Character table for $C_5^2$

The column representing the conjugacy class 5C1 is highlighted below.

1A

5A1

5A-1

5A2

5A-2

5B1

5B-1

5B2

5B-2

5C1

5C-1

5C2

5C-2

5D1

5D-1

5D2

5D-2

5E1

5E-1

5E2

5E-2

5F1

5F-1

5F2

5F-2

Size

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

5 P

1A

5A2

5A-2

5A-1

5A1

5B2

5B-2

5B-1

5B1

5C2

5C-2

5C-1

5C1

5D2

5D-2

5D-1

5D1

5E2

5E-2

5E-1

5E1

5F2

5F-2

5F-1

5F1

Type

25.2.1a

R

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

25.2.1b1

C

$1$

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

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

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

${\zeta }_5^2$

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

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

${\zeta }_5$

${\zeta }_5$

${\zeta }_5^2$

${\zeta }_5$

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

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

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

${\zeta }_5^2$

${\zeta }_5^2$

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

${\zeta }_5$

$1$

$1$

$1$

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

${\zeta }_5$

${\zeta }_5^2$

$1$

25.2.1b2

C

$1$

${\zeta }_5^2$

${\zeta }_5^2$

${\zeta }_5$

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

${\zeta }_5$

${\zeta }_5^2$

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

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

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

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

${\zeta }_5$

${\zeta }_5$

${\zeta }_5$

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

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

${\zeta }_5^2$

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

$1$

$1$

$1$

${\zeta }_5^2$

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

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

$1$

25.2.1b3

C

$1$

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

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

${\zeta }_5^2$

${\zeta }_5$

${\zeta }_5^2$

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

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

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

${\zeta }_5$

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

${\zeta }_5^2$

${\zeta }_5^2$

${\zeta }_5^2$

${\zeta }_5$

${\zeta }_5$

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

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

$1$

$1$

$1$

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

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

${\zeta }_5$

$1$

25.2.1b4

C

$1$

${\zeta }_5$

${\zeta }_5$

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

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

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

${\zeta }_5$

${\zeta }_5^2$

${\zeta }_5^2$

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

${\zeta }_5^2$

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

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

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

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

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

${\zeta }_5$

${\zeta }_5^2$

$1$

$1$

$1$

${\zeta }_5$

${\zeta }_5^2$

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

$1$

25.2.1c1

C

$1$

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

${\zeta }_5$

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

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

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

${\zeta }_5^2$

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

${\zeta }_5$

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

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

${\zeta }_5$

$1$

${\zeta }_5^2$

${\zeta }_5^2$

$1$

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

${\zeta }_5^2$

${\zeta }_5^2$

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

${\zeta }_5$

$1$

$1$

${\zeta }_5$

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

25.2.1c2

C

$1$

${\zeta }_5^2$

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

${\zeta }_5^2$

${\zeta }_5$

${\zeta }_5$

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

${\zeta }_5$

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

${\zeta }_5^2$

${\zeta }_5^2$

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

$1$

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

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

$1$

${\zeta }_5$

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

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

${\zeta }_5^2$

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

$1$

$1$

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

${\zeta }_5$

25.2.1c3

C

$1$

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

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

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

${\zeta }_5^2$

${\zeta }_5^2$

${\zeta }_5$

${\zeta }_5^2$

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

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

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

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

$1$

${\zeta }_5$

${\zeta }_5$

$1$

${\zeta }_5^2$

${\zeta }_5$

${\zeta }_5$

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

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

$1$

$1$

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

${\zeta }_5^2$

25.2.1c4

C

$1$

${\zeta }_5$

${\zeta }_5^2$

${\zeta }_5$

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

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

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

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

${\zeta }_5^2$

${\zeta }_5$

${\zeta }_5$

${\zeta }_5^2$

$1$

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

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

$1$

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

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

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

${\zeta }_5$

${\zeta }_5^2$

$1$

$1$

${\zeta }_5^2$

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

25.2.1d1

C

$1$

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

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

${\zeta }_5^2$

${\zeta }_5$

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

${\zeta }_5$

${\zeta }_5^2$

${\zeta }_5$

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

$1$

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

${\zeta }_5$

$1$

${\zeta }_5^2$

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

$1$

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

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

${\zeta }_5$

${\zeta }_5^2$

${\zeta }_5^2$

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

$1$

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

25.2.1d2

C

$1$

${\zeta }_5^2$

${\zeta }_5$

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

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

${\zeta }_5$

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

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

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

${\zeta }_5$

$1$

${\zeta }_5^2$

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

$1$

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

${\zeta }_5^2$

$1$

${\zeta }_5^2$

${\zeta }_5$

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

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

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

${\zeta }_5$

$1$

${\zeta }_5^2$

25.2.1d3

C

$1$

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

${\zeta }_5^2$

${\zeta }_5$

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

${\zeta }_5^2$

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

${\zeta }_5$

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

${\zeta }_5^2$

$1$

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

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

$1$

${\zeta }_5$

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

$1$

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

${\zeta }_5^2$

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

${\zeta }_5$

${\zeta }_5$

${\zeta }_5^2$

$1$

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

25.2.1d4

C

$1$

${\zeta }_5$

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

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

${\zeta }_5^2$

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

${\zeta }_5^2$

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

${\zeta }_5^2$

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

$1$

${\zeta }_5$

${\zeta }_5^2$

$1$

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

${\zeta }_5$

$1$

${\zeta }_5$

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

${\zeta }_5^2$

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

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

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

$1$

${\zeta }_5$

25.2.1e1

C

$1$

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

${\zeta }_5^2$

${\zeta }_5$

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

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

$1$

$1$

${\zeta }_5$

$1$

${\zeta }_5^2$

$1$

${\zeta }_5^2$

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

${\zeta }_5^2$

${\zeta }_5$

${\zeta }_5$

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

${\zeta }_5$

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

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

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

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

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

${\zeta }_5^2$

25.2.1e2

C

$1$

${\zeta }_5^2$

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

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

${\zeta }_5^2$

${\zeta }_5$

$1$

$1$

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

$1$

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

$1$

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

${\zeta }_5^2$

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

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

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

${\zeta }_5$

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

${\zeta }_5$

${\zeta }_5^2$

${\zeta }_5$

${\zeta }_5^2$

${\zeta }_5$

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

25.2.1e3

C

$1$

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

${\zeta }_5$

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

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

${\zeta }_5^2$

$1$

$1$

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

$1$

${\zeta }_5$

$1$

${\zeta }_5$

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

${\zeta }_5$

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

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

${\zeta }_5^2$

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

${\zeta }_5^2$

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

${\zeta }_5^2$

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

${\zeta }_5^2$

${\zeta }_5$

25.2.1e4

C

$1$

${\zeta }_5$

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

${\zeta }_5^2$

${\zeta }_5$

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

$1$

$1$

${\zeta }_5^2$

$1$

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

$1$

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

${\zeta }_5$

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

${\zeta }_5^2$

${\zeta }_5^2$

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

${\zeta }_5^2$

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

${\zeta }_5$

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

${\zeta }_5$

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

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

25.2.1f1

C

$1$

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

$1$

$1$

$1$

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

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

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

${\zeta }_5$

${\zeta }_5$

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

${\zeta }_5^2$

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

${\zeta }_5$

${\zeta }_5^2$

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

${\zeta }_5^2$

$1$

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

${\zeta }_5^2$

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

${\zeta }_5$

${\zeta }_5^2$

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

${\zeta }_5$

25.2.1f2

C

$1$

${\zeta }_5^2$

$1$

$1$

$1$

${\zeta }_5$

${\zeta }_5$

${\zeta }_5^2$

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

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

${\zeta }_5$

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

${\zeta }_5^2$

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

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

${\zeta }_5$

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

$1$

${\zeta }_5^2$

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

${\zeta }_5$

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

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

${\zeta }_5^2$

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

25.2.1f3

C

$1$

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

$1$

$1$

$1$

${\zeta }_5^2$

${\zeta }_5^2$

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

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

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

${\zeta }_5^2$

${\zeta }_5$

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

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

${\zeta }_5$

${\zeta }_5^2$

${\zeta }_5$

$1$

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

${\zeta }_5$

${\zeta }_5^2$

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

${\zeta }_5$

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

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

25.2.1f4

C

$1$

${\zeta }_5$

$1$

$1$

$1$

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

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

${\zeta }_5$

${\zeta }_5^2$

${\zeta }_5^2$

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

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

${\zeta }_5$

${\zeta }_5^2$

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

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

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

$1$

${\zeta }_5$

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

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

${\zeta }_5^2$

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

${\zeta }_5$

${\zeta }_5^2$

25.2.1g1

C

$1$

$1$

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

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

${\zeta }_5^2$

$1$

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

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

$1$

${\zeta }_5$

${\zeta }_5^2$

${\zeta }_5^2$

${\zeta }_5$

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

$1$

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

${\zeta }_5$

${\zeta }_5$

${\zeta }_5^2$

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

${\zeta }_5$

${\zeta }_5^2$

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

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

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

25.2.1g2

C

$1$

$1$

${\zeta }_5^2$

${\zeta }_5$

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

$1$

${\zeta }_5$

${\zeta }_5^2$

$1$

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

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

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

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

${\zeta }_5^2$

$1$

${\zeta }_5^2$

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

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

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

${\zeta }_5^2$

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

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

${\zeta }_5$

${\zeta }_5$

${\zeta }_5$

25.2.1g3

C

$1$

$1$

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

${\zeta }_5^2$

${\zeta }_5$

$1$

${\zeta }_5^2$

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

$1$

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

${\zeta }_5$

${\zeta }_5$

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

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

$1$

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

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

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

${\zeta }_5$

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

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

${\zeta }_5$

${\zeta }_5^2$

${\zeta }_5^2$

${\zeta }_5^2$

25.2.1g4

C

$1$

$1$

${\zeta }_5$

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

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

$1$

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

${\zeta }_5$

$1$

${\zeta }_5^2$

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

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

${\zeta }_5^2$

${\zeta }_5$

$1$

${\zeta }_5$

${\zeta }_5^2$

${\zeta }_5^2$

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

${\zeta }_5$

${\zeta }_5^2$

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

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

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

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