Character table for $C_{20}:C_4$

The column representing the conjugacy class 10C3 is highlighted below.

		1A	2A	2B	2C	4A	4B	4C1	4C-1	4D1	4D-1	5A1	5A2	10A1	10A3	10B1	10B3	10C1	10C3	20A1	20A3	20A7	20A9	20B1	20B3	20B7	20B9
	Size	1	1	1	1	2	2	10	10	10	10	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2
	2 P	1A	1A	1A	1A	2C	2C	2A	2A	2A	2A	5A2	5A1	5A1	5A2	5A2	5A1	5A2	5A1	10C1	10C3	10C3	10C1	10C1	10C3	10C3	10C1
	5 P	1A	2A	2B	2C	4A	4B	4C1	4C-1	4D1	4D-1	1A	1A	2A	2A	2B	2B	2C	2C	4A	4A	4A	4A	4B	4B	4B	4B
	Type
80.13.1a	R	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
80.13.1b	R	$1$	$1$	$1$	$1$	$-1$	$-1$	$-1$	$-1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$-1$	$-1$	$-1$	$-1$	$-1$	$-1$	$-1$	$-1$
80.13.1c	R	$1$	$1$	$1$	$1$	$-1$	$-1$	$1$	$1$	$-1$	$-1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$-1$	$-1$	$-1$	$-1$	$-1$	$-1$	$-1$	$-1$
80.13.1d	R	$1$	$1$	$1$	$1$	$1$	$1$	$-1$	$-1$	$-1$	$-1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
80.13.1e1	C	$1$	$-1$	$-1$	$1$	$-1$	$1$	$-i$	$i$	$-i$	$i$	$1$	$1$	$-1$	$-1$	$-1$	$-1$	$1$	$1$	$1$	$-1$	$-1$	$1$	$-1$	$-1$	$1$	$1$
80.13.1e2	C	$1$	$-1$	$-1$	$1$	$-1$	$1$	$i$	$-i$	$i$	$-i$	$1$	$1$	$-1$	$-1$	$-1$	$-1$	$1$	$1$	$1$	$-1$	$-1$	$1$	$-1$	$-1$	$1$	$1$
80.13.1f1	C	$1$	$-1$	$-1$	$1$	$1$	$-1$	$-i$	$i$	$i$	$-i$	$1$	$1$	$-1$	$-1$	$-1$	$-1$	$1$	$1$	$-1$	$1$	$1$	$-1$	$1$	$1$	$-1$	$-1$
80.13.1f2	C	$1$	$-1$	$-1$	$1$	$1$	$-1$	$i$	$-i$	$-i$	$i$	$1$	$1$	$-1$	$-1$	$-1$	$-1$	$1$	$1$	$-1$	$1$	$1$	$-1$	$1$	$1$	$-1$	$-1$
80.13.2a	R	$2$	$2$	$-2$	$-2$	$0$	$0$	$0$	$0$	$0$	$0$	$2$	$2$	$2$	$2$	$-2$	$-2$	$-2$	$-2$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$
80.13.2b	S	$2$	$-2$	$2$	$-2$	$0$	$0$	$0$	$0$	$0$	$0$	$2$	$2$	$-2$	$-2$	$2$	$2$	$-2$	$-2$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$
80.13.2c1	R	$2$	$2$	$2$	$2$	$2$	$2$	$0$	$0$	$0$	$0$	${\zeta }_5^{-2}+{\zeta }_5^2$	${\zeta }_5^{-1}+{\zeta }_5$	${\zeta }_5^{-1}+{\zeta }_5$	${\zeta }_5^{-2}+{\zeta }_5^2$	${\zeta }_5^{-2}+{\zeta }_5^2$	${\zeta }_5^{-1}+{\zeta }_5$	${\zeta }_5^{-2}+{\zeta }_5^2$	${\zeta }_5^{-1}+{\zeta }_5$	${\zeta }_5^{-1}+{\zeta }_5$	${\zeta }_5^{-2}+{\zeta }_5^2$	${\zeta }_5^{-1}+{\zeta }_5$	${\zeta }_5^{-1}+{\zeta }_5$	${\zeta }_5^{-2}+{\zeta }_5^2$	${\zeta }_5^{-1}+{\zeta }_5$	${\zeta }_5^{-2}+{\zeta }_5^2$	${\zeta }_5^{-2}+{\zeta }_5^2$
80.13.2c2	R	$2$	$2$	$2$	$2$	$2$	$2$	$0$	$0$	$0$	$0$	${\zeta }_5^{-1}+{\zeta }_5$	${\zeta }_5^{-2}+{\zeta }_5^2$	${\zeta }_5^{-2}+{\zeta }_5^2$	${\zeta }_5^{-1}+{\zeta }_5$	${\zeta }_5^{-1}+{\zeta }_5$	${\zeta }_5^{-2}+{\zeta }_5^2$	${\zeta }_5^{-1}+{\zeta }_5$	${\zeta }_5^{-2}+{\zeta }_5^2$	${\zeta }_5^{-2}+{\zeta }_5^2$	${\zeta }_5^{-1}+{\zeta }_5$	${\zeta }_5^{-2}+{\zeta }_5^2$	${\zeta }_5^{-2}+{\zeta }_5^2$	${\zeta }_5^{-1}+{\zeta }_5$	${\zeta }_5^{-2}+{\zeta }_5^2$	${\zeta }_5^{-1}+{\zeta }_5$	${\zeta }_5^{-1}+{\zeta }_5$
80.13.2d1	R	$2$	$2$	$2$	$2$	$-2$	$-2$	$0$	$0$	$0$	$0$	${\zeta }_5^{-2}+{\zeta }_5^2$	${\zeta }_5^{-1}+{\zeta }_5$	${\zeta }_5^{-1}+{\zeta }_5$	${\zeta }_5^{-2}+{\zeta }_5^2$	${\zeta }_5^{-2}+{\zeta }_5^2$	${\zeta }_5^{-1}+{\zeta }_5$	${\zeta }_5^{-2}+{\zeta }_5^2$	${\zeta }_5^{-1}+{\zeta }_5$	$-{\zeta }_5^{-1}-{\zeta }_5$	$-{\zeta }_5^{-2}-{\zeta }_5^2$	$-{\zeta }_5^{-1}-{\zeta }_5$	$-{\zeta }_5^{-1}-{\zeta }_5$	$-{\zeta }_5^{-2}-{\zeta }_5^2$	$-{\zeta }_5^{-1}-{\zeta }_5$	$-{\zeta }_5^{-2}-{\zeta }_5^2$	$-{\zeta }_5^{-2}-{\zeta }_5^2$
80.13.2d2	R	$2$	$2$	$2$	$2$	$-2$	$-2$	$0$	$0$	$0$	$0$	${\zeta }_5^{-1}+{\zeta }_5$	${\zeta }_5^{-2}+{\zeta }_5^2$	${\zeta }_5^{-2}+{\zeta }_5^2$	${\zeta }_5^{-1}+{\zeta }_5$	${\zeta }_5^{-1}+{\zeta }_5$	${\zeta }_5^{-2}+{\zeta }_5^2$	${\zeta }_5^{-1}+{\zeta }_5$	${\zeta }_5^{-2}+{\zeta }_5^2$	$-{\zeta }_5^{-2}-{\zeta }_5^2$	$-{\zeta }_5^{-1}-{\zeta }_5$	$-{\zeta }_5^{-2}-{\zeta }_5^2$	$-{\zeta }_5^{-2}-{\zeta }_5^2$	$-{\zeta }_5^{-1}-{\zeta }_5$	$-{\zeta }_5^{-2}-{\zeta }_5^2$	$-{\zeta }_5^{-1}-{\zeta }_5$	$-{\zeta }_5^{-1}-{\zeta }_5$
80.13.2e1	S	$2$	$-2$	$-2$	$2$	$-2$	$2$	$0$	$0$	$0$	$0$	${\zeta }_5^{-2}+{\zeta }_5^2$	${\zeta }_5^{-1}+{\zeta }_5$	$-{\zeta }_5^{-1}-{\zeta }_5$	$-{\zeta }_5^{-2}-{\zeta }_5^2$	$-{\zeta }_5^{-2}-{\zeta }_5^2$	$-{\zeta }_5^{-1}-{\zeta }_5$	${\zeta }_5^{-2}+{\zeta }_5^2$	${\zeta }_5^{-1}+{\zeta }_5$	${\zeta }_5^{-1}+{\zeta }_5$	$-{\zeta }_5^{-2}-{\zeta }_5^2$	$-{\zeta }_5^{-1}-{\zeta }_5$	${\zeta }_5^{-1}+{\zeta }_5$	$-{\zeta }_5^{-2}-{\zeta }_5^2$	$-{\zeta }_5^{-1}-{\zeta }_5$	${\zeta }_5^{-2}+{\zeta }_5^2$	${\zeta }_5^{-2}+{\zeta }_5^2$
80.13.2e2	S	$2$	$-2$	$-2$	$2$	$-2$	$2$	$0$	$0$	$0$	$0$	${\zeta }_5^{-1}+{\zeta }_5$	${\zeta }_5^{-2}+{\zeta }_5^2$	$-{\zeta }_5^{-2}-{\zeta }_5^2$	$-{\zeta }_5^{-1}-{\zeta }_5$	$-{\zeta }_5^{-1}-{\zeta }_5$	$-{\zeta }_5^{-2}-{\zeta }_5^2$	${\zeta }_5^{-1}+{\zeta }_5$	${\zeta }_5^{-2}+{\zeta }_5^2$	${\zeta }_5^{-2}+{\zeta }_5^2$	$-{\zeta }_5^{-1}-{\zeta }_5$	$-{\zeta }_5^{-2}-{\zeta }_5^2$	${\zeta }_5^{-2}+{\zeta }_5^2$	$-{\zeta }_5^{-1}-{\zeta }_5$	$-{\zeta }_5^{-2}-{\zeta }_5^2$	${\zeta }_5^{-1}+{\zeta }_5$	${\zeta }_5^{-1}+{\zeta }_5$
80.13.2f1	S	$2$	$-2$	$-2$	$2$	$2$	$-2$	$0$	$0$	$0$	$0$	${\zeta }_5^{-2}+{\zeta }_5^2$	${\zeta }_5^{-1}+{\zeta }_5$	$-{\zeta }_5^{-1}-{\zeta }_5$	$-{\zeta }_5^{-2}-{\zeta }_5^2$	$-{\zeta }_5^{-2}-{\zeta }_5^2$	$-{\zeta }_5^{-1}-{\zeta }_5$	${\zeta }_5^{-2}+{\zeta }_5^2$	${\zeta }_5^{-1}+{\zeta }_5$	$-{\zeta }_5^{-1}-{\zeta }_5$	${\zeta }_5^{-2}+{\zeta }_5^2$	${\zeta }_5^{-1}+{\zeta }_5$	$-{\zeta }_5^{-1}-{\zeta }_5$	${\zeta }_5^{-2}+{\zeta }_5^2$	${\zeta }_5^{-1}+{\zeta }_5$	$-{\zeta }_5^{-2}-{\zeta }_5^2$	$-{\zeta }_5^{-2}-{\zeta }_5^2$
80.13.2f2	S	$2$	$-2$	$-2$	$2$	$2$	$-2$	$0$	$0$	$0$	$0$	${\zeta }_5^{-1}+{\zeta }_5$	${\zeta }_5^{-2}+{\zeta }_5^2$	$-{\zeta }_5^{-2}-{\zeta }_5^2$	$-{\zeta }_5^{-1}-{\zeta }_5$	$-{\zeta }_5^{-1}-{\zeta }_5$	$-{\zeta }_5^{-2}-{\zeta }_5^2$	${\zeta }_5^{-1}+{\zeta }_5$	${\zeta }_5^{-2}+{\zeta }_5^2$	$-{\zeta }_5^{-2}-{\zeta }_5^2$	${\zeta }_5^{-1}+{\zeta }_5$	${\zeta }_5^{-2}+{\zeta }_5^2$	$-{\zeta }_5^{-2}-{\zeta }_5^2$	${\zeta }_5^{-1}+{\zeta }_5$	${\zeta }_5^{-2}+{\zeta }_5^2$	$-{\zeta }_5^{-1}-{\zeta }_5$	$-{\zeta }_5^{-1}-{\zeta }_5$
80.13.2g1	R	$2$	$2$	$-2$	$-2$	$0$	$0$	$0$	$0$	$0$	$0$	$-{\zeta }_{20}^{-2}-{\zeta }_{20}^2$	${\zeta }_{20}^{-4}+{\zeta }_{20}^4$	${\zeta }_{20}^{-4}+{\zeta }_{20}^4$	$-{\zeta }_{20}^{-2}-{\zeta }_{20}^2$	${\zeta }_{20}^{-2}+{\zeta }_{20}^2$	$-{\zeta }_{20}^{-4}-{\zeta }_{20}^4$	${\zeta }_{20}^{-2}+{\zeta }_{20}^2$	$-{\zeta }_{20}^{-4}-{\zeta }_{20}^4$	$-{\zeta }_{20}^{-1}-{\zeta }_{20}$	$-{\zeta }_{20}^{-3}-{\zeta }_{20}^3$	$-{\zeta }_{20}^{-1}-{\zeta }_{20}$	${\zeta }_{20}^{-1}+{\zeta }_{20}$	${\zeta }_{20}^{-3}+{\zeta }_{20}^3$	${\zeta }_{20}^{-1}+{\zeta }_{20}$	${\zeta }_{20}^{-3}+{\zeta }_{20}^3$	$-{\zeta }_{20}^{-3}-{\zeta }_{20}^3$
80.13.2g2	R	$2$	$2$	$-2$	$-2$	$0$	$0$	$0$	$0$	$0$	$0$	$-{\zeta }_{20}^{-2}-{\zeta }_{20}^2$	${\zeta }_{20}^{-4}+{\zeta }_{20}^4$	${\zeta }_{20}^{-4}+{\zeta }_{20}^4$	$-{\zeta }_{20}^{-2}-{\zeta }_{20}^2$	${\zeta }_{20}^{-2}+{\zeta }_{20}^2$	$-{\zeta }_{20}^{-4}-{\zeta }_{20}^4$	${\zeta }_{20}^{-2}+{\zeta }_{20}^2$	$-{\zeta }_{20}^{-4}-{\zeta }_{20}^4$	${\zeta }_{20}^{-1}+{\zeta }_{20}$	${\zeta }_{20}^{-3}+{\zeta }_{20}^3$	${\zeta }_{20}^{-1}+{\zeta }_{20}$	$-{\zeta }_{20}^{-1}-{\zeta }_{20}$	$-{\zeta }_{20}^{-3}-{\zeta }_{20}^3$	$-{\zeta }_{20}^{-1}-{\zeta }_{20}$	$-{\zeta }_{20}^{-3}-{\zeta }_{20}^3$	${\zeta }_{20}^{-3}+{\zeta }_{20}^3$
80.13.2g3	R	$2$	$2$	$-2$	$-2$	$0$	$0$	$0$	$0$	$0$	$0$	${\zeta }_{20}^{-4}+{\zeta }_{20}^4$	$-{\zeta }_{20}^{-2}-{\zeta }_{20}^2$	$-{\zeta }_{20}^{-2}-{\zeta }_{20}^2$	${\zeta }_{20}^{-4}+{\zeta }_{20}^4$	$-{\zeta }_{20}^{-4}-{\zeta }_{20}^4$	${\zeta }_{20}^{-2}+{\zeta }_{20}^2$	$-{\zeta }_{20}^{-4}-{\zeta }_{20}^4$	${\zeta }_{20}^{-2}+{\zeta }_{20}^2$	$-{\zeta }_{20}^{-3}-{\zeta }_{20}^3$	${\zeta }_{20}^{-1}+{\zeta }_{20}$	$-{\zeta }_{20}^{-3}-{\zeta }_{20}^3$	${\zeta }_{20}^{-3}+{\zeta }_{20}^3$	$-{\zeta }_{20}^{-1}-{\zeta }_{20}$	${\zeta }_{20}^{-3}+{\zeta }_{20}^3$	$-{\zeta }_{20}^{-1}-{\zeta }_{20}$	${\zeta }_{20}^{-1}+{\zeta }_{20}$
80.13.2g4	R	$2$	$2$	$-2$	$-2$	$0$	$0$	$0$	$0$	$0$	$0$	${\zeta }_{20}^{-4}+{\zeta }_{20}^4$	$-{\zeta }_{20}^{-2}-{\zeta }_{20}^2$	$-{\zeta }_{20}^{-2}-{\zeta }_{20}^2$	${\zeta }_{20}^{-4}+{\zeta }_{20}^4$	$-{\zeta }_{20}^{-4}-{\zeta }_{20}^4$	${\zeta }_{20}^{-2}+{\zeta }_{20}^2$	$-{\zeta }_{20}^{-4}-{\zeta }_{20}^4$	${\zeta }_{20}^{-2}+{\zeta }_{20}^2$	${\zeta }_{20}^{-3}+{\zeta }_{20}^3$	$-{\zeta }_{20}^{-1}-{\zeta }_{20}$	${\zeta }_{20}^{-3}+{\zeta }_{20}^3$	$-{\zeta }_{20}^{-3}-{\zeta }_{20}^3$	${\zeta }_{20}^{-1}+{\zeta }_{20}$	$-{\zeta }_{20}^{-3}-{\zeta }_{20}^3$	${\zeta }_{20}^{-1}+{\zeta }_{20}$	$-{\zeta }_{20}^{-1}-{\zeta }_{20}$
80.13.2h1	S	$2$	$-2$	$2$	$-2$	$0$	$0$	$0$	$0$	$0$	$0$	$-{\zeta }_{20}^{-2}-{\zeta }_{20}^2$	${\zeta }_{20}^{-4}+{\zeta }_{20}^4$	$-{\zeta }_{20}^{-4}-{\zeta }_{20}^4$	${\zeta }_{20}^{-2}+{\zeta }_{20}^2$	$-{\zeta }_{20}^{-2}-{\zeta }_{20}^2$	${\zeta }_{20}^{-4}+{\zeta }_{20}^4$	${\zeta }_{20}^{-2}+{\zeta }_{20}^2$	$-{\zeta }_{20}^{-4}-{\zeta }_{20}^4$	$-{\zeta }_{20}^{-1}-{\zeta }_{20}$	${\zeta }_{20}^{-3}+{\zeta }_{20}^3$	${\zeta }_{20}^{-1}+{\zeta }_{20}$	${\zeta }_{20}^{-1}+{\zeta }_{20}$	$-{\zeta }_{20}^{-3}-{\zeta }_{20}^3$	$-{\zeta }_{20}^{-1}-{\zeta }_{20}$	${\zeta }_{20}^{-3}+{\zeta }_{20}^3$	$-{\zeta }_{20}^{-3}-{\zeta }_{20}^3$
80.13.2h2	S	$2$	$-2$	$2$	$-2$	$0$	$0$	$0$	$0$	$0$	$0$	$-{\zeta }_{20}^{-2}-{\zeta }_{20}^2$	${\zeta }_{20}^{-4}+{\zeta }_{20}^4$	$-{\zeta }_{20}^{-4}-{\zeta }_{20}^4$	${\zeta }_{20}^{-2}+{\zeta }_{20}^2$	$-{\zeta }_{20}^{-2}-{\zeta }_{20}^2$	${\zeta }_{20}^{-4}+{\zeta }_{20}^4$	${\zeta }_{20}^{-2}+{\zeta }_{20}^2$	$-{\zeta }_{20}^{-4}-{\zeta }_{20}^4$	${\zeta }_{20}^{-1}+{\zeta }_{20}$	$-{\zeta }_{20}^{-3}-{\zeta }_{20}^3$	$-{\zeta }_{20}^{-1}-{\zeta }_{20}$	$-{\zeta }_{20}^{-1}-{\zeta }_{20}$	${\zeta }_{20}^{-3}+{\zeta }_{20}^3$	${\zeta }_{20}^{-1}+{\zeta }_{20}$	$-{\zeta }_{20}^{-3}-{\zeta }_{20}^3$	${\zeta }_{20}^{-3}+{\zeta }_{20}^3$
80.13.2h3	S	$2$	$-2$	$2$	$-2$	$0$	$0$	$0$	$0$	$0$	$0$	${\zeta }_{20}^{-4}+{\zeta }_{20}^4$	$-{\zeta }_{20}^{-2}-{\zeta }_{20}^2$	${\zeta }_{20}^{-2}+{\zeta }_{20}^2$	$-{\zeta }_{20}^{-4}-{\zeta }_{20}^4$	${\zeta }_{20}^{-4}+{\zeta }_{20}^4$	$-{\zeta }_{20}^{-2}-{\zeta }_{20}^2$	$-{\zeta }_{20}^{-4}-{\zeta }_{20}^4$	${\zeta }_{20}^{-2}+{\zeta }_{20}^2$	$-{\zeta }_{20}^{-3}-{\zeta }_{20}^3$	$-{\zeta }_{20}^{-1}-{\zeta }_{20}$	${\zeta }_{20}^{-3}+{\zeta }_{20}^3$	${\zeta }_{20}^{-3}+{\zeta }_{20}^3$	${\zeta }_{20}^{-1}+{\zeta }_{20}$	$-{\zeta }_{20}^{-3}-{\zeta }_{20}^3$	$-{\zeta }_{20}^{-1}-{\zeta }_{20}$	${\zeta }_{20}^{-1}+{\zeta }_{20}$
80.13.2h4	S	$2$	$-2$	$2$	$-2$	$0$	$0$	$0$	$0$	$0$	$0$	${\zeta }_{20}^{-4}+{\zeta }_{20}^4$	$-{\zeta }_{20}^{-2}-{\zeta }_{20}^2$	${\zeta }_{20}^{-2}+{\zeta }_{20}^2$	$-{\zeta }_{20}^{-4}-{\zeta }_{20}^4$	${\zeta }_{20}^{-4}+{\zeta }_{20}^4$	$-{\zeta }_{20}^{-2}-{\zeta }_{20}^2$	$-{\zeta }_{20}^{-4}-{\zeta }_{20}^4$	${\zeta }_{20}^{-2}+{\zeta }_{20}^2$	${\zeta }_{20}^{-3}+{\zeta }_{20}^3$	${\zeta }_{20}^{-1}+{\zeta }_{20}$	$-{\zeta }_{20}^{-3}-{\zeta }_{20}^3$	$-{\zeta }_{20}^{-3}-{\zeta }_{20}^3$	$-{\zeta }_{20}^{-1}-{\zeta }_{20}$	${\zeta }_{20}^{-3}+{\zeta }_{20}^3$	${\zeta }_{20}^{-1}+{\zeta }_{20}$	$-{\zeta }_{20}^{-1}-{\zeta }_{20}$