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Elements of the group are displayed as words in the presentation $\langle a, b \mid a^{119}=b^{478}=1, b^{a}=b^{437} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 7P 17P 239P
$C_{239}:C_{238}$ 1A $1$ $1$ $C_{239}:C_{238}$ 1A 1A 1A 1A $1$
$C_{239}:C_{238}$ 2A $2$ $1$ $C_{239}:C_{238}$ 1A 2A 2A 2A $b^{239}$
$C_{239}:C_{238}$ 7A1 $7$ $239$ $C_{238}$ 7A2 7A3 1A 7A3 $a^{102}b^{356}$
$C_{239}:C_{238}$ 7A-1 $7$ $239$ $C_{238}$ 7A-2 7A-3 1A 7A-3 $a^{17}b^{110}$
$C_{239}:C_{238}$ 7A2 $7$ $239$ $C_{238}$ 7A-3 7A-1 1A 7A-1 $a^{85}b^{212}$
$C_{239}:C_{238}$ 7A-2 $7$ $239$ $C_{238}$ 7A3 7A1 1A 7A1 $a^{34}b^{170}$
$C_{239}:C_{238}$ 7A3 $7$ $239$ $C_{238}$ 7A-1 7A2 1A 7A2 $a^{68}b^{426}$
$C_{239}:C_{238}$ 7A-3 $7$ $239$ $C_{238}$ 7A1 7A-2 1A 7A-2 $a^{51}b^{420}$
$C_{239}:C_{238}$ 14A1 $14$ $239$ $C_{238}$ 7A1 14A3 2A 14A3 $a^{51}b^{181}$
$C_{239}:C_{238}$ 14A-1 $14$ $239$ $C_{238}$ 7A-1 14A-3 2A 14A-3 $a^{68}b^{187}$
$C_{239}:C_{238}$ 14A3 $14$ $239$ $C_{238}$ 7A3 14A-5 2A 14A-5 $a^{34}b^{409}$
$C_{239}:C_{238}$ 14A-3 $14$ $239$ $C_{238}$ 7A-3 14A5 2A 14A5 $a^{85}b^{451}$
$C_{239}:C_{238}$ 14A5 $14$ $239$ $C_{238}$ 7A-2 14A1 2A 14A1 $a^{17}b^{349}$
$C_{239}:C_{238}$ 14A-5 $14$ $239$ $C_{238}$ 7A2 14A-1 2A 14A-1 $a^{102}b^{117}$
$C_{239}:C_{238}$ 17A1 $17$ $239$ $C_{238}$ 17A2 17A3 17A7 1A $a^{98}b^{72}$
$C_{239}:C_{238}$ 17A-1 $17$ $239$ $C_{238}$ 17A-2 17A-3 17A-7 1A $a^{21}b^{398}$
$C_{239}:C_{238}$ 17A2 $17$ $239$ $C_{238}$ 17A4 17A6 17A-3 1A $a^{77}b^{328}$
$C_{239}:C_{238}$ 17A-2 $17$ $239$ $C_{238}$ 17A-4 17A-6 17A3 1A $a^{42}b^{256}$
$C_{239}:C_{238}$ 17A3 $17$ $239$ $C_{238}$ 17A6 17A-8 17A4 1A $a^{56}b^{176}$
$C_{239}:C_{238}$ 17A-3 $17$ $239$ $C_{238}$ 17A-6 17A8 17A-4 1A $a^{63}b^{470}$
$C_{239}:C_{238}$ 17A4 $17$ $239$ $C_{238}$ 17A8 17A-5 17A-6 1A $a^{35}b^{326}$
$C_{239}:C_{238}$ 17A-4 $17$ $239$ $C_{238}$ 17A-8 17A5 17A6 1A $a^{84}b^{336}$
$C_{239}:C_{238}$ 17A5 $17$ $239$ $C_{238}$ 17A-7 17A-2 17A1 1A $a^{14}b^{222}$
$C_{239}:C_{238}$ 17A-5 $17$ $239$ $C_{238}$ 17A7 17A2 17A-1 1A $a^{105}b^{134}$
$C_{239}:C_{238}$ 17A6 $17$ $239$ $C_{238}$ 17A-5 17A1 17A8 1A $a^{112}b^{224}$
$C_{239}:C_{238}$ 17A-6 $17$ $239$ $C_{238}$ 17A5 17A-1 17A-8 1A $a^{7}b^{122}$
$C_{239}:C_{238}$ 17A7 $17$ $239$ $C_{238}$ 17A-3 17A4 17A-2 1A $a^{91}b^{178}$
$C_{239}:C_{238}$ 17A-7 $17$ $239$ $C_{238}$ 17A3 17A-4 17A2 1A $a^{28}b^{268}$
$C_{239}:C_{238}$ 17A8 $17$ $239$ $C_{238}$ 17A-1 17A7 17A5 1A $a^{70}b^{280}$
$C_{239}:C_{238}$ 17A-8 $17$ $239$ $C_{238}$ 17A1 17A-7 17A-5 1A $a^{49}b^{324}$
$C_{239}:C_{238}$ 34A1 $34$ $239$ $C_{238}$ 17A1 34A3 34A7 2A $a^{49}b^{85}$
$C_{239}:C_{238}$ 34A-1 $34$ $239$ $C_{238}$ 17A-1 34A-3 34A-7 2A $a^{70}b^{41}$
$C_{239}:C_{238}$ 34A3 $34$ $239$ $C_{238}$ 17A3 34A9 34A-13 2A $a^{28}b^{29}$
$C_{239}:C_{238}$ 34A-3 $34$ $239$ $C_{238}$ 17A-3 34A-9 34A13 2A $a^{91}b^{417}$
$C_{239}:C_{238}$ 34A5 $34$ $239$ $C_{238}$ 17A5 34A15 34A1 2A $a^{7}b^{361}$
$C_{239}:C_{238}$ 34A-5 $34$ $239$ $C_{238}$ 17A-5 34A-15 34A-1 2A $a^{112}b^{463}$
$C_{239}:C_{238}$ 34A7 $34$ $239$ $C_{238}$ 17A7 34A-13 34A15 2A $a^{105}b^{373}$
$C_{239}:C_{238}$ 34A-7 $34$ $239$ $C_{238}$ 17A-7 34A13 34A-15 2A $a^{14}b^{461}$
$C_{239}:C_{238}$ 34A9 $34$ $239$ $C_{238}$ 17A-8 34A-7 34A-5 2A $a^{84}b^{97}$
$C_{239}:C_{238}$ 34A-9 $34$ $239$ $C_{238}$ 17A8 34A7 34A5 2A $a^{35}b^{87}$
$C_{239}:C_{238}$ 34A11 $34$ $239$ $C_{238}$ 17A-6 34A-1 34A9 2A $a^{63}b^{231}$
$C_{239}:C_{238}$ 34A-11 $34$ $239$ $C_{238}$ 17A6 34A1 34A-9 2A $a^{56}b^{415}$
$C_{239}:C_{238}$ 34A13 $34$ $239$ $C_{238}$ 17A-4 34A5 34A-11 2A $a^{42}b^{17}$
$C_{239}:C_{238}$ 34A-13 $34$ $239$ $C_{238}$ 17A4 34A-5 34A11 2A $a^{77}b^{89}$
$C_{239}:C_{238}$ 34A15 $34$ $239$ $C_{238}$ 17A-2 34A11 34A3 2A $a^{21}b^{159}$
$C_{239}:C_{238}$ 34A-15 $34$ $239$ $C_{238}$ 17A2 34A-11 34A-3 2A $a^{98}b^{311}$
$C_{239}:C_{238}$ 119A1 $119$ $239$ $C_{238}$ 119A2 119A3 17A1 7A1 $a^{48}b^{240}$
$C_{239}:C_{238}$ 119A-1 $119$ $239$ $C_{238}$ 119A-2 119A-3 17A-1 7A-1 $a^{71}b^{118}$
$C_{239}:C_{238}$ 119A2 $119$ $239$ $C_{238}$ 119A4 119A6 17A2 7A2 $a^{96}b^{400}$
$C_{239}:C_{238}$ 119A-2 $119$ $239$ $C_{238}$ 119A-4 119A-6 17A-2 7A-2 $a^{23}b^{56}$
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