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Elements of the group are displayed as words in the presentation $\langle a, b, c \mid a^{4}=b^{2}=c^{115}=[a,b]=1, c^{a}=c^{24}, c^{b}=c^{114} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 5P 23P
$D_{115}:C_4$ 1A $1$ $1$ $D_{115}:C_4$ 1A 1A 1A $1$
$D_{115}:C_4$ 2A $2$ $1$ $D_{115}:C_4$ 1A 2A 2A $a^{2}$
$D_{115}:C_4$ 2B $2$ $115$ $C_2\times C_4$ 1A 2B 2B $a^{2}bc^{78}$
$D_{115}:C_4$ 2C $2$ $115$ $C_2\times C_4$ 1A 2C 2C $bc^{42}$
$D_{115}:C_4$ 4A1 $4$ $5$ $C_4\times D_{23}$ 2A 4A1 4A-1 $a^{3}$
$D_{115}:C_4$ 4A-1 $4$ $5$ $C_4\times D_{23}$ 2A 4A-1 4A1 $a$
$D_{115}:C_4$ 4B1 $4$ $23$ $C_4\times D_5$ 2A 4B1 4B-1 $a^{3}bc^{5}$
$D_{115}:C_4$ 4B-1 $4$ $23$ $C_4\times D_5$ 2A 4B-1 4B1 $abc^{5}$
$D_{115}:C_4$ 5A1 $5$ $2$ $C_{115}:C_4$ 5A2 1A 5A1 $c^{46}$
$D_{115}:C_4$ 5A2 $5$ $2$ $C_{115}:C_4$ 5A1 1A 5A2 $c^{92}$
$D_{115}:C_4$ 10A1 $10$ $2$ $C_{115}:C_4$ 5A1 2A 10A1 $a^{2}c^{23}$
$D_{115}:C_4$ 10A3 $10$ $2$ $C_{115}:C_4$ 5A2 2A 10A3 $a^{2}c^{69}$
$D_{115}:C_4$ 20A1 $20$ $46$ $C_{20}$ 10A3 4B1 20A-1 $a^{3}bc^{97}$
$D_{115}:C_4$ 20A-1 $20$ $46$ $C_{20}$ 10A3 4B-1 20A1 $abc^{28}$
$D_{115}:C_4$ 20A3 $20$ $46$ $C_{20}$ 10A1 4B-1 20A-3 $abc^{51}$
$D_{115}:C_4$ 20A-3 $20$ $46$ $C_{20}$ 10A1 4B1 20A3 $a^{3}bc^{74}$
$D_{115}:C_4$ 23A1 $23$ $2$ $C_5:C_{92}$ 23A2 23A5 23A11 $c^{20}$
$D_{115}:C_4$ 23A2 $23$ $2$ $C_5:C_{92}$ 23A4 23A10 23A1 $c^{40}$
$D_{115}:C_4$ 23A3 $23$ $2$ $C_5:C_{92}$ 23A6 23A8 23A10 $c^{60}$
$D_{115}:C_4$ 23A4 $23$ $2$ $C_5:C_{92}$ 23A8 23A3 23A2 $c^{80}$
$D_{115}:C_4$ 23A5 $23$ $2$ $C_5:C_{92}$ 23A10 23A2 23A9 $c^{100}$
$D_{115}:C_4$ 23A6 $23$ $2$ $C_5:C_{92}$ 23A11 23A7 23A3 $c^{5}$
$D_{115}:C_4$ 23A7 $23$ $2$ $C_5:C_{92}$ 23A9 23A11 23A8 $c^{25}$
$D_{115}:C_4$ 23A8 $23$ $2$ $C_5:C_{92}$ 23A7 23A6 23A4 $c^{45}$
$D_{115}:C_4$ 23A9 $23$ $2$ $C_5:C_{92}$ 23A5 23A1 23A7 $c^{65}$
$D_{115}:C_4$ 23A10 $23$ $2$ $C_5:C_{92}$ 23A3 23A4 23A5 $c^{85}$
$D_{115}:C_4$ 23A11 $23$ $2$ $C_5:C_{92}$ 23A1 23A9 23A6 $c^{105}$
$D_{115}:C_4$ 46A1 $46$ $2$ $C_5:C_{92}$ 23A1 46A5 46A11 $a^{2}c^{10}$
$D_{115}:C_4$ 46A3 $46$ $2$ $C_5:C_{92}$ 23A3 46A15 46A13 $a^{2}c^{30}$
$D_{115}:C_4$ 46A5 $46$ $2$ $C_5:C_{92}$ 23A5 46A21 46A9 $a^{2}c^{50}$
$D_{115}:C_4$ 46A7 $46$ $2$ $C_5:C_{92}$ 23A7 46A11 46A15 $a^{2}c^{70}$
$D_{115}:C_4$ 46A9 $46$ $2$ $C_5:C_{92}$ 23A9 46A1 46A7 $a^{2}c^{90}$
$D_{115}:C_4$ 46A11 $46$ $2$ $C_5:C_{92}$ 23A11 46A9 46A17 $a^{2}c^{110}$
$D_{115}:C_4$ 46A13 $46$ $2$ $C_5:C_{92}$ 23A10 46A19 46A5 $a^{2}c^{15}$
$D_{115}:C_4$ 46A15 $46$ $2$ $C_5:C_{92}$ 23A8 46A17 46A19 $a^{2}c^{35}$
$D_{115}:C_4$ 46A17 $46$ $2$ $C_5:C_{92}$ 23A6 46A7 46A3 $a^{2}c^{55}$
$D_{115}:C_4$ 46A19 $46$ $2$ $C_5:C_{92}$ 23A4 46A3 46A21 $a^{2}c^{75}$
$D_{115}:C_4$ 46A21 $46$ $2$ $C_5:C_{92}$ 23A2 46A13 46A1 $a^{2}c^{95}$
$D_{115}:C_4$ 92A1 $92$ $10$ $C_{92}$ 46A1 92A5 92A11 $ac^{5}$
$D_{115}:C_4$ 92A-1 $92$ $10$ $C_{92}$ 46A1 92A-5 92A-11 $a^{3}c^{5}$
$D_{115}:C_4$ 92A3 $92$ $10$ $C_{92}$ 46A3 92A15 92A13 $a^{3}c^{15}$
$D_{115}:C_4$ 92A-3 $92$ $10$ $C_{92}$ 46A3 92A-15 92A-13 $ac^{15}$
$D_{115}:C_4$ 92A5 $92$ $10$ $C_{92}$ 46A5 92A21 92A-9 $ac^{2}$
$D_{115}:C_4$ 92A-5 $92$ $10$ $C_{92}$ 46A5 92A-21 92A9 $a^{3}c^{2}$
$D_{115}:C_4$ 92A7 $92$ $10$ $C_{92}$ 46A7 92A11 92A-15 $a^{3}c^{35}$
$D_{115}:C_4$ 92A-7 $92$ $10$ $C_{92}$ 46A7 92A-11 92A15 $ac^{35}$
$D_{115}:C_4$ 92A9 $92$ $10$ $C_{92}$ 46A9 92A1 92A7 $ac$
$D_{115}:C_4$ 92A-9 $92$ $10$ $C_{92}$ 46A9 92A-1 92A-7 $a^{3}c$
$D_{115}:C_4$ 92A11 $92$ $10$ $C_{92}$ 46A11 92A-9 92A17 $a^{3}c^{55}$
$D_{115}:C_4$ 92A-11 $92$ $10$ $C_{92}$ 46A11 92A9 92A-17 $ac^{55}$
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