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Elements of the group are displayed as words in the presentation $\langle a, b \mid a^{4}=b^{104}=1, b^{a}=b^{57} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 13P
$C_{104}:C_4$ 1A $1$ $1$ $C_{104}:C_4$ 1A 1A $1$
$C_{104}:C_4$ 2A $2$ $1$ $C_{104}:C_4$ 1A 2A $b^{52}$
$C_{104}:C_4$ 2B $2$ $13$ $C_4\times C_8$ 1A 2B $a^{2}$
$C_{104}:C_4$ 2C $2$ $13$ $C_4\times C_8$ 1A 2C $a^{2}b^{12}$
$C_{104}:C_4$ 4A1 $4$ $1$ $C_{104}:C_4$ 2A 4A-1 $b^{26}$
$C_{104}:C_4$ 4A-1 $4$ $1$ $C_{104}:C_4$ 2A 4A1 $b^{78}$
$C_{104}:C_4$ 4B1 $4$ $13$ $C_4\times C_8$ 2B 4B-1 $a$
$C_{104}:C_4$ 4B-1 $4$ $13$ $C_4\times C_8$ 2B 4B1 $a^{3}$
$C_{104}:C_4$ 4C1 $4$ $13$ $C_4\times C_8$ 2B 4C-1 $ab^{4}$
$C_{104}:C_4$ 4C-1 $4$ $13$ $C_4\times C_8$ 2B 4C1 $a^{3}b^{4}$
$C_{104}:C_4$ 4D1 $4$ $13$ $C_4\times C_8$ 2C 4D-1 $ab^{2}$
$C_{104}:C_4$ 4D-1 $4$ $13$ $C_4\times C_8$ 2C 4D1 $a^{3}b^{6}$
$C_{104}:C_4$ 4E1 $4$ $13$ $C_4\times C_8$ 2C 4E-1 $ab^{6}$
$C_{104}:C_4$ 4E-1 $4$ $13$ $C_4\times C_8$ 2C 4E1 $a^{3}b^{2}$
$C_{104}:C_4$ 4F1 $4$ $13$ $C_4\times C_8$ 2A 4F-1 $a^{2}b^{58}$
$C_{104}:C_4$ 4F-1 $4$ $13$ $C_4\times C_8$ 2A 4F1 $a^{2}b^{6}$
$C_{104}:C_4$ 8A1 $8$ $1$ $C_{104}:C_4$ 4A1 8A3 $b^{13}$
$C_{104}:C_4$ 8A-1 $8$ $1$ $C_{104}:C_4$ 4A-1 8A-3 $b^{91}$
$C_{104}:C_4$ 8A3 $8$ $1$ $C_{104}:C_4$ 4A-1 8A1 $b^{39}$
$C_{104}:C_4$ 8A-3 $8$ $1$ $C_{104}:C_4$ 4A1 8A-1 $b^{65}$
$C_{104}:C_4$ 8B1 $8$ $13$ $C_4\times C_8$ 4A1 8B3 $a^{2}b$
$C_{104}:C_4$ 8B-1 $8$ $13$ $C_4\times C_8$ 4A-1 8B-3 $a^{2}b^{7}$
$C_{104}:C_4$ 8B3 $8$ $13$ $C_4\times C_8$ 4A-1 8B1 $a^{2}b^{3}$
$C_{104}:C_4$ 8B-3 $8$ $13$ $C_4\times C_8$ 4A1 8B-1 $a^{2}b^{5}$
$C_{104}:C_4$ 8C1 $8$ $13$ $C_4\times C_8$ 4F1 8C3 $ab$
$C_{104}:C_4$ 8C-1 $8$ $13$ $C_4\times C_8$ 4F-1 8C-3 $a^{3}b^{7}$
$C_{104}:C_4$ 8C3 $8$ $13$ $C_4\times C_8$ 4F-1 8C1 $a^{3}b^{3}$
$C_{104}:C_4$ 8C-3 $8$ $13$ $C_4\times C_8$ 4F1 8C-1 $ab^{5}$
$C_{104}:C_4$ 8D1 $8$ $13$ $C_4\times C_8$ 4F-1 8D3 $ab^{3}$
$C_{104}:C_4$ 8D-1 $8$ $13$ $C_4\times C_8$ 4F1 8D-3 $a^{3}b^{5}$
$C_{104}:C_4$ 8D3 $8$ $13$ $C_4\times C_8$ 4F1 8D1 $a^{3}b$
$C_{104}:C_4$ 8D-3 $8$ $13$ $C_4\times C_8$ 4F-1 8D-1 $ab^{7}$
$C_{104}:C_4$ 13A1 $13$ $4$ $C_{104}$ 13A2 13A2 $b^{8}$
$C_{104}:C_4$ 13A2 $13$ $4$ $C_{104}$ 13A4 13A4 $b^{16}$
$C_{104}:C_4$ 13A4 $13$ $4$ $C_{104}$ 13A1 13A1 $b^{32}$
$C_{104}:C_4$ 26A1 $26$ $4$ $C_{104}$ 13A1 26A3 $b^{4}$
$C_{104}:C_4$ 26A3 $26$ $4$ $C_{104}$ 13A2 26A7 $b^{12}$
$C_{104}:C_4$ 26A7 $26$ $4$ $C_{104}$ 13A4 26A1 $b^{28}$
$C_{104}:C_4$ 52A1 $52$ $4$ $C_{104}$ 26A1 52A3 $b^{2}$
$C_{104}:C_4$ 52A-1 $52$ $4$ $C_{104}$ 26A1 52A-3 $b^{102}$
$C_{104}:C_4$ 52A3 $52$ $4$ $C_{104}$ 26A3 52A-7 $b^{6}$
$C_{104}:C_4$ 52A-3 $52$ $4$ $C_{104}$ 26A3 52A7 $b^{98}$
$C_{104}:C_4$ 52A7 $52$ $4$ $C_{104}$ 26A7 52A1 $b^{14}$
$C_{104}:C_4$ 52A-7 $52$ $4$ $C_{104}$ 26A7 52A-1 $b^{90}$
$C_{104}:C_4$ 104A1 $104$ $4$ $C_{104}$ 52A1 104A3 $b$
$C_{104}:C_4$ 104A-1 $104$ $4$ $C_{104}$ 52A-1 104A-3 $b^{31}$
$C_{104}:C_4$ 104A3 $104$ $4$ $C_{104}$ 52A3 104A-7 $b^{3}$
$C_{104}:C_4$ 104A-3 $104$ $4$ $C_{104}$ 52A-3 104A7 $b^{29}$
$C_{104}:C_4$ 104A5 $104$ $4$ $C_{104}$ 52A1 104A15 $b^{5}$
$C_{104}:C_4$ 104A-5 $104$ $4$ $C_{104}$ 52A-1 104A-15 $b^{27}$
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