1 | $18$ | $199$ | $C_3\times C_{198}$ | 9A1 | 6D1 | 18A5 | 18A-7 | $a^{11}$ |
| $C_3\times F_{199}$ | 18A-1 | $18$ | $199$ | $C_3\times C_{198}$ | 9A-1 | 6D-1 | 18A-5 | 18A7 | $a^{187}$ |
| $C_3\times F_{199}$ | 18A5 | $18$ | $199$ | $C_3\times C_{198}$ | 9A-4 | 6D-1 | 18A7 | 18A1 | $a^{55}$ |
| $C_3\times F_{199}$ | 18A-5 | $18$ | $199$ | $C_3\times C_{198}$ | 9A4 | 6D1 | 18A-7 | 18A-1 | $a^{143}$ |