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Elements of the group are displayed as words in the presentation $\langle a, b \mid a^{228}=b^{229}=1, b^{a}=b^{142} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 3P 19P 229P
$F_{229}$ 1A $1$ $1$ $F_{229}$ 1A 1A 1A 1A $1$
$F_{229}$ 2A $2$ $229$ $C_{228}$ 1A 2A 2A 2A $a^{114}b^{143}$
$F_{229}$ 3A1 $3$ $229$ $C_{228}$ 3A-1 1A 3A1 3A1 $a^{76}b^{106}$
$F_{229}$ 3A-1 $3$ $229$ $C_{228}$ 3A1 1A 3A-1 3A-1 $a^{152}b^{223}$
$F_{229}$ 4A1 $4$ $229$ $C_{228}$ 2A 4A-1 4A-1 4A1 $a^{171}b^{165}$
$F_{229}$ 4A-1 $4$ $229$ $C_{228}$ 2A 4A1 4A1 4A-1 $a^{57}b^{207}$
$F_{229}$ 6A1 $6$ $229$ $C_{228}$ 3A1 2A 6A1 6A1 $a^{38}b^{149}$
$F_{229}$ 6A-1 $6$ $229$ $C_{228}$ 3A-1 2A 6A-1 6A-1 $a^{190}b^{37}$
$F_{229}$ 12A1 $12$ $229$ $C_{228}$ 6A1 4A1 12A-5 12A1 $a^{133}b^{99}$
$F_{229}$ 12A-1 $12$ $229$ $C_{228}$ 6A-1 4A-1 12A5 12A-1 $a^{95}b^{120}$
$F_{229}$ 12A5 $12$ $229$ $C_{228}$ 6A-1 4A1 12A-1 12A5 $a^{209}b^{23}$
$F_{229}$ 12A-5 $12$ $229$ $C_{228}$ 6A1 4A-1 12A1 12A-5 $a^{19}b^{44}$
$F_{229}$ 19A1 $19$ $229$ $C_{228}$ 19A2 19A3 1A 19A1 $a^{132}b^{187}$
$F_{229}$ 19A-1 $19$ $229$ $C_{228}$ 19A-2 19A-3 1A 19A-1 $a^{96}b^{203}$
$F_{229}$ 19A2 $19$ $229$ $C_{228}$ 19A4 19A6 1A 19A2 $a^{36}b^{202}$
$F_{229}$ 19A-2 $19$ $229$ $C_{228}$ 19A-4 19A-6 1A 19A-2 $a^{192}b$
$F_{229}$ 19A3 $19$ $229$ $C_{228}$ 19A6 19A9 1A 19A3 $a^{168}b^{213}$
$F_{229}$ 19A-3 $19$ $229$ $C_{228}$ 19A-6 19A-9 1A 19A-3 $a^{60}b^{17}$
$F_{229}$ 19A4 $19$ $229$ $C_{228}$ 19A8 19A-7 1A 19A4 $a^{72}b^{160}$
$F_{229}$ 19A-4 $19$ $229$ $C_{228}$ 19A-8 19A7 1A 19A-4 $a^{156}b^{18}$
$F_{229}$ 19A5 $19$ $229$ $C_{228}$ 19A-9 19A-4 1A 19A5 $a^{204}b^{228}$
$F_{229}$ 19A-5 $19$ $229$ $C_{228}$ 19A9 19A4 1A 19A-5 $a^{24}b^{61}$
$F_{229}$ 19A6 $19$ $229$ $C_{228}$ 19A-7 19A-1 1A 19A6 $a^{108}b^{171}$
$F_{229}$ 19A-6 $19$ $229$ $C_{228}$ 19A7 19A1 1A 19A-6 $a^{120}b^{78}$
$F_{229}$ 19A7 $19$ $229$ $C_{228}$ 19A-5 19A2 1A 19A7 $a^{12}b^{175}$
$F_{229}$ 19A-7 $19$ $229$ $C_{228}$ 19A5 19A-2 1A 19A-7 $a^{216}b^{122}$
$F_{229}$ 19A8 $19$ $229$ $C_{228}$ 19A-3 19A5 1A 19A8 $a^{144}b^{10}$
$F_{229}$ 19A-8 $19$ $229$ $C_{228}$ 19A3 19A-5 1A 19A-8 $a^{84}b^{182}$
$F_{229}$ 19A9 $19$ $229$ $C_{228}$ 19A-1 19A8 1A 19A9 $a^{48}b^{118}$
$F_{229}$ 19A-9 $19$ $229$ $C_{228}$ 19A1 19A-8 1A 19A-9 $a^{180}b^{14}$
$F_{229}$ 38A1 $38$ $229$ $C_{228}$ 19A1 38A3 2A 38A1 $a^{66}b^{129}$
$F_{229}$ 38A-1 $38$ $229$ $C_{228}$ 19A-1 38A-3 2A 38A-1 $a^{162}b^{25}$
$F_{229}$ 38A3 $38$ $229$ $C_{228}$ 19A3 38A9 2A 38A3 $a^{198}b^{190}$
$F_{229}$ 38A-3 $38$ $229$ $C_{228}$ 19A-3 38A-9 2A 38A-3 $a^{30}b^{133}$
$F_{229}$ 38A5 $38$ $229$ $C_{228}$ 19A5 38A15 2A 38A5 $a^{102}b^{21}$
$F_{229}$ 38A-5 $38$ $229$ $C_{228}$ 19A-5 38A-15 2A 38A-5 $a^{126}b^{197}$
$F_{229}$ 38A7 $38$ $229$ $C_{228}$ 19A7 38A-17 2A 38A7 $a^{6}b^{65}$
$F_{229}$ 38A-7 $38$ $229$ $C_{228}$ 19A-7 38A17 2A 38A-7 $a^{222}b^{201}$
$F_{229}$ 38A9 $38$ $229$ $C_{228}$ 19A9 38A-11 2A 38A9 $a^{138}b^{82}$
$F_{229}$ 38A-9 $38$ $229$ $C_{228}$ 19A-9 38A11 2A 38A-9 $a^{90}b^{144}$
$F_{229}$ 38A11 $38$ $229$ $C_{228}$ 19A-8 38A-5 2A 38A11 $a^{42}b^{125}$
$F_{229}$ 38A-11 $38$ $229$ $C_{228}$ 19A8 38A5 2A 38A-11 $a^{186}b^{212}$
$F_{229}$ 38A13 $38$ $229$ $C_{228}$ 19A-6 38A1 2A 38A13 $a^{174}b^{126}$
$F_{229}$ 38A-13 $38$ $229$ $C_{228}$ 19A6 38A-1 2A 38A-13 $a^{54}b^{159}$
$F_{229}$ 38A15 $38$ $229$ $C_{228}$ 19A-4 38A7 2A 38A15 $a^{78}b^{142}$
$F_{229}$ 38A-15 $38$ $229$ $C_{228}$ 19A4 38A-7 2A 38A-15 $a^{150}b^{170}$
$F_{229}$ 38A17 $38$ $229$ $C_{228}$ 19A-2 38A13 2A 38A17 $a^{210}b^{169}$
$F_{229}$ 38A-17 $38$ $229$ $C_{228}$ 19A2 38A-13 2A 38A-17 $a^{18}b^{185}$
$F_{229}$ 57A1 $57$ $229$ $C_{228}$ 57A2 19A1 3A1 57A1 $a^{196}b^{110}$
$F_{229}$ 57A-1 $57$ $229$ $C_{228}$ 57A-2 19A-1 3A-1 57A-1 $a^{32}b^{8}$
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