Character table for $C_{24}$

1A

2A

3A1

3A-1

4A1

4A-1

6A1

6A-1

8A1

8A-1

8A3

8A-3

12A1

12A-1

12A5

12A-5

24A1

24A-1

24A5

24A-5

24A7

24A-7

24A11

24A-11

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

2 P

1A

1A

3A-1

3A1

2A

2A

3A1

3A-1

4A1

4A-1

4A-1

4A1

6A1

6A-1

6A-1

6A1

12A1

12A-1

12A5

12A-5

12A-5

12A5

12A-1

12A1

3 P

1A

2A

1A

1A

4A-1

4A1

2A

2A

8A3

8A-3

8A1

8A-1

4A1

4A-1

4A1

4A-1

8A1

8A-1

8A-3

8A3

8A-1

8A1

8A3

8A-3

Type

24.2.1a

R

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

24.2.1b

R

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$-1$

$-1$

$-1$

$-1$

$1$

$1$

$1$

$1$

$-1$

$-1$

$-1$

$-1$

$-1$

$-1$

$-1$

$-1$

24.2.1c1

C

$1$

$1$

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

${\zeta }_3$

$1$

$1$

${\zeta }_3$

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

$1$

$1$

$1$

$1$

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

${\zeta }_3$

${\zeta }_3$

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

${\zeta }_3$

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

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

${\zeta }_3$

${\zeta }_3$

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

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

${\zeta }_3$

24.2.1c2

C

$1$

$1$

${\zeta }_3$

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

$1$

$1$

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

${\zeta }_3$

$1$

$1$

$1$

$1$

${\zeta }_3$

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

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

${\zeta }_3$

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

${\zeta }_3$

${\zeta }_3$

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

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

${\zeta }_3$

${\zeta }_3$

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

24.2.1d1

C

$1$

$1$

$1$

$1$

$-1$

$-1$

$1$

$1$

$-i$

$i$

$i$

$-i$

$-1$

$-1$

$-1$

$-1$

$i$

$-i$

$i$

$-i$

$-i$

$i$

$-i$

$i$

24.2.1d2

C

$1$

$1$

$1$

$1$

$-1$

$-1$

$1$

$1$

$i$

$-i$

$-i$

$i$

$-1$

$-1$

$-1$

$-1$

$-i$

$i$

$-i$

$i$

$i$

$-i$

$i$

$-i$

24.2.1e1

C

$1$

$1$

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

${\zeta }_3$

$1$

$1$

${\zeta }_3$

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

$-1$

$-1$

$-1$

$-1$

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

${\zeta }_3$

${\zeta }_3$

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

$-{\zeta }_3$

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

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

$-{\zeta }_3$

$-{\zeta }_3$

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

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

$-{\zeta }_3$

24.2.1e2

C

$1$

$1$

${\zeta }_3$

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

$1$

$1$

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

${\zeta }_3$

$-1$

$-1$

$-1$

$-1$

${\zeta }_3$

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

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

${\zeta }_3$

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

$-{\zeta }_3$

$-{\zeta }_3$

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

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

$-{\zeta }_3$

$-{\zeta }_3$

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

24.2.1f1

C

$1$

$-1$

$1$

$1$

$-{\zeta }_8^2$

${\zeta }_8^2$

$-1$

$-1$

${\zeta }_8^3$

$-{\zeta }_8$

${\zeta }_8$

$-{\zeta }_8^3$

${\zeta }_8^2$

$-{\zeta }_8^2$

${\zeta }_8^2$

$-{\zeta }_8^2$

${\zeta }_8$

$-{\zeta }_8^3$

$-{\zeta }_8$

${\zeta }_8^3$

$-{\zeta }_8^3$

${\zeta }_8$

${\zeta }_8^3$

$-{\zeta }_8$

24.2.1f2

C

$1$

$-1$

$1$

$1$

${\zeta }_8^2$

$-{\zeta }_8^2$

$-1$

$-1$

$-{\zeta }_8$

${\zeta }_8^3$

$-{\zeta }_8^3$

${\zeta }_8$

$-{\zeta }_8^2$

${\zeta }_8^2$

$-{\zeta }_8^2$

${\zeta }_8^2$

$-{\zeta }_8^3$

${\zeta }_8$

${\zeta }_8^3$

$-{\zeta }_8$

${\zeta }_8$

$-{\zeta }_8^3$

$-{\zeta }_8$

${\zeta }_8^3$

24.2.1f3

C

$1$

$-1$

$1$

$1$

$-{\zeta }_8^2$

${\zeta }_8^2$

$-1$

$-1$

$-{\zeta }_8^3$

${\zeta }_8$

$-{\zeta }_8$

${\zeta }_8^3$

${\zeta }_8^2$

$-{\zeta }_8^2$

${\zeta }_8^2$

$-{\zeta }_8^2$

$-{\zeta }_8$

${\zeta }_8^3$

${\zeta }_8$

$-{\zeta }_8^3$

${\zeta }_8^3$

$-{\zeta }_8$

$-{\zeta }_8^3$

${\zeta }_8$

24.2.1f4

C

$1$

$-1$

$1$

$1$

${\zeta }_8^2$

$-{\zeta }_8^2$

$-1$

$-1$

${\zeta }_8$

$-{\zeta }_8^3$

${\zeta }_8^3$

$-{\zeta }_8$

$-{\zeta }_8^2$

${\zeta }_8^2$

$-{\zeta }_8^2$

${\zeta }_8^2$

${\zeta }_8^3$

$-{\zeta }_8$

$-{\zeta }_8^3$

${\zeta }_8$

$-{\zeta }_8$

${\zeta }_8^3$

${\zeta }_8$

$-{\zeta }_8^3$

24.2.1g1

C

$1$

$1$

$-{\zeta }_{12}^2$

${\zeta }_{12}^4$

$-1$

$-1$

${\zeta }_{12}^4$

$-{\zeta }_{12}^2$

$-{\zeta }_{12}^3$

${\zeta }_{12}^3$

${\zeta }_{12}^3$

$-{\zeta }_{12}^3$

${\zeta }_{12}^2$

$-{\zeta }_{12}^4$

$-{\zeta }_{12}^4$

${\zeta }_{12}^2$

$-{\zeta }_{12}$

${\zeta }_{12}^5$

$-{\zeta }_{12}^5$

${\zeta }_{12}$

${\zeta }_{12}$

$-{\zeta }_{12}^5$

${\zeta }_{12}^5$

$-{\zeta }_{12}$

24.2.1g2

C

$1$

$1$

${\zeta }_{12}^4$

$-{\zeta }_{12}^2$

$-1$

$-1$

$-{\zeta }_{12}^2$

${\zeta }_{12}^4$

${\zeta }_{12}^3$

$-{\zeta }_{12}^3$

$-{\zeta }_{12}^3$

${\zeta }_{12}^3$

$-{\zeta }_{12}^4$

${\zeta }_{12}^2$

${\zeta }_{12}^2$

$-{\zeta }_{12}^4$

${\zeta }_{12}^5$

$-{\zeta }_{12}$

${\zeta }_{12}$

$-{\zeta }_{12}^5$

$-{\zeta }_{12}^5$

${\zeta }_{12}$

$-{\zeta }_{12}$

${\zeta }_{12}^5$

24.2.1g3

C

$1$

$1$

$-{\zeta }_{12}^2$

${\zeta }_{12}^4$

$-1$

$-1$

${\zeta }_{12}^4$

$-{\zeta }_{12}^2$

${\zeta }_{12}^3$

$-{\zeta }_{12}^3$

$-{\zeta }_{12}^3$

${\zeta }_{12}^3$

${\zeta }_{12}^2$

$-{\zeta }_{12}^4$

$-{\zeta }_{12}^4$

${\zeta }_{12}^2$

${\zeta }_{12}$

$-{\zeta }_{12}^5$

${\zeta }_{12}^5$

$-{\zeta }_{12}$

$-{\zeta }_{12}$

${\zeta }_{12}^5$

$-{\zeta }_{12}^5$

${\zeta }_{12}$

24.2.1g4

C

$1$

$1$

${\zeta }_{12}^4$

$-{\zeta }_{12}^2$

$-1$

$-1$

$-{\zeta }_{12}^2$

${\zeta }_{12}^4$

$-{\zeta }_{12}^3$

${\zeta }_{12}^3$

${\zeta }_{12}^3$

$-{\zeta }_{12}^3$

$-{\zeta }_{12}^4$

${\zeta }_{12}^2$

${\zeta }_{12}^2$

$-{\zeta }_{12}^4$

$-{\zeta }_{12}^5$

${\zeta }_{12}$

$-{\zeta }_{12}$

${\zeta }_{12}^5$

${\zeta }_{12}^5$

$-{\zeta }_{12}$

${\zeta }_{12}$

$-{\zeta }_{12}^5$

24.2.1h1

C

$1$

$-1$

$-{\zeta }_{24}^4$

${\zeta }_{24}^8$

$-{\zeta }_{24}^6$

${\zeta }_{24}^6$

$-{\zeta }_{24}^8$

${\zeta }_{24}^4$

${\zeta }_{24}^9$

$-{\zeta }_{24}^3$

${\zeta }_{24}^3$

$-{\zeta }_{24}^9$

$-{\zeta }_{24}^{10}$

${\zeta }_{24}^2$

$-{\zeta }_{24}^2$

${\zeta }_{24}^{10}$

${\zeta }_{24}^{11}$

$-{\zeta }_{24}$

${\zeta }_{24}^7$

$-{\zeta }_{24}^5$

${\zeta }_{24}^5$

$-{\zeta }_{24}^7$

${\zeta }_{24}$

$-{\zeta }_{24}^{11}$

24.2.1h2

C

$1$

$-1$

${\zeta }_{24}^8$

$-{\zeta }_{24}^4$

${\zeta }_{24}^6$

$-{\zeta }_{24}^6$

${\zeta }_{24}^4$

$-{\zeta }_{24}^8$

$-{\zeta }_{24}^3$

${\zeta }_{24}^9$

$-{\zeta }_{24}^9$

${\zeta }_{24}^3$

${\zeta }_{24}^2$

$-{\zeta }_{24}^{10}$

${\zeta }_{24}^{10}$

$-{\zeta }_{24}^2$

$-{\zeta }_{24}$

${\zeta }_{24}^{11}$

$-{\zeta }_{24}^5$

${\zeta }_{24}^7$

$-{\zeta }_{24}^7$

${\zeta }_{24}^5$

$-{\zeta }_{24}^{11}$

${\zeta }_{24}$

24.2.1h3

C

$1$

$-1$

$-{\zeta }_{24}^4$

${\zeta }_{24}^8$

$-{\zeta }_{24}^6$

${\zeta }_{24}^6$

$-{\zeta }_{24}^8$

${\zeta }_{24}^4$

$-{\zeta }_{24}^9$

${\zeta }_{24}^3$

$-{\zeta }_{24}^3$

${\zeta }_{24}^9$

$-{\zeta }_{24}^{10}$

${\zeta }_{24}^2$

$-{\zeta }_{24}^2$

${\zeta }_{24}^{10}$

$-{\zeta }_{24}^{11}$

${\zeta }_{24}$

$-{\zeta }_{24}^7$

${\zeta }_{24}^5$

$-{\zeta }_{24}^5$

${\zeta }_{24}^7$

$-{\zeta }_{24}$

${\zeta }_{24}^{11}$

24.2.1h4

C

$1$

$-1$

${\zeta }_{24}^8$

$-{\zeta }_{24}^4$

${\zeta }_{24}^6$

$-{\zeta }_{24}^6$

${\zeta }_{24}^4$

$-{\zeta }_{24}^8$

${\zeta }_{24}^3$

$-{\zeta }_{24}^9$

${\zeta }_{24}^9$

$-{\zeta }_{24}^3$

${\zeta }_{24}^2$

$-{\zeta }_{24}^{10}$

${\zeta }_{24}^{10}$

$-{\zeta }_{24}^2$

${\zeta }_{24}$

$-{\zeta }_{24}^{11}$

${\zeta }_{24}^5$

$-{\zeta }_{24}^7$

${\zeta }_{24}^7$

$-{\zeta }_{24}^5$

${\zeta }_{24}^{11}$

$-{\zeta }_{24}$

24.2.1h5

C

$1$

$-1$

$-{\zeta }_{24}^4$

${\zeta }_{24}^8$

${\zeta }_{24}^6$

$-{\zeta }_{24}^6$

$-{\zeta }_{24}^8$

${\zeta }_{24}^4$

$-{\zeta }_{24}^3$

${\zeta }_{24}^9$

$-{\zeta }_{24}^9$

${\zeta }_{24}^3$

${\zeta }_{24}^{10}$

$-{\zeta }_{24}^2$

${\zeta }_{24}^2$

$-{\zeta }_{24}^{10}$

${\zeta }_{24}^5$

$-{\zeta }_{24}^7$

${\zeta }_{24}$

$-{\zeta }_{24}^{11}$

${\zeta }_{24}^{11}$

$-{\zeta }_{24}$

${\zeta }_{24}^7$

$-{\zeta }_{24}^5$

24.2.1h6

C

$1$

$-1$

${\zeta }_{24}^8$

$-{\zeta }_{24}^4$

$-{\zeta }_{24}^6$

${\zeta }_{24}^6$

${\zeta }_{24}^4$

$-{\zeta }_{24}^8$

${\zeta }_{24}^9$

$-{\zeta }_{24}^3$

${\zeta }_{24}^3$

$-{\zeta }_{24}^9$

$-{\zeta }_{24}^2$

${\zeta }_{24}^{10}$

$-{\zeta }_{24}^{10}$

${\zeta }_{24}^2$

$-{\zeta }_{24}^7$

${\zeta }_{24}^5$

$-{\zeta }_{24}^{11}$

${\zeta }_{24}$

$-{\zeta }_{24}$

${\zeta }_{24}^{11}$

$-{\zeta }_{24}^5$

${\zeta }_{24}^7$

24.2.1h7

C

$1$

$-1$

$-{\zeta }_{24}^4$

${\zeta }_{24}^8$

${\zeta }_{24}^6$

$-{\zeta }_{24}^6$

$-{\zeta }_{24}^8$

${\zeta }_{24}^4$

${\zeta }_{24}^3$

$-{\zeta }_{24}^9$

${\zeta }_{24}^9$

$-{\zeta }_{24}^3$

${\zeta }_{24}^{10}$

$-{\zeta }_{24}^2$

${\zeta }_{24}^2$

$-{\zeta }_{24}^{10}$

$-{\zeta }_{24}^5$

${\zeta }_{24}^7$

$-{\zeta }_{24}$

${\zeta }_{24}^{11}$

$-{\zeta }_{24}^{11}$

${\zeta }_{24}$

$-{\zeta }_{24}^7$

${\zeta }_{24}^5$

24.2.1h8

C

$1$

$-1$

${\zeta }_{24}^8$

$-{\zeta }_{24}^4$

$-{\zeta }_{24}^6$

${\zeta }_{24}^6$

${\zeta }_{24}^4$

$-{\zeta }_{24}^8$

$-{\zeta }_{24}^9$

${\zeta }_{24}^3$

$-{\zeta }_{24}^3$

${\zeta }_{24}^9$

$-{\zeta }_{24}^2$

${\zeta }_{24}^{10}$

$-{\zeta }_{24}^{10}$

${\zeta }_{24}^2$

${\zeta }_{24}^7$

$-{\zeta }_{24}^5$

${\zeta }_{24}^{11}$

$-{\zeta }_{24}$

${\zeta }_{24}$

$-{\zeta }_{24}^{11}$

${\zeta }_{24}^5$

$-{\zeta }_{24}^7$