Character table for $C_{25}:C_{10}$

The row representing the character 250.6.10a2 is highlighted below.

1A

2A

5A1

5A2

5B1

5B-1

5B2

5B-2

10A1

10A-1

10A3

10A-3

25A1

25A2

25B1

25B-1

25B2

25B-2

25C1

25C-1

25C2

25C-2

Size

1

25

2

2

5

5

5

5

25

25

25

25

10

10

10

10

10

10

10

10

10

10

2 P

1A

1A

5A2

5A1

5B2

5B-2

5B-1

5B1

5B1

5B-1

5B-2

5B2

25A2

25A1

25B2

25B-2

25B-1

25B1

25C2

25C-2

25C-1

25C1

5 P

1A

2A

1A

1A

1A

1A

1A

1A

2A

2A

2A

2A

5A1

5A2

5A1

5A1

5A2

5A2

5A2

5A2

5A1

5A1

Type

250.6.1a

R

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

250.6.1b

R

$1$

$-1$

$1$

$1$

$1$

$1$

$1$

$1$

$-1$

$-1$

$-1$

$-1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

250.6.1c1

C

$1$

$1$

$1$

$1$

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

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

${\zeta }_5^2$

${\zeta }_5$

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

${\zeta }_5$

${\zeta }_5^2$

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

$1$

${\zeta }_5^2$

${\zeta }_5$

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

${\zeta }_5$

$1$

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

${\zeta }_5^2$

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

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

250.6.1c2

C

$1$

$1$

$1$

$1$

${\zeta }_5^2$

${\zeta }_5$

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

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

${\zeta }_5$

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

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

${\zeta }_5^2$

$1$

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

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

${\zeta }_5^2$

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

$1$

${\zeta }_5$

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

${\zeta }_5$

${\zeta }_5^2$

250.6.1c3

C

$1$

$1$

$1$

$1$

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

${\zeta }_5^2$

${\zeta }_5$

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

${\zeta }_5^2$

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

${\zeta }_5$

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

$1$

${\zeta }_5$

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

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

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

$1$

${\zeta }_5^2$

${\zeta }_5$

${\zeta }_5^2$

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

250.6.1c4

C

$1$

$1$

$1$

$1$

${\zeta }_5$

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

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

${\zeta }_5^2$

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

${\zeta }_5^2$

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

${\zeta }_5$

$1$

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

${\zeta }_5^2$

${\zeta }_5$

${\zeta }_5^2$

$1$

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

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

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

${\zeta }_5$

250.6.1d1

C

$1$

$-1$

$1$

$1$

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

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

${\zeta }_5^2$

${\zeta }_5$

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

$-{\zeta }_5$

$-{\zeta }_5^2$

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

$1$

${\zeta }_5^2$

${\zeta }_5$

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

${\zeta }_5$

$1$

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

${\zeta }_5^2$

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

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

250.6.1d2

C

$1$

$-1$

$1$

$1$

${\zeta }_5^2$

${\zeta }_5$

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

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

$-{\zeta }_5$

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

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

$-{\zeta }_5^2$

$1$

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

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

${\zeta }_5^2$

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

$1$

${\zeta }_5$

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

${\zeta }_5$

${\zeta }_5^2$

250.6.1d3

C

$1$

$-1$

$1$

$1$

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

${\zeta }_5^2$

${\zeta }_5$

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

$-{\zeta }_5^2$

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

$-{\zeta }_5$

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

$1$

${\zeta }_5$

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

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

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

$1$

${\zeta }_5^2$

${\zeta }_5$

${\zeta }_5^2$

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

250.6.1d4

C

$1$

$-1$

$1$

$1$

${\zeta }_5$

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

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

${\zeta }_5^2$

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

$-{\zeta }_5^2$

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

$-{\zeta }_5$

$1$

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

${\zeta }_5^2$

${\zeta }_5$

${\zeta }_5^2$

$1$

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

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

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

${\zeta }_5$

250.6.2a1

R

$2$

$0$

$2$

$2$

$2$

$2$

$2$

$2$

$0$

$0$

$0$

$0$

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

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

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

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

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

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

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

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

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

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

250.6.2a2

R

$2$

$0$

$2$

$2$

$2$

$2$

$2$

$2$

$0$

$0$

$0$

$0$

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

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

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

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

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

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

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

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

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

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

250.6.2b1

C

$2$

$0$

$2$

$2$

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

$2{\zeta }_5^{-1}$

$2{\zeta }_5^2$

$2{\zeta }_5$

$0$

$0$

$0$

$0$

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

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

$1+{\zeta }_5^2$

$1+{\zeta }_5$

$-1-{\zeta }_5-{\zeta }_5^2$

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

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

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

${\zeta }_5^{-2}+1$

$-{\zeta }_5^{-2}-1-{\zeta }_5$

250.6.2b2

C

$2$

$0$

$2$

$2$

$2{\zeta }_5^2$

$2{\zeta }_5$

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

$2{\zeta }_5^{-1}$

$0$

$0$

$0$

$0$

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

$-{\zeta }_5^{-2}-1-{\zeta }_5$

${\zeta }_5^{-2}+1$

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

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

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

$-1-{\zeta }_5-{\zeta }_5^2$

$1+{\zeta }_5$

$1+{\zeta }_5^2$

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

250.6.2b3

C

$2$

$0$

$2$

$2$

$2{\zeta }_5^{-1}$

$2{\zeta }_5^2$

$2{\zeta }_5$

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

$0$

$0$

$0$

$0$

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

$-1-{\zeta }_5-{\zeta }_5^2$

$1+{\zeta }_5$

${\zeta }_5^{-2}+1$

$-{\zeta }_5^{-2}-1-{\zeta }_5$

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

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

$1+{\zeta }_5^2$

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

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

250.6.2b4

C

$2$

$0$

$2$

$2$

$2{\zeta }_5$

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

$2{\zeta }_5^{-1}$

$2{\zeta }_5^2$

$0$

$0$

$0$

$0$

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

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

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

$1+{\zeta }_5^2$

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

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

$-{\zeta }_5^{-2}-1-{\zeta }_5$

${\zeta }_5^{-2}+1$

$1+{\zeta }_5$

$-1-{\zeta }_5-{\zeta }_5^2$

250.6.2c1

C

$2$

$0$

$2$

$2$

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

$2{\zeta }_5^{-1}$

$2{\zeta }_5^2$

$2{\zeta }_5$

$0$

$0$

$0$

$0$

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

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

$-1-{\zeta }_5-{\zeta }_5^2$

$-{\zeta }_5^{-2}-1-{\zeta }_5$

$1+{\zeta }_5^2$

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

${\zeta }_5^{-2}+1$

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

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

$1+{\zeta }_5$

250.6.2c2

C

$2$

$0$

$2$

$2$

$2{\zeta }_5^2$

$2{\zeta }_5$

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

$2{\zeta }_5^{-1}$

$0$

$0$

$0$

$0$

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

$1+{\zeta }_5$

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

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

${\zeta }_5^{-2}+1$

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

$1+{\zeta }_5^2$

$-{\zeta }_5^{-2}-1-{\zeta }_5$

$-1-{\zeta }_5-{\zeta }_5^2$

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

250.6.2c3

C

$2$

$0$

$2$

$2$

$2{\zeta }_5^{-1}$

$2{\zeta }_5^2$

$2{\zeta }_5$

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

$0$

$0$

$0$

$0$

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

$1+{\zeta }_5^2$

$-{\zeta }_5^{-2}-1-{\zeta }_5$

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

$1+{\zeta }_5$

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

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

$-1-{\zeta }_5-{\zeta }_5^2$

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

${\zeta }_5^{-2}+1$

250.6.2c4

C

$2$

$0$

$2$

$2$

$2{\zeta }_5$

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

$2{\zeta }_5^{-1}$

$2{\zeta }_5^2$

$0$

$0$

$0$

$0$

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

${\zeta }_5^{-2}+1$

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

$-1-{\zeta }_5-{\zeta }_5^2$

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

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

$1+{\zeta }_5$

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

$-{\zeta }_5^{-2}-1-{\zeta }_5$

$1+{\zeta }_5^2$

250.6.10a1

R

$10$

$0$

$5{\zeta }_5^{-2}+5{\zeta }_5^2$

$5{\zeta }_5^{-1}+5{\zeta }_5$

$0$

$0$

$0$

$0$

$0$

$0$

$0$

$0$

$0$

$0$

$0$

$0$

$0$

$0$

$0$

$0$

$0$

$0$

250.6.10a2

R

$10$

$0$

$5{\zeta }_5^{-1}+5{\zeta }_5$

$5{\zeta }_5^{-2}+5{\zeta }_5^2$

$0$

$0$

$0$

$0$

$0$

$0$

$0$

$0$

$0$

$0$

$0$

$0$

$0$

$0$

$0$

$0$

$0$

$0$