Character table for $D_{40}$

The column representing the conjugacy class 1A is highlighted below.

1A

2A

2B

2C

4A

5A1

5A2

8A1

8A3

10A1

10A3

20A1

20A3

20A7

20A9

40A1

40A3

40A7

40A9

40A11

40A13

40A17

40A19

Size

1

1

20

20

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2 P

1A

1A

1A

1A

2A

5A2

5A1

4A

4A

5A1

5A2

10A1

10A3

10A3

10A1

20A1

20A3

20A7

20A9

20A9

20A7

20A3

20A1

5 P

1A

2A

2B

2C

4A

1A

1A

8A3

8A1

2A

2A

4A

4A

4A

4A

8A1

8A3

8A1

8A1

8A3

8A3

8A1

8A3

Type

80.7.1a

R

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

80.7.1b

R

$1$

$1$

$-1$

$-1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

80.7.1c

R

$1$

$1$

$-1$

$1$

$1$

$1$

$1$

$-1$

$-1$

$1$

$1$

$1$

$1$

$1$

$1$

$-1$

$-1$

$-1$

$-1$

$-1$

$-1$

$-1$

$-1$

80.7.1d

R

$1$

$1$

$1$

$-1$

$1$

$1$

$1$

$-1$

$-1$

$1$

$1$

$1$

$1$

$1$

$1$

$-1$

$-1$

$-1$

$-1$

$-1$

$-1$

$-1$

$-1$

80.7.2a

R

$2$

$2$

$0$

$0$

$-2$

$2$

$2$

$0$

$0$

$2$

$2$

$-2$

$-2$

$-2$

$-2$

$0$

$0$

$0$

$0$

$0$

$0$

$0$

$0$

80.7.2b1

R

$2$

$2$

$0$

$0$

$2$

${\zeta }_5^{-2}+{\zeta }_5^2$

${\zeta }_5^{-1}+{\zeta }_5$

$2$

$2$

${\zeta }_5^{-1}+{\zeta }_5$

${\zeta }_5^{-2}+{\zeta }_5^2$

${\zeta }_5^{-2}+{\zeta }_5^2$

${\zeta }_5^{-1}+{\zeta }_5$

${\zeta }_5^{-1}+{\zeta }_5$

${\zeta }_5^{-2}+{\zeta }_5^2$

${\zeta }_5^{-2}+{\zeta }_5^2$

${\zeta }_5^{-1}+{\zeta }_5$

${\zeta }_5^{-2}+{\zeta }_5^2$

${\zeta }_5^{-2}+{\zeta }_5^2$

${\zeta }_5^{-1}+{\zeta }_5$

${\zeta }_5^{-2}+{\zeta }_5^2$

${\zeta }_5^{-1}+{\zeta }_5$

${\zeta }_5^{-1}+{\zeta }_5$

80.7.2b2

R

$2$

$2$

$0$

$0$

$2$

${\zeta }_5^{-1}+{\zeta }_5$

${\zeta }_5^{-2}+{\zeta }_5^2$

$2$

$2$

${\zeta }_5^{-2}+{\zeta }_5^2$

${\zeta }_5^{-1}+{\zeta }_5$

${\zeta }_5^{-1}+{\zeta }_5$

${\zeta }_5^{-2}+{\zeta }_5^2$

${\zeta }_5^{-2}+{\zeta }_5^2$

${\zeta }_5^{-1}+{\zeta }_5$

${\zeta }_5^{-1}+{\zeta }_5$

${\zeta }_5^{-2}+{\zeta }_5^2$

${\zeta }_5^{-1}+{\zeta }_5$

${\zeta }_5^{-1}+{\zeta }_5$

${\zeta }_5^{-2}+{\zeta }_5^2$

${\zeta }_5^{-1}+{\zeta }_5$

${\zeta }_5^{-2}+{\zeta }_5^2$

${\zeta }_5^{-2}+{\zeta }_5^2$

80.7.2c1

R

$2$

$-2$

$0$

$0$

$0$

$2$

$2$

$-{\zeta }_8^{-1}-{\zeta }_8$

${\zeta }_8^{-1}+{\zeta }_8$

$-2$

$-2$

$0$

$0$

$0$

$0$

$-{\zeta }_8^{-1}-{\zeta }_8$

${\zeta }_8^{-1}+{\zeta }_8$

$-{\zeta }_8^{-1}-{\zeta }_8$

${\zeta }_8^{-1}+{\zeta }_8$

$-{\zeta }_8^{-1}-{\zeta }_8$

${\zeta }_8^{-1}+{\zeta }_8$

$-{\zeta }_8^{-1}-{\zeta }_8$

${\zeta }_8^{-1}+{\zeta }_8$

80.7.2c2

R

$2$

$-2$

$0$

$0$

$0$

$2$

$2$

${\zeta }_8^{-1}+{\zeta }_8$

$-{\zeta }_8^{-1}-{\zeta }_8$

$-2$

$-2$

$0$

$0$

$0$

$0$

${\zeta }_8^{-1}+{\zeta }_8$

$-{\zeta }_8^{-1}-{\zeta }_8$

${\zeta }_8^{-1}+{\zeta }_8$

$-{\zeta }_8^{-1}-{\zeta }_8$

${\zeta }_8^{-1}+{\zeta }_8$

$-{\zeta }_8^{-1}-{\zeta }_8$

${\zeta }_8^{-1}+{\zeta }_8$

$-{\zeta }_8^{-1}-{\zeta }_8$

80.7.2d1

R

$2$

$2$

$0$

$0$

$2$

${\zeta }_5^{-2}+{\zeta }_5^2$

${\zeta }_5^{-1}+{\zeta }_5$

$-2$

$-2$

${\zeta }_5^{-1}+{\zeta }_5$

${\zeta }_5^{-2}+{\zeta }_5^2$

${\zeta }_5^{-2}+{\zeta }_5^2$

${\zeta }_5^{-1}+{\zeta }_5$

${\zeta }_5^{-1}+{\zeta }_5$

${\zeta }_5^{-2}+{\zeta }_5^2$

$-{\zeta }_5^{-2}-{\zeta }_5^2$

$-{\zeta }_5^{-1}-{\zeta }_5$

$-{\zeta }_5^{-2}-{\zeta }_5^2$

$-{\zeta }_5^{-2}-{\zeta }_5^2$

$-{\zeta }_5^{-1}-{\zeta }_5$

$-{\zeta }_5^{-2}-{\zeta }_5^2$

$-{\zeta }_5^{-1}-{\zeta }_5$

$-{\zeta }_5^{-1}-{\zeta }_5$

80.7.2d2

R

$2$

$2$

$0$

$0$

$2$

${\zeta }_5^{-1}+{\zeta }_5$

${\zeta }_5^{-2}+{\zeta }_5^2$

$-2$

$-2$

${\zeta }_5^{-2}+{\zeta }_5^2$

${\zeta }_5^{-1}+{\zeta }_5$

${\zeta }_5^{-1}+{\zeta }_5$

${\zeta }_5^{-2}+{\zeta }_5^2$

${\zeta }_5^{-2}+{\zeta }_5^2$

${\zeta }_5^{-1}+{\zeta }_5$

$-{\zeta }_5^{-1}-{\zeta }_5$

$-{\zeta }_5^{-2}-{\zeta }_5^2$

$-{\zeta }_5^{-1}-{\zeta }_5$

$-{\zeta }_5^{-1}-{\zeta }_5$

$-{\zeta }_5^{-2}-{\zeta }_5^2$

$-{\zeta }_5^{-1}-{\zeta }_5$

$-{\zeta }_5^{-2}-{\zeta }_5^2$

$-{\zeta }_5^{-2}-{\zeta }_5^2$

80.7.2e1

R

$2$

$2$

$0$

$0$

$-2$

$-{\zeta }_{20}^{-2}-{\zeta }_{20}^2$

${\zeta }_{20}^{-4}+{\zeta }_{20}^4$

$0$

$0$

${\zeta }_{20}^{-4}+{\zeta }_{20}^4$

$-{\zeta }_{20}^{-2}-{\zeta }_{20}^2$

${\zeta }_{20}^{-2}+{\zeta }_{20}^2$

$-{\zeta }_{20}^{-4}-{\zeta }_{20}^4$

$-{\zeta }_{20}^{-4}-{\zeta }_{20}^4$

${\zeta }_{20}^{-2}+{\zeta }_{20}^2$

$-{\zeta }_{20}^{-3}-{\zeta }_{20}^3$

${\zeta }_{20}^{-1}+{\zeta }_{20}$

${\zeta }_{20}^{-3}+{\zeta }_{20}^3$

${\zeta }_{20}^{-3}+{\zeta }_{20}^3$

${\zeta }_{20}^{-1}+{\zeta }_{20}$

$-{\zeta }_{20}^{-3}-{\zeta }_{20}^3$

$-{\zeta }_{20}^{-1}-{\zeta }_{20}$

$-{\zeta }_{20}^{-1}-{\zeta }_{20}$

80.7.2e2

R

$2$

$2$

$0$

$0$

$-2$

$-{\zeta }_{20}^{-2}-{\zeta }_{20}^2$

${\zeta }_{20}^{-4}+{\zeta }_{20}^4$

$0$

$0$

${\zeta }_{20}^{-4}+{\zeta }_{20}^4$

$-{\zeta }_{20}^{-2}-{\zeta }_{20}^2$

${\zeta }_{20}^{-2}+{\zeta }_{20}^2$

$-{\zeta }_{20}^{-4}-{\zeta }_{20}^4$

$-{\zeta }_{20}^{-4}-{\zeta }_{20}^4$

${\zeta }_{20}^{-2}+{\zeta }_{20}^2$

${\zeta }_{20}^{-3}+{\zeta }_{20}^3$

$-{\zeta }_{20}^{-1}-{\zeta }_{20}$

$-{\zeta }_{20}^{-3}-{\zeta }_{20}^3$

$-{\zeta }_{20}^{-3}-{\zeta }_{20}^3$

$-{\zeta }_{20}^{-1}-{\zeta }_{20}$

${\zeta }_{20}^{-3}+{\zeta }_{20}^3$

${\zeta }_{20}^{-1}+{\zeta }_{20}$

${\zeta }_{20}^{-1}+{\zeta }_{20}$

80.7.2e3

R

$2$

$2$

$0$

$0$

$-2$

${\zeta }_{20}^{-4}+{\zeta }_{20}^4$

$-{\zeta }_{20}^{-2}-{\zeta }_{20}^2$

$0$

$0$

$-{\zeta }_{20}^{-2}-{\zeta }_{20}^2$

${\zeta }_{20}^{-4}+{\zeta }_{20}^4$

$-{\zeta }_{20}^{-4}-{\zeta }_{20}^4$

${\zeta }_{20}^{-2}+{\zeta }_{20}^2$

${\zeta }_{20}^{-2}+{\zeta }_{20}^2$

$-{\zeta }_{20}^{-4}-{\zeta }_{20}^4$

$-{\zeta }_{20}^{-1}-{\zeta }_{20}$

$-{\zeta }_{20}^{-3}-{\zeta }_{20}^3$

${\zeta }_{20}^{-1}+{\zeta }_{20}$

${\zeta }_{20}^{-1}+{\zeta }_{20}$

$-{\zeta }_{20}^{-3}-{\zeta }_{20}^3$

$-{\zeta }_{20}^{-1}-{\zeta }_{20}$

${\zeta }_{20}^{-3}+{\zeta }_{20}^3$

${\zeta }_{20}^{-3}+{\zeta }_{20}^3$

80.7.2e4

R

$2$

$2$

$0$

$0$

$-2$

${\zeta }_{20}^{-4}+{\zeta }_{20}^4$

$-{\zeta }_{20}^{-2}-{\zeta }_{20}^2$

$0$

$0$

$-{\zeta }_{20}^{-2}-{\zeta }_{20}^2$

${\zeta }_{20}^{-4}+{\zeta }_{20}^4$

$-{\zeta }_{20}^{-4}-{\zeta }_{20}^4$

${\zeta }_{20}^{-2}+{\zeta }_{20}^2$

${\zeta }_{20}^{-2}+{\zeta }_{20}^2$

$-{\zeta }_{20}^{-4}-{\zeta }_{20}^4$

${\zeta }_{20}^{-1}+{\zeta }_{20}$

${\zeta }_{20}^{-3}+{\zeta }_{20}^3$

$-{\zeta }_{20}^{-1}-{\zeta }_{20}$

$-{\zeta }_{20}^{-1}-{\zeta }_{20}$

${\zeta }_{20}^{-3}+{\zeta }_{20}^3$

${\zeta }_{20}^{-1}+{\zeta }_{20}$

$-{\zeta }_{20}^{-3}-{\zeta }_{20}^3$

$-{\zeta }_{20}^{-3}-{\zeta }_{20}^3$

80.7.2f1

R

$2$

$-2$

$0$

$0$

$0$

$-{\zeta }_{40}^{-4}-{\zeta }_{40}^4$

${\zeta }_{40}^{-8}+{\zeta }_{40}^8$

$-{\zeta }_{40}^{-5}-{\zeta }_{40}^5$

${\zeta }_{40}^{-5}+{\zeta }_{40}^5$

$-{\zeta }_{40}^{-8}-{\zeta }_{40}^8$

${\zeta }_{40}^{-4}+{\zeta }_{40}^4$

$-{\zeta }_{40}^{-6}-{\zeta }_{40}^6$

${\zeta }_{40}^{-2}+{\zeta }_{40}^2$

$-{\zeta }_{40}^{-2}-{\zeta }_{40}^2$

${\zeta }_{40}^{-6}+{\zeta }_{40}^6$

${\zeta }_{40}^{-1}+{\zeta }_{40}$

${\zeta }_{40}^{-3}+{\zeta }_{40}^3$

${\zeta }_{40}^{-9}+{\zeta }_{40}^9$

$-{\zeta }_{40}^{-9}-{\zeta }_{40}^9$

$-{\zeta }_{40}^{-3}-{\zeta }_{40}^3$

$-{\zeta }_{40}^{-1}-{\zeta }_{40}$

${\zeta }_{40}^{-7}+{\zeta }_{40}^7$

$-{\zeta }_{40}^{-7}-{\zeta }_{40}^7$

80.7.2f2

R

$2$

$-2$

$0$

$0$

$0$

$-{\zeta }_{40}^{-4}-{\zeta }_{40}^4$

${\zeta }_{40}^{-8}+{\zeta }_{40}^8$

$-{\zeta }_{40}^{-5}-{\zeta }_{40}^5$

${\zeta }_{40}^{-5}+{\zeta }_{40}^5$

$-{\zeta }_{40}^{-8}-{\zeta }_{40}^8$

${\zeta }_{40}^{-4}+{\zeta }_{40}^4$

${\zeta }_{40}^{-6}+{\zeta }_{40}^6$

$-{\zeta }_{40}^{-2}-{\zeta }_{40}^2$

${\zeta }_{40}^{-2}+{\zeta }_{40}^2$

$-{\zeta }_{40}^{-6}-{\zeta }_{40}^6$

${\zeta }_{40}^{-9}+{\zeta }_{40}^9$

$-{\zeta }_{40}^{-7}-{\zeta }_{40}^7$

${\zeta }_{40}^{-1}+{\zeta }_{40}$

$-{\zeta }_{40}^{-1}-{\zeta }_{40}$

${\zeta }_{40}^{-7}+{\zeta }_{40}^7$

$-{\zeta }_{40}^{-9}-{\zeta }_{40}^9$

$-{\zeta }_{40}^{-3}-{\zeta }_{40}^3$

${\zeta }_{40}^{-3}+{\zeta }_{40}^3$

80.7.2f3

R

$2$

$-2$

$0$

$0$

$0$

$-{\zeta }_{40}^{-4}-{\zeta }_{40}^4$

${\zeta }_{40}^{-8}+{\zeta }_{40}^8$

${\zeta }_{40}^{-5}+{\zeta }_{40}^5$

$-{\zeta }_{40}^{-5}-{\zeta }_{40}^5$

$-{\zeta }_{40}^{-8}-{\zeta }_{40}^8$

${\zeta }_{40}^{-4}+{\zeta }_{40}^4$

$-{\zeta }_{40}^{-6}-{\zeta }_{40}^6$

${\zeta }_{40}^{-2}+{\zeta }_{40}^2$

$-{\zeta }_{40}^{-2}-{\zeta }_{40}^2$

${\zeta }_{40}^{-6}+{\zeta }_{40}^6$

$-{\zeta }_{40}^{-1}-{\zeta }_{40}$

$-{\zeta }_{40}^{-3}-{\zeta }_{40}^3$

$-{\zeta }_{40}^{-9}-{\zeta }_{40}^9$

${\zeta }_{40}^{-9}+{\zeta }_{40}^9$

${\zeta }_{40}^{-3}+{\zeta }_{40}^3$

${\zeta }_{40}^{-1}+{\zeta }_{40}$

$-{\zeta }_{40}^{-7}-{\zeta }_{40}^7$

${\zeta }_{40}^{-7}+{\zeta }_{40}^7$

80.7.2f4

R

$2$

$-2$

$0$

$0$

$0$

$-{\zeta }_{40}^{-4}-{\zeta }_{40}^4$

${\zeta }_{40}^{-8}+{\zeta }_{40}^8$

${\zeta }_{40}^{-5}+{\zeta }_{40}^5$

$-{\zeta }_{40}^{-5}-{\zeta }_{40}^5$

$-{\zeta }_{40}^{-8}-{\zeta }_{40}^8$

${\zeta }_{40}^{-4}+{\zeta }_{40}^4$

${\zeta }_{40}^{-6}+{\zeta }_{40}^6$

$-{\zeta }_{40}^{-2}-{\zeta }_{40}^2$

${\zeta }_{40}^{-2}+{\zeta }_{40}^2$

$-{\zeta }_{40}^{-6}-{\zeta }_{40}^6$

$-{\zeta }_{40}^{-9}-{\zeta }_{40}^9$

${\zeta }_{40}^{-7}+{\zeta }_{40}^7$

$-{\zeta }_{40}^{-1}-{\zeta }_{40}$

${\zeta }_{40}^{-1}+{\zeta }_{40}$

$-{\zeta }_{40}^{-7}-{\zeta }_{40}^7$

${\zeta }_{40}^{-9}+{\zeta }_{40}^9$

${\zeta }_{40}^{-3}+{\zeta }_{40}^3$

$-{\zeta }_{40}^{-3}-{\zeta }_{40}^3$

80.7.2f5

R

$2$

$-2$

$0$

$0$

$0$

${\zeta }_{40}^{-8}+{\zeta }_{40}^8$

$-{\zeta }_{40}^{-4}-{\zeta }_{40}^4$

$-{\zeta }_{40}^{-5}-{\zeta }_{40}^5$

${\zeta }_{40}^{-5}+{\zeta }_{40}^5$

${\zeta }_{40}^{-4}+{\zeta }_{40}^4$

$-{\zeta }_{40}^{-8}-{\zeta }_{40}^8$

$-{\zeta }_{40}^{-2}-{\zeta }_{40}^2$

$-{\zeta }_{40}^{-6}-{\zeta }_{40}^6$

${\zeta }_{40}^{-6}+{\zeta }_{40}^6$

${\zeta }_{40}^{-2}+{\zeta }_{40}^2$

${\zeta }_{40}^{-7}+{\zeta }_{40}^7$

$-{\zeta }_{40}^{-1}-{\zeta }_{40}$

$-{\zeta }_{40}^{-3}-{\zeta }_{40}^3$

${\zeta }_{40}^{-3}+{\zeta }_{40}^3$

${\zeta }_{40}^{-1}+{\zeta }_{40}$

$-{\zeta }_{40}^{-7}-{\zeta }_{40}^7$

${\zeta }_{40}^{-9}+{\zeta }_{40}^9$

$-{\zeta }_{40}^{-9}-{\zeta }_{40}^9$

80.7.2f6

R

$2$

$-2$

$0$

$0$

$0$

${\zeta }_{40}^{-8}+{\zeta }_{40}^8$

$-{\zeta }_{40}^{-4}-{\zeta }_{40}^4$

$-{\zeta }_{40}^{-5}-{\zeta }_{40}^5$

${\zeta }_{40}^{-5}+{\zeta }_{40}^5$

${\zeta }_{40}^{-4}+{\zeta }_{40}^4$

$-{\zeta }_{40}^{-8}-{\zeta }_{40}^8$

${\zeta }_{40}^{-2}+{\zeta }_{40}^2$

${\zeta }_{40}^{-6}+{\zeta }_{40}^6$

$-{\zeta }_{40}^{-6}-{\zeta }_{40}^6$

$-{\zeta }_{40}^{-2}-{\zeta }_{40}^2$

$-{\zeta }_{40}^{-3}-{\zeta }_{40}^3$

$-{\zeta }_{40}^{-9}-{\zeta }_{40}^9$

${\zeta }_{40}^{-7}+{\zeta }_{40}^7$

$-{\zeta }_{40}^{-7}-{\zeta }_{40}^7$

${\zeta }_{40}^{-9}+{\zeta }_{40}^9$

${\zeta }_{40}^{-3}+{\zeta }_{40}^3$

${\zeta }_{40}^{-1}+{\zeta }_{40}$

$-{\zeta }_{40}^{-1}-{\zeta }_{40}$

80.7.2f7

R

$2$

$-2$

$0$

$0$

$0$

${\zeta }_{40}^{-8}+{\zeta }_{40}^8$

$-{\zeta }_{40}^{-4}-{\zeta }_{40}^4$

${\zeta }_{40}^{-5}+{\zeta }_{40}^5$

$-{\zeta }_{40}^{-5}-{\zeta }_{40}^5$

${\zeta }_{40}^{-4}+{\zeta }_{40}^4$

$-{\zeta }_{40}^{-8}-{\zeta }_{40}^8$

$-{\zeta }_{40}^{-2}-{\zeta }_{40}^2$

$-{\zeta }_{40}^{-6}-{\zeta }_{40}^6$

${\zeta }_{40}^{-6}+{\zeta }_{40}^6$

${\zeta }_{40}^{-2}+{\zeta }_{40}^2$

$-{\zeta }_{40}^{-7}-{\zeta }_{40}^7$

${\zeta }_{40}^{-1}+{\zeta }_{40}$

${\zeta }_{40}^{-3}+{\zeta }_{40}^3$

$-{\zeta }_{40}^{-3}-{\zeta }_{40}^3$

$-{\zeta }_{40}^{-1}-{\zeta }_{40}$

${\zeta }_{40}^{-7}+{\zeta }_{40}^7$

$-{\zeta }_{40}^{-9}-{\zeta }_{40}^9$

${\zeta }_{40}^{-9}+{\zeta }_{40}^9$

80.7.2f8

R

$2$

$-2$

$0$

$0$

$0$

${\zeta }_{40}^{-8}+{\zeta }_{40}^8$

$-{\zeta }_{40}^{-4}-{\zeta }_{40}^4$

${\zeta }_{40}^{-5}+{\zeta }_{40}^5$

$-{\zeta }_{40}^{-5}-{\zeta }_{40}^5$

${\zeta }_{40}^{-4}+{\zeta }_{40}^4$

$-{\zeta }_{40}^{-8}-{\zeta }_{40}^8$

${\zeta }_{40}^{-2}+{\zeta }_{40}^2$

${\zeta }_{40}^{-6}+{\zeta }_{40}^6$

$-{\zeta }_{40}^{-6}-{\zeta }_{40}^6$

$-{\zeta }_{40}^{-2}-{\zeta }_{40}^2$

${\zeta }_{40}^{-3}+{\zeta }_{40}^3$

${\zeta }_{40}^{-9}+{\zeta }_{40}^9$

$-{\zeta }_{40}^{-7}-{\zeta }_{40}^7$

${\zeta }_{40}^{-7}+{\zeta }_{40}^7$

$-{\zeta }_{40}^{-9}-{\zeta }_{40}^9$

$-{\zeta }_{40}^{-3}-{\zeta }_{40}^3$

$-{\zeta }_{40}^{-1}-{\zeta }_{40}$

${\zeta }_{40}^{-1}+{\zeta }_{40}$