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Elements of the group are displayed as words in the presentation $\langle a, b \mid a^{156}=b^{157}=1, b^{a}=b^{26} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 3P 13P 157P
$F_{157}$ 1A $1$ $1$ $F_{157}$ 1A 1A 1A 1A $1$
$F_{157}$ 2A $2$ $157$ $C_{156}$ 1A 2A 2A 2A $a^{78}b^{125}$
$F_{157}$ 3A1 $3$ $157$ $C_{156}$ 3A-1 1A 3A1 3A1 $a^{52}b^{90}$
$F_{157}$ 3A-1 $3$ $157$ $C_{156}$ 3A1 1A 3A-1 3A-1 $a^{104}b^{19}$
$F_{157}$ 4A1 $4$ $157$ $C_{156}$ 2A 4A-1 4A1 4A1 $a^{117}b^{7}$
$F_{157}$ 4A-1 $4$ $157$ $C_{156}$ 2A 4A1 4A-1 4A-1 $a^{39}b^{118}$
$F_{157}$ 6A1 $6$ $157$ $C_{156}$ 3A1 2A 6A1 6A1 $a^{26}b^{106}$
$F_{157}$ 6A-1 $6$ $157$ $C_{156}$ 3A-1 2A 6A-1 6A-1 $a^{130}b^{35}$
$F_{157}$ 12A1 $12$ $157$ $C_{156}$ 6A1 4A1 12A1 12A1 $a^{91}b^{126}$
$F_{157}$ 12A-1 $12$ $157$ $C_{156}$ 6A-1 4A-1 12A-1 12A-1 $a^{65}b^{103}$
$F_{157}$ 12A5 $12$ $157$ $C_{156}$ 6A-1 4A1 12A5 12A5 $a^{143}b^{22}$
$F_{157}$ 12A-5 $12$ $157$ $C_{156}$ 6A1 4A-1 12A-5 12A-5 $a^{13}b^{156}$
$F_{157}$ 13A1 $13$ $157$ $C_{156}$ 13A2 13A3 1A 13A1 $a^{84}b^{59}$
$F_{157}$ 13A-1 $13$ $157$ $C_{156}$ 13A-2 13A-3 1A 13A-1 $a^{72}b^{23}$
$F_{157}$ 13A2 $13$ $157$ $C_{156}$ 13A4 13A6 1A 13A2 $a^{12}b^{51}$
$F_{157}$ 13A-2 $13$ $157$ $C_{156}$ 13A-4 13A-6 1A 13A-2 $a^{144}b^{30}$
$F_{157}$ 13A3 $13$ $157$ $C_{156}$ 13A6 13A-4 1A 13A3 $a^{96}b^{92}$
$F_{157}$ 13A-3 $13$ $157$ $C_{156}$ 13A-6 13A4 1A 13A-3 $a^{60}b^{155}$
$F_{157}$ 13A4 $13$ $157$ $C_{156}$ 13A-5 13A-1 1A 13A4 $a^{24}b^{137}$
$F_{157}$ 13A-4 $13$ $157$ $C_{156}$ 13A5 13A1 1A 13A-4 $a^{132}b^{77}$
$F_{157}$ 13A5 $13$ $157$ $C_{156}$ 13A-3 13A2 1A 13A5 $a^{108}b^{83}$
$F_{157}$ 13A-5 $13$ $157$ $C_{156}$ 13A3 13A-2 1A 13A-5 $a^{48}b^{142}$
$F_{157}$ 13A6 $13$ $157$ $C_{156}$ 13A-1 13A5 1A 13A6 $a^{36}b^{85}$
$F_{157}$ 13A-6 $13$ $157$ $C_{156}$ 13A1 13A-5 1A 13A-6 $a^{120}b^{114}$
$F_{157}$ 26A1 $26$ $157$ $C_{156}$ 13A1 26A3 2A 26A1 $a^{42}b^{11}$
$F_{157}$ 26A-1 $26$ $157$ $C_{156}$ 13A-1 26A-3 2A 26A-1 $a^{114}b^{40}$
$F_{157}$ 26A3 $26$ $157$ $C_{156}$ 13A3 26A9 2A 26A3 $a^{126}b^{140}$
$F_{157}$ 26A-3 $26$ $157$ $C_{156}$ 13A-3 26A-9 2A 26A-3 $a^{30}b^{42}$
$F_{157}$ 26A5 $26$ $157$ $C_{156}$ 13A5 26A-11 2A 26A5 $a^{54}b^{48}$
$F_{157}$ 26A-5 $26$ $157$ $C_{156}$ 13A-5 26A11 2A 26A-5 $a^{102}b^{145}$
$F_{157}$ 26A7 $26$ $157$ $C_{156}$ 13A-6 26A-5 2A 26A7 $a^{138}b^{127}$
$F_{157}$ 26A-7 $26$ $157$ $C_{156}$ 13A6 26A5 2A 26A-7 $a^{18}b^{33}$
$F_{157}$ 26A9 $26$ $157$ $C_{156}$ 13A-4 26A1 2A 26A9 $a^{66}b^{95}$
$F_{157}$ 26A-9 $26$ $157$ $C_{156}$ 13A4 26A-1 2A 26A-9 $a^{90}b^{74}$
$F_{157}$ 26A11 $26$ $157$ $C_{156}$ 13A-2 26A7 2A 26A11 $a^{150}b^{102}$
$F_{157}$ 26A-11 $26$ $157$ $C_{156}$ 13A2 26A-7 2A 26A-11 $a^{6}b^{66}$
$F_{157}$ 39A1 $39$ $157$ $C_{156}$ 39A2 13A1 3A1 39A1 $a^{28}b^{31}$
$F_{157}$ 39A-1 $39$ $157$ $C_{156}$ 39A-2 13A-1 3A-1 39A-1 $a^{128}b^{93}$
$F_{157}$ 39A2 $39$ $157$ $C_{156}$ 39A4 13A2 3A-1 39A2 $a^{56}b^{73}$
$F_{157}$ 39A-2 $39$ $157$ $C_{156}$ 39A-4 13A-2 3A1 39A-2 $a^{100}b^{128}$
$F_{157}$ 39A4 $39$ $157$ $C_{156}$ 39A8 13A4 3A1 39A4 $a^{112}b^{116}$
$F_{157}$ 39A-4 $39$ $157$ $C_{156}$ 39A-8 13A-4 3A-1 39A-4 $a^{44}b^{24}$
$F_{157}$ 39A5 $39$ $157$ $C_{156}$ 39A10 13A5 3A-1 39A5 $a^{140}b^{97}$
$F_{157}$ 39A-5 $39$ $157$ $C_{156}$ 39A-10 13A-5 3A1 39A-5 $a^{16}b^{21}$
$F_{157}$ 39A7 $39$ $157$ $C_{156}$ 39A14 13A-6 3A1 39A7 $a^{40}b^{14}$
$F_{157}$ 39A-7 $39$ $157$ $C_{156}$ 39A-14 13A6 3A-1 39A-7 $a^{116}b^{3}$
$F_{157}$ 39A8 $39$ $157$ $C_{156}$ 39A16 13A-5 3A-1 39A8 $a^{68}b^{131}$
$F_{157}$ 39A-8 $39$ $157$ $C_{156}$ 39A-16 13A5 3A1 39A-8 $a^{88}b^{84}$
$F_{157}$ 39A10 $39$ $157$ $C_{156}$ 39A-19 13A-3 3A1 39A10 $a^{124}b^{105}$
$F_{157}$ 39A-10 $39$ $157$ $C_{156}$ 39A19 13A3 3A-1 39A-10 $a^{32}b^{99}$
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