Character table for $C_5:Q_8$

The column representing the conjugacy class 4B is highlighted below.

		1A	2A	4A	4B	4C	5A1	5A2	10A1	10A3	20A1	20A3	20A7	20A9
	Size	1	1	2	10	10	2	2	2	2	2	2	2	2
	2 P	1A	1A	2A	2A	2A	5A2	5A1	5A1	5A2	10A1	10A3	10A3	10A1
	5 P	1A	2A	4A	4B	4C	1A	1A	2A	2A	4A	4A	4A	4A
	Type
40.4.1a	R	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
40.4.1b	R	$1$	$1$	$-1$	$-1$	$1$	$1$	$1$	$1$	$1$	$-1$	$-1$	$-1$	$-1$
40.4.1c	R	$1$	$1$	$-1$	$1$	$-1$	$1$	$1$	$1$	$1$	$-1$	$-1$	$-1$	$-1$
40.4.1d	R	$1$	$1$	$1$	$-1$	$-1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
40.4.2a	S	$2$	$-2$	$0$	$0$	$0$	$2$	$2$	$-2$	$-2$	$0$	$0$	$0$	$0$
40.4.2b1	R	$2$	$2$	$2$	$0$	$0$	${\zeta }_5^{-2}+{\zeta }_5^2$	${\zeta }_5^{-1}+{\zeta }_5$	${\zeta }_5^{-1}+{\zeta }_5$	${\zeta }_5^{-2}+{\zeta }_5^2$	${\zeta }_5^{-2}+{\zeta }_5^2$	${\zeta }_5^{-1}+{\zeta }_5$	${\zeta }_5^{-1}+{\zeta }_5$	${\zeta }_5^{-2}+{\zeta }_5^2$
40.4.2b2	R	$2$	$2$	$2$	$0$	$0$	${\zeta }_5^{-1}+{\zeta }_5$	${\zeta }_5^{-2}+{\zeta }_5^2$	${\zeta }_5^{-2}+{\zeta }_5^2$	${\zeta }_5^{-1}+{\zeta }_5$	${\zeta }_5^{-1}+{\zeta }_5$	${\zeta }_5^{-2}+{\zeta }_5^2$	${\zeta }_5^{-2}+{\zeta }_5^2$	${\zeta }_5^{-1}+{\zeta }_5$
40.4.2c1	R	$2$	$2$	$-2$	$0$	$0$	${\zeta }_5^{-2}+{\zeta }_5^2$	${\zeta }_5^{-1}+{\zeta }_5$	${\zeta }_5^{-1}+{\zeta }_5$	${\zeta }_5^{-2}+{\zeta }_5^2$	$-{\zeta }_5^{-2}-{\zeta }_5^2$	$-{\zeta }_5^{-1}-{\zeta }_5$	$-{\zeta }_5^{-1}-{\zeta }_5$	$-{\zeta }_5^{-2}-{\zeta }_5^2$
40.4.2c2	R	$2$	$2$	$-2$	$0$	$0$	${\zeta }_5^{-1}+{\zeta }_5$	${\zeta }_5^{-2}+{\zeta }_5^2$	${\zeta }_5^{-2}+{\zeta }_5^2$	${\zeta }_5^{-1}+{\zeta }_5$	$-{\zeta }_5^{-1}-{\zeta }_5$	$-{\zeta }_5^{-2}-{\zeta }_5^2$	$-{\zeta }_5^{-2}-{\zeta }_5^2$	$-{\zeta }_5^{-1}-{\zeta }_5$
40.4.2d1	S	$2$	$-2$	$0$	$0$	$0$	$-{\zeta }_{20}^{-2}-{\zeta }_{20}^2$	${\zeta }_{20}^{-4}+{\zeta }_{20}^4$	$-{\zeta }_{20}^{-4}-{\zeta }_{20}^4$	${\zeta }_{20}^{-2}+{\zeta }_{20}^2$	$-{\zeta }_{20}^{-3}-{\zeta }_{20}^3$	${\zeta }_{20}^{-1}+{\zeta }_{20}$	$-{\zeta }_{20}^{-1}-{\zeta }_{20}$	${\zeta }_{20}^{-3}+{\zeta }_{20}^3$
40.4.2d2	S	$2$	$-2$	$0$	$0$	$0$	$-{\zeta }_{20}^{-2}-{\zeta }_{20}^2$	${\zeta }_{20}^{-4}+{\zeta }_{20}^4$	$-{\zeta }_{20}^{-4}-{\zeta }_{20}^4$	${\zeta }_{20}^{-2}+{\zeta }_{20}^2$	${\zeta }_{20}^{-3}+{\zeta }_{20}^3$	$-{\zeta }_{20}^{-1}-{\zeta }_{20}$	${\zeta }_{20}^{-1}+{\zeta }_{20}$	$-{\zeta }_{20}^{-3}-{\zeta }_{20}^3$
40.4.2d3	S	$2$	$-2$	$0$	$0$	$0$	${\zeta }_{20}^{-4}+{\zeta }_{20}^4$	$-{\zeta }_{20}^{-2}-{\zeta }_{20}^2$	${\zeta }_{20}^{-2}+{\zeta }_{20}^2$	$-{\zeta }_{20}^{-4}-{\zeta }_{20}^4$	$-{\zeta }_{20}^{-1}-{\zeta }_{20}$	$-{\zeta }_{20}^{-3}-{\zeta }_{20}^3$	${\zeta }_{20}^{-3}+{\zeta }_{20}^3$	${\zeta }_{20}^{-1}+{\zeta }_{20}$
40.4.2d4	S	$2$	$-2$	$0$	$0$	$0$	${\zeta }_{20}^{-4}+{\zeta }_{20}^4$	$-{\zeta }_{20}^{-2}-{\zeta }_{20}^2$	${\zeta }_{20}^{-2}+{\zeta }_{20}^2$	$-{\zeta }_{20}^{-4}-{\zeta }_{20}^4$	${\zeta }_{20}^{-1}+{\zeta }_{20}$	${\zeta }_{20}^{-3}+{\zeta }_{20}^3$	$-{\zeta }_{20}^{-3}-{\zeta }_{20}^3$	$-{\zeta }_{20}^{-1}-{\zeta }_{20}$