Character table for $S_3\times C_9$

The column representing the conjugacy class 6A-1 is highlighted below.

1A

2A

3A1

3A-1

3B

3C1

3C-1

6A1

6A-1

9A1

9A-1

9A2

9A-2

9A4

9A-4

9B1

9B-1

9B2

9B-2

9B4

9B-4

18A1

18A-1

18A5

18A-5

18A7

18A-7

Size

1

3

1

1

2

2

2

3

3

1

1

1

1

1

1

2

2

2

2

2

2

3

3

3

3

3

3

2 P

1A

1A

3A-1

3A1

3B

3C-1

3C1

3A1

3A-1

9A2

9A-2

9A4

9A-4

9A-1

9A1

9B2

9B-2

9B4

9B-4

9B-1

9B1

9A1

9A-1

9A-4

9A4

9A-2

9A2

3 P

1A

2A

1A

1A

1A

1A

1A

2A

2A

3A1

3A-1

3A-1

3A1

3A1

3A-1

3A1

3A-1

3A-1

3A1

3A1

3A-1

6A1

6A-1

6A-1

6A1

6A1

6A-1

Type

54.4.1a

R

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

54.4.1b

R

$1$

$-1$

$1$

$1$

$1$

$1$

$1$

$-1$

$-1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$-1$

$-1$

$-1$

$-1$

$-1$

$-1$

54.4.1c1

C

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

${\zeta }_3^{-1}$

${\zeta }_3$

${\zeta }_3$

${\zeta }_3^{-1}$

${\zeta }_3^{-1}$

${\zeta }_3$

${\zeta }_3^{-1}$

${\zeta }_3$

${\zeta }_3$

${\zeta }_3^{-1}$

${\zeta }_3^{-1}$

${\zeta }_3$

${\zeta }_3$

${\zeta }_3^{-1}$

${\zeta }_3^{-1}$

${\zeta }_3$

${\zeta }_3$

${\zeta }_3^{-1}$

54.4.1c2

C

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

${\zeta }_3$

${\zeta }_3^{-1}$

${\zeta }_3^{-1}$

${\zeta }_3$

${\zeta }_3$

${\zeta }_3^{-1}$

${\zeta }_3$

${\zeta }_3^{-1}$

${\zeta }_3^{-1}$

${\zeta }_3$

${\zeta }_3$

${\zeta }_3^{-1}$

${\zeta }_3^{-1}$

${\zeta }_3$

${\zeta }_3$

${\zeta }_3^{-1}$

${\zeta }_3^{-1}$

${\zeta }_3$

54.4.1d1

C

$1$

$-1$

$1$

$1$

$1$

$1$

$1$

$-1$

$-1$

${\zeta }_3^{-1}$

${\zeta }_3$

${\zeta }_3$

${\zeta }_3^{-1}$

${\zeta }_3^{-1}$

${\zeta }_3$

${\zeta }_3^{-1}$

${\zeta }_3$

${\zeta }_3$

${\zeta }_3^{-1}$

${\zeta }_3^{-1}$

${\zeta }_3$

$-{\zeta }_3$

$-{\zeta }_3^{-1}$

$-{\zeta }_3^{-1}$

$-{\zeta }_3$

$-{\zeta }_3$

$-{\zeta }_3^{-1}$

54.4.1d2

C

$1$

$-1$

$1$

$1$

$1$

$1$

$1$

$-1$

$-1$

${\zeta }_3$

${\zeta }_3^{-1}$

${\zeta }_3^{-1}$

${\zeta }_3$

${\zeta }_3$

${\zeta }_3^{-1}$

${\zeta }_3$

${\zeta }_3^{-1}$

${\zeta }_3^{-1}$

${\zeta }_3$

${\zeta }_3$

${\zeta }_3^{-1}$

$-{\zeta }_3^{-1}$

$-{\zeta }_3$

$-{\zeta }_3$

$-{\zeta }_3^{-1}$

$-{\zeta }_3^{-1}$

$-{\zeta }_3$

54.4.1e1

C

$1$

$1$

${\zeta }_9^{-3}$

${\zeta }_9^3$

$1$

${\zeta }_9^{-3}$

${\zeta }_9^3$

${\zeta }_9^3$

${\zeta }_9^{-3}$

${\zeta }_9^{-4}$

${\zeta }_9^4$

${\zeta }_9$

${\zeta }_9^{-1}$

${\zeta }_9^2$

${\zeta }_9^{-2}$

${\zeta }_9^{-4}$

${\zeta }_9^4$

${\zeta }_9$

${\zeta }_9^{-1}$

${\zeta }_9^2$

${\zeta }_9^{-2}$

${\zeta }_9^{-2}$

${\zeta }_9^2$

${\zeta }_9^{-1}$

${\zeta }_9$

${\zeta }_9^4$

${\zeta }_9^{-4}$

54.4.1e2

C

$1$

$1$

${\zeta }_9^3$

${\zeta }_9^{-3}$

$1$

${\zeta }_9^3$

${\zeta }_9^{-3}$

${\zeta }_9^{-3}$

${\zeta }_9^3$

${\zeta }_9^4$

${\zeta }_9^{-4}$

${\zeta }_9^{-1}$

${\zeta }_9$

${\zeta }_9^{-2}$

${\zeta }_9^2$

${\zeta }_9^4$

${\zeta }_9^{-4}$

${\zeta }_9^{-1}$

${\zeta }_9$

${\zeta }_9^{-2}$

${\zeta }_9^2$

${\zeta }_9^2$

${\zeta }_9^{-2}$

${\zeta }_9$

${\zeta }_9^{-1}$

${\zeta }_9^{-4}$

${\zeta }_9^4$

54.4.1e3

C

$1$

$1$

${\zeta }_9^{-3}$

${\zeta }_9^3$

$1$

${\zeta }_9^{-3}$

${\zeta }_9^3$

${\zeta }_9^3$

${\zeta }_9^{-3}$

${\zeta }_9^2$

${\zeta }_9^{-2}$

${\zeta }_9^4$

${\zeta }_9^{-4}$

${\zeta }_9^{-1}$

${\zeta }_9$

${\zeta }_9^2$

${\zeta }_9^{-2}$

${\zeta }_9^4$

${\zeta }_9^{-4}$

${\zeta }_9^{-1}$

${\zeta }_9$

${\zeta }_9$

${\zeta }_9^{-1}$

${\zeta }_9^{-4}$

${\zeta }_9^4$

${\zeta }_9^{-2}$

${\zeta }_9^2$

54.4.1e4

C

$1$

$1$

${\zeta }_9^3$

${\zeta }_9^{-3}$

$1$

${\zeta }_9^3$

${\zeta }_9^{-3}$

${\zeta }_9^{-3}$

${\zeta }_9^3$

${\zeta }_9^{-2}$

${\zeta }_9^2$

${\zeta }_9^{-4}$

${\zeta }_9^4$

${\zeta }_9$

${\zeta }_9^{-1}$

${\zeta }_9^{-2}$

${\zeta }_9^2$

${\zeta }_9^{-4}$

${\zeta }_9^4$

${\zeta }_9$

${\zeta }_9^{-1}$

${\zeta }_9^{-1}$

${\zeta }_9$

${\zeta }_9^4$

${\zeta }_9^{-4}$

${\zeta }_9^2$

${\zeta }_9^{-2}$

54.4.1e5

C

$1$

$1$

${\zeta }_9^{-3}$

${\zeta }_9^3$

$1$

${\zeta }_9^{-3}$

${\zeta }_9^3$

${\zeta }_9^3$

${\zeta }_9^{-3}$

${\zeta }_9^{-1}$

${\zeta }_9$

${\zeta }_9^{-2}$

${\zeta }_9^2$

${\zeta }_9^{-4}$

${\zeta }_9^4$

${\zeta }_9^{-1}$

${\zeta }_9$

${\zeta }_9^{-2}$

${\zeta }_9^2$

${\zeta }_9^{-4}$

${\zeta }_9^4$

${\zeta }_9^4$

${\zeta }_9^{-4}$

${\zeta }_9^2$

${\zeta }_9^{-2}$

${\zeta }_9$

${\zeta }_9^{-1}$

54.4.1e6

C

$1$

$1$

${\zeta }_9^3$

${\zeta }_9^{-3}$

$1$

${\zeta }_9^3$

${\zeta }_9^{-3}$

${\zeta }_9^{-3}$

${\zeta }_9^3$

${\zeta }_9$

${\zeta }_9^{-1}$

${\zeta }_9^2$

${\zeta }_9^{-2}$

${\zeta }_9^4$

${\zeta }_9^{-4}$

${\zeta }_9$

${\zeta }_9^{-1}$

${\zeta }_9^2$

${\zeta }_9^{-2}$

${\zeta }_9^4$

${\zeta }_9^{-4}$

${\zeta }_9^{-4}$

${\zeta }_9^4$

${\zeta }_9^{-2}$

${\zeta }_9^2$

${\zeta }_9^{-1}$

${\zeta }_9$

54.4.1f1

C

$1$

$-1$

${\zeta }_9^{-3}$

${\zeta }_9^3$

$1$

${\zeta }_9^{-3}$

${\zeta }_9^3$

$-{\zeta }_9^3$

$-{\zeta }_9^{-3}$

${\zeta }_9^{-4}$

${\zeta }_9^4$

${\zeta }_9$

${\zeta }_9^{-1}$

${\zeta }_9^2$

${\zeta }_9^{-2}$

${\zeta }_9^{-4}$

${\zeta }_9^4$

${\zeta }_9$

${\zeta }_9^{-1}$

${\zeta }_9^2$

${\zeta }_9^{-2}$

$-{\zeta }_9^{-2}$

$-{\zeta }_9^2$

$-{\zeta }_9^{-1}$

$-{\zeta }_9$

$-{\zeta }_9^4$

$-{\zeta }_9^{-4}$

54.4.1f2

C

$1$

$-1$

${\zeta }_9^3$

${\zeta }_9^{-3}$

$1$

${\zeta }_9^3$

${\zeta }_9^{-3}$

$-{\zeta }_9^{-3}$

$-{\zeta }_9^3$

${\zeta }_9^4$

${\zeta }_9^{-4}$

${\zeta }_9^{-1}$

${\zeta }_9$

${\zeta }_9^{-2}$

${\zeta }_9^2$

${\zeta }_9^4$

${\zeta }_9^{-4}$

${\zeta }_9^{-1}$

${\zeta }_9$

${\zeta }_9^{-2}$

${\zeta }_9^2$

$-{\zeta }_9^2$

$-{\zeta }_9^{-2}$

$-{\zeta }_9$

$-{\zeta }_9^{-1}$

$-{\zeta }_9^{-4}$

$-{\zeta }_9^4$

54.4.1f3

C

$1$

$-1$

${\zeta }_9^{-3}$

${\zeta }_9^3$

$1$

${\zeta }_9^{-3}$

${\zeta }_9^3$

$-{\zeta }_9^3$

$-{\zeta }_9^{-3}$

${\zeta }_9^2$

${\zeta }_9^{-2}$

${\zeta }_9^4$

${\zeta }_9^{-4}$

${\zeta }_9^{-1}$

${\zeta }_9$

${\zeta }_9^2$

${\zeta }_9^{-2}$

${\zeta }_9^4$

${\zeta }_9^{-4}$

${\zeta }_9^{-1}$

${\zeta }_9$

$-{\zeta }_9$

$-{\zeta }_9^{-1}$

$-{\zeta }_9^{-4}$

$-{\zeta }_9^4$

$-{\zeta }_9^{-2}$

$-{\zeta }_9^2$

54.4.1f4

C

$1$

$-1$

${\zeta }_9^3$

${\zeta }_9^{-3}$

$1$

${\zeta }_9^3$

${\zeta }_9^{-3}$

$-{\zeta }_9^{-3}$

$-{\zeta }_9^3$

${\zeta }_9^{-2}$

${\zeta }_9^2$

${\zeta }_9^{-4}$

${\zeta }_9^4$

${\zeta }_9$

${\zeta }_9^{-1}$

${\zeta }_9^{-2}$

${\zeta }_9^2$

${\zeta }_9^{-4}$

${\zeta }_9^4$

${\zeta }_9$

${\zeta }_9^{-1}$

$-{\zeta }_9^{-1}$

$-{\zeta }_9$

$-{\zeta }_9^4$

$-{\zeta }_9^{-4}$

$-{\zeta }_9^2$

$-{\zeta }_9^{-2}$

54.4.1f5

C

$1$

$-1$

${\zeta }_9^{-3}$

${\zeta }_9^3$

$1$

${\zeta }_9^{-3}$

${\zeta }_9^3$

$-{\zeta }_9^3$

$-{\zeta }_9^{-3}$

${\zeta }_9^{-1}$

${\zeta }_9$

${\zeta }_9^{-2}$

${\zeta }_9^2$

${\zeta }_9^{-4}$

${\zeta }_9^4$

${\zeta }_9^{-1}$

${\zeta }_9$

${\zeta }_9^{-2}$

${\zeta }_9^2$

${\zeta }_9^{-4}$

${\zeta }_9^4$

$-{\zeta }_9^4$

$-{\zeta }_9^{-4}$

$-{\zeta }_9^2$

$-{\zeta }_9^{-2}$

$-{\zeta }_9$

$-{\zeta }_9^{-1}$

54.4.1f6

C

$1$

$-1$

${\zeta }_9^3$

${\zeta }_9^{-3}$

$1$

${\zeta }_9^3$

${\zeta }_9^{-3}$

$-{\zeta }_9^{-3}$

$-{\zeta }_9^3$

${\zeta }_9$

${\zeta }_9^{-1}$

${\zeta }_9^2$

${\zeta }_9^{-2}$

${\zeta }_9^4$

${\zeta }_9^{-4}$

${\zeta }_9$

${\zeta }_9^{-1}$

${\zeta }_9^2$

${\zeta }_9^{-2}$

${\zeta }_9^4$

${\zeta }_9^{-4}$

$-{\zeta }_9^{-4}$

$-{\zeta }_9^4$

$-{\zeta }_9^{-2}$

$-{\zeta }_9^2$

$-{\zeta }_9^{-1}$

$-{\zeta }_9$

54.4.2a

R

$2$

$0$

$2$

$2$

$-1$

$-1$

$-1$

$0$

$0$

$2$

$2$

$2$

$2$

$2$

$2$

$-1$

$-1$

$-1$

$-1$

$-1$

$-1$

$0$

$0$

$0$

$0$

$0$

$0$

54.4.2b1

C

$2$

$0$

$2$

$2$

$-1$

$-1$

$-1$

$0$

$0$

$2{\zeta }_3^{-1}$

$2{\zeta }_3$

$2{\zeta }_3$

$2{\zeta }_3^{-1}$

$2{\zeta }_3^{-1}$

$2{\zeta }_3$

$-{\zeta }_3^{-1}$

$-{\zeta }_3$

$-{\zeta }_3$

$-{\zeta }_3^{-1}$

$-{\zeta }_3^{-1}$

$-{\zeta }_3$

$0$

$0$

$0$

$0$

$0$

$0$

54.4.2b2

C

$2$

$0$

$2$

$2$

$-1$

$-1$

$-1$

$0$

$0$

$2{\zeta }_3$

$2{\zeta }_3^{-1}$

$2{\zeta }_3^{-1}$

$2{\zeta }_3$

$2{\zeta }_3$

$2{\zeta }_3^{-1}$

$-{\zeta }_3$

$-{\zeta }_3^{-1}$

$-{\zeta }_3^{-1}$

$-{\zeta }_3$

$-{\zeta }_3$

$-{\zeta }_3^{-1}$

$0$

$0$

$0$

$0$

$0$

$0$

54.4.2c1

C

$2$

$0$

$2{\zeta }_9^{-3}$

$2{\zeta }_9^3$

$-1$

$-{\zeta }_9^{-3}$

$-{\zeta }_9^3$

$0$

$0$

$2{\zeta }_9^{-4}$

$2{\zeta }_9^4$

$2{\zeta }_9$

$2{\zeta }_9^{-1}$

$2{\zeta }_9^2$

$2{\zeta }_9^{-2}$

$-{\zeta }_9^{-4}$

$-{\zeta }_9^4$

$-{\zeta }_9$

$-{\zeta }_9^{-1}$

$-{\zeta }_9^2$

$-{\zeta }_9^{-2}$

$0$

$0$

$0$

$0$

$0$

$0$

54.4.2c2

C

$2$

$0$

$2{\zeta }_9^3$

$2{\zeta }_9^{-3}$

$-1$

$-{\zeta }_9^3$

$-{\zeta }_9^{-3}$

$0$

$0$

$2{\zeta }_9^4$

$2{\zeta }_9^{-4}$

$2{\zeta }_9^{-1}$

$2{\zeta }_9$

$2{\zeta }_9^{-2}$

$2{\zeta }_9^2$

$-{\zeta }_9^4$

$-{\zeta }_9^{-4}$

$-{\zeta }_9^{-1}$

$-{\zeta }_9$

$-{\zeta }_9^{-2}$

$-{\zeta }_9^2$

$0$

$0$

$0$

$0$

$0$

$0$

54.4.2c3

C

$2$

$0$

$2{\zeta }_9^{-3}$

$2{\zeta }_9^3$

$-1$

$-{\zeta }_9^{-3}$

$-{\zeta }_9^3$

$0$

$0$

$2{\zeta }_9^2$

$2{\zeta }_9^{-2}$

$2{\zeta }_9^4$

$2{\zeta }_9^{-4}$

$2{\zeta }_9^{-1}$

$2{\zeta }_9$

$-{\zeta }_9^2$

$-{\zeta }_9^{-2}$

$-{\zeta }_9^4$

$-{\zeta }_9^{-4}$

$-{\zeta }_9^{-1}$

$-{\zeta }_9$

$0$

$0$

$0$

$0$

$0$

$0$

54.4.2c4

C

$2$

$0$

$2{\zeta }_9^3$

$2{\zeta }_9^{-3}$

$-1$

$-{\zeta }_9^3$

$-{\zeta }_9^{-3}$

$0$

$0$

$2{\zeta }_9^{-2}$

$2{\zeta }_9^2$

$2{\zeta }_9^{-4}$

$2{\zeta }_9^4$

$2{\zeta }_9$

$2{\zeta }_9^{-1}$

$-{\zeta }_9^{-2}$

$-{\zeta }_9^2$

$-{\zeta }_9^{-4}$

$-{\zeta }_9^4$

$-{\zeta }_9$

$-{\zeta }_9^{-1}$

$0$

$0$

$0$

$0$

$0$

$0$

54.4.2c5

C

$2$

$0$

$2{\zeta }_9^{-3}$

$2{\zeta }_9^3$

$-1$

$-{\zeta }_9^{-3}$

$-{\zeta }_9^3$

$0$

$0$

$2{\zeta }_9^{-1}$

$2{\zeta }_9$

$2{\zeta }_9^{-2}$

$2{\zeta }_9^2$

$2{\zeta }_9^{-4}$

$2{\zeta }_9^4$

$-{\zeta }_9^{-1}$

$-{\zeta }_9$

$-{\zeta }_9^{-2}$

$-{\zeta }_9^2$

$-{\zeta }_9^{-4}$

$-{\zeta }_9^4$

$0$

$0$

$0$

$0$

$0$

$0$

54.4.2c6

C

$2$

$0$

$2{\zeta }_9^3$

$2{\zeta }_9^{-3}$

$-1$

$-{\zeta }_9^3$

$-{\zeta }_9^{-3}$

$0$

$0$

$2{\zeta }_9$

$2{\zeta }_9^{-1}$

$2{\zeta }_9^2$

$2{\zeta }_9^{-2}$

$2{\zeta }_9^4$

$2{\zeta }_9^{-4}$

$-{\zeta }_9$

$-{\zeta }_9^{-1}$

$-{\zeta }_9^2$

$-{\zeta }_9^{-2}$

$-{\zeta }_9^4$

$-{\zeta }_9^{-4}$

$0$

$0$

$0$

$0$

$0$

$0$