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Elements of the group are displayed as words in the presentation $\langle a, b \mid a^{210}=b^{211}=1, b^{a}=b^{92} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 3P 5P 7P 211P
$F_{211}$ 1A $1$ $1$ $F_{211}$ 1A 1A 1A 1A 1A $1$
$F_{211}$ 2A $2$ $211$ $C_{210}$ 1A 2A 2A 2A 2A $a^{105}b^{121}$
$F_{211}$ 3A1 $3$ $211$ $C_{210}$ 3A-1 1A 3A-1 3A1 3A1 $a^{70}b^{163}$
$F_{211}$ 3A-1 $3$ $211$ $C_{210}$ 3A1 1A 3A1 3A-1 3A-1 $a^{140}b^{124}$
$F_{211}$ 5A1 $5$ $211$ $C_{210}$ 5A2 5A-2 1A 5A2 5A1 $a^{84}b^{128}$
$F_{211}$ 5A-1 $5$ $211$ $C_{210}$ 5A-2 5A2 1A 5A-2 5A-1 $a^{126}b^{196}$
$F_{211}$ 5A2 $5$ $211$ $C_{210}$ 5A-1 5A1 1A 5A-1 5A2 $a^{168}b^{109}$
$F_{211}$ 5A-2 $5$ $211$ $C_{210}$ 5A1 5A-1 1A 5A1 5A-2 $a^{42}b^{186}$
$F_{211}$ 6A1 $6$ $211$ $C_{210}$ 3A1 2A 6A-1 6A1 6A1 $a^{35}b^{208}$
$F_{211}$ 6A-1 $6$ $211$ $C_{210}$ 3A-1 2A 6A1 6A-1 6A-1 $a^{175}b^{169}$
$F_{211}$ 7A1 $7$ $211$ $C_{210}$ 7A2 7A3 7A-2 1A 7A1 $a^{90}b^{33}$
$F_{211}$ 7A-1 $7$ $211$ $C_{210}$ 7A-2 7A-3 7A2 1A 7A-1 $a^{120}b^{54}$
$F_{211}$ 7A2 $7$ $211$ $C_{210}$ 7A-3 7A-1 7A3 1A 7A2 $a^{180}b^{48}$
$F_{211}$ 7A-2 $7$ $211$ $C_{210}$ 7A3 7A1 7A-3 1A 7A-2 $a^{30}b^{4}$
$F_{211}$ 7A3 $7$ $211$ $C_{210}$ 7A-1 7A2 7A1 1A 7A3 $a^{60}b^{74}$
$F_{211}$ 7A-3 $7$ $211$ $C_{210}$ 7A1 7A-2 7A-1 1A 7A-3 $a^{150}b^{105}$
$F_{211}$ 10A1 $10$ $211$ $C_{210}$ 5A1 10A3 2A 10A-3 10A1 $a^{147}b^{146}$
$F_{211}$ 10A-1 $10$ $211$ $C_{210}$ 5A-1 10A-3 2A 10A3 10A-1 $a^{63}b^{12}$
$F_{211}$ 10A3 $10$ $211$ $C_{210}$ 5A-2 10A-1 2A 10A1 10A3 $a^{21}b^{136}$
$F_{211}$ 10A-3 $10$ $211$ $C_{210}$ 5A2 10A1 2A 10A-1 10A-3 $a^{189}b^{204}$
$F_{211}$ 14A1 $14$ $211$ $C_{210}$ 7A1 14A3 14A5 2A 14A1 $a^{45}b^{16}$
$F_{211}$ 14A-1 $14$ $211$ $C_{210}$ 7A-1 14A-3 14A-5 2A 14A-1 $a^{165}b^{47}$
$F_{211}$ 14A3 $14$ $211$ $C_{210}$ 7A3 14A-5 14A1 2A 14A3 $a^{135}b^{117}$
$F_{211}$ 14A-3 $14$ $211$ $C_{210}$ 7A-3 14A5 14A-1 2A 14A-3 $a^{75}b^{73}$
$F_{211}$ 14A5 $14$ $211$ $C_{210}$ 7A-2 14A1 14A-3 2A 14A5 $a^{15}b^{67}$
$F_{211}$ 14A-5 $14$ $211$ $C_{210}$ 7A2 14A-1 14A3 2A 14A-5 $a^{195}b^{88}$
$F_{211}$ 15A1 $15$ $211$ $C_{210}$ 15A2 5A1 3A1 15A7 15A1 $a^{98}b^{177}$
$F_{211}$ 15A-1 $15$ $211$ $C_{210}$ 15A-2 5A-1 3A-1 15A-7 15A-1 $a^{112}b^{24}$
$F_{211}$ 15A2 $15$ $211$ $C_{210}$ 15A4 5A2 3A-1 15A-1 15A2 $a^{196}b^{164}$
$F_{211}$ 15A-2 $15$ $211$ $C_{210}$ 15A-4 5A-2 3A1 15A1 15A-2 $a^{14}b^{103}$
$F_{211}$ 15A4 $15$ $211$ $C_{210}$ 15A-7 5A-1 3A1 15A-2 15A4 $a^{182}b^{77}$
$F_{211}$ 15A-4 $15$ $211$ $C_{210}$ 15A7 5A1 3A-1 15A2 15A-4 $a^{28}b$
$F_{211}$ 15A7 $15$ $211$ $C_{210}$ 15A-1 5A2 3A1 15A4 15A7 $a^{56}b^{138}$
$F_{211}$ 15A-7 $15$ $211$ $C_{210}$ 15A1 5A-2 3A-1 15A-4 15A-7 $a^{154}b^{56}$
$F_{211}$ 21A1 $21$ $211$ $C_{210}$ 21A2 7A1 21A5 3A1 21A1 $a^{100}b^{8}$
$F_{211}$ 21A-1 $21$ $211$ $C_{210}$ 21A-2 7A-1 21A-5 3A-1 21A-1 $a^{110}b^{37}$
$F_{211}$ 21A2 $21$ $211$ $C_{210}$ 21A4 7A2 21A10 3A-1 21A2 $a^{200}b^{69}$
$F_{211}$ 21A-2 $21$ $211$ $C_{210}$ 21A-4 7A-2 21A-10 3A1 21A-2 $a^{10}b^{156}$
$F_{211}$ 21A4 $21$ $211$ $C_{210}$ 21A8 7A-3 21A-1 3A1 21A4 $a^{190}b^{75}$
$F_{211}$ 21A-4 $21$ $211$ $C_{210}$ 21A-8 7A3 21A1 3A-1 21A-4 $a^{20}b^{51}$
$F_{211}$ 21A5 $21$ $211$ $C_{210}$ 21A10 7A-2 21A4 3A-1 21A5 $a^{80}b^{26}$
$F_{211}$ 21A-5 $21$ $211$ $C_{210}$ 21A-10 7A2 21A-4 3A1 21A-5 $a^{130}b^{144}$
$F_{211}$ 21A8 $21$ $211$ $C_{210}$ 21A-5 7A1 21A-2 3A-1 21A8 $a^{170}b^{64}$
$F_{211}$ 21A-8 $21$ $211$ $C_{210}$ 21A5 7A-1 21A2 3A1 21A-8 $a^{40}b^{202}$
$F_{211}$ 21A10 $21$ $211$ $C_{210}$ 21A-1 7A3 21A8 3A1 21A10 $a^{160}b^{203}$
$F_{211}$ 21A-10 $21$ $211$ $C_{210}$ 21A1 7A-3 21A-8 3A-1 21A-10 $a^{50}b^{158}$
$F_{211}$ 30A1 $30$ $211$ $C_{210}$ 15A1 10A1 6A1 30A7 30A1 $a^{49}b^{65}$
$F_{211}$ 30A-1 $30$ $211$ $C_{210}$ 15A-1 10A-1 6A-1 30A-7 30A-1 $a^{161}b^{194}$
$F_{211}$ 30A7 $30$ $211$ $C_{210}$ 15A7 10A-3 6A1 30A-11 30A7 $a^{133}b^{120}$
$F_{211}$ 30A-7 $30$ $211$ $C_{210}$ 15A-7 10A3 6A-1 30A11 30A-7 $a^{77}b^{44}$
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