Character table for $S_4\times A_5$

		1A	2A	2B	2C	2D	2E	3A	3B	3C	4A	4B	5A1	5A2	6A	6B	6C	10A1	10A3	10B1	10B3	12A	15A1	15A2	20A1	20A3
	Size	1	3	6	15	45	90	8	20	160	6	90	12	12	60	120	120	36	36	72	72	120	96	96	72	72
	2 P	1A	1A	1A	1A	1A	1A	3A	3B	3C	2A	2A	5A2	5A1	3B	3B	3A	5A2	5A1	5A1	5A2	6A	15A2	15A1	10A1	10A3
	3 P	1A	2A	2B	2C	2D	2E	1A	1A	1A	4A	4B	5A2	5A1	2A	2B	2C	10A3	10A1	10B3	10B1	4A	5A1	5A2	20A3	20A1
	5 P	1A	2A	2B	2C	2D	2E	3A	3B	3C	4A	4B	1A	1A	6A	6B	6C	2A	2A	2B	2B	12A	3A	3A	4A	4A
	Type
1440.5848.1a	R	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
1440.5848.1b	R	$1$	$1$	$-1$	$1$	$1$	$-1$	$1$	$1$	$1$	$-1$	$-1$	$1$	$1$	$1$	$-1$	$1$	$1$	$1$	$-1$	$-1$	$-1$	$1$	$1$	$-1$	$-1$
1440.5848.2a	R	$2$	$2$	$0$	$2$	$2$	$0$	$-1$	$2$	$-1$	$0$	$0$	$2$	$2$	$2$	$0$	$-1$	$2$	$2$	$0$	$0$	$0$	$-1$	$-1$	$0$	$0$
1440.5848.3a	R	$3$	$-1$	$1$	$3$	$-1$	$1$	$0$	$3$	$0$	$-1$	$-1$	$3$	$3$	$-1$	$1$	$0$	$-1$	$-1$	$1$	$1$	$-1$	$0$	$0$	$-1$	$-1$
1440.5848.3b	R	$3$	$-1$	$-1$	$3$	$-1$	$-1$	$0$	$3$	$0$	$1$	$1$	$3$	$3$	$-1$	$-1$	$0$	$-1$	$-1$	$-1$	$-1$	$1$	$0$	$0$	$1$	$1$
1440.5848.3c1	R	$3$	$3$	$3$	$-1$	$-1$	$-1$	$3$	$0$	$0$	$3$	$-1$	$-{\zeta }_5^{-1}-{\zeta }_5$	$-{\zeta }_5^{-2}-{\zeta }_5^2$	$0$	$0$	$-1$	$-{\zeta }_5^{-1}-{\zeta }_5$	$-{\zeta }_5^{-2}-{\zeta }_5^2$	$-{\zeta }_5^{-2}-{\zeta }_5^2$	$-{\zeta }_5^{-1}-{\zeta }_5$	$0$	$-{\zeta }_5^{-2}-{\zeta }_5^2$	$-{\zeta }_5^{-1}-{\zeta }_5$	$-{\zeta }_5^{-2}-{\zeta }_5^2$	$-{\zeta }_5^{-1}-{\zeta }_5$
1440.5848.3c2	R	$3$	$3$	$3$	$-1$	$-1$	$-1$	$3$	$0$	$0$	$3$	$-1$	$-{\zeta }_5^{-2}-{\zeta }_5^2$	$-{\zeta }_5^{-1}-{\zeta }_5$	$0$	$0$	$-1$	$-{\zeta }_5^{-2}-{\zeta }_5^2$	$-{\zeta }_5^{-1}-{\zeta }_5$	$-{\zeta }_5^{-1}-{\zeta }_5$	$-{\zeta }_5^{-2}-{\zeta }_5^2$	$0$	$-{\zeta }_5^{-1}-{\zeta }_5$	$-{\zeta }_5^{-2}-{\zeta }_5^2$	$-{\zeta }_5^{-1}-{\zeta }_5$	$-{\zeta }_5^{-2}-{\zeta }_5^2$
1440.5848.3d1	R	$3$	$3$	$-3$	$-1$	$-1$	$1$	$3$	$0$	$0$	$-3$	$1$	$-{\zeta }_5^{-1}-{\zeta }_5$	$-{\zeta }_5^{-2}-{\zeta }_5^2$	$0$	$0$	$-1$	$-{\zeta }_5^{-1}-{\zeta }_5$	$-{\zeta }_5^{-2}-{\zeta }_5^2$	${\zeta }_5^{-2}+{\zeta }_5^2$	${\zeta }_5^{-1}+{\zeta }_5$	$0$	$-{\zeta }_5^{-2}-{\zeta }_5^2$	$-{\zeta }_5^{-1}-{\zeta }_5$	${\zeta }_5^{-2}+{\zeta }_5^2$	${\zeta }_5^{-1}+{\zeta }_5$
1440.5848.3d2	R	$3$	$3$	$-3$	$-1$	$-1$	$1$	$3$	$0$	$0$	$-3$	$1$	$-{\zeta }_5^{-2}-{\zeta }_5^2$	$-{\zeta }_5^{-1}-{\zeta }_5$	$0$	$0$	$-1$	$-{\zeta }_5^{-2}-{\zeta }_5^2$	$-{\zeta }_5^{-1}-{\zeta }_5$	${\zeta }_5^{-1}+{\zeta }_5$	${\zeta }_5^{-2}+{\zeta }_5^2$	$0$	$-{\zeta }_5^{-1}-{\zeta }_5$	$-{\zeta }_5^{-2}-{\zeta }_5^2$	${\zeta }_5^{-1}+{\zeta }_5$	${\zeta }_5^{-2}+{\zeta }_5^2$
1440.5848.4a	R	$4$	$4$	$4$	$0$	$0$	$0$	$4$	$1$	$1$	$4$	$0$	$-1$	$-1$	$1$	$1$	$0$	$-1$	$-1$	$-1$	$-1$	$1$	$-1$	$-1$	$-1$	$-1$
1440.5848.4b	R	$4$	$4$	$-4$	$0$	$0$	$0$	$4$	$1$	$1$	$-4$	$0$	$-1$	$-1$	$1$	$-1$	$0$	$-1$	$-1$	$1$	$1$	$-1$	$-1$	$-1$	$1$	$1$
1440.5848.5a	R	$5$	$5$	$5$	$1$	$1$	$1$	$5$	$-1$	$-1$	$5$	$1$	$0$	$0$	$-1$	$-1$	$1$	$0$	$0$	$0$	$0$	$-1$	$0$	$0$	$0$	$0$
1440.5848.5b	R	$5$	$5$	$-5$	$1$	$1$	$-1$	$5$	$-1$	$-1$	$-5$	$-1$	$0$	$0$	$-1$	$1$	$1$	$0$	$0$	$0$	$0$	$1$	$0$	$0$	$0$	$0$
1440.5848.6a1	R	$6$	$6$	$0$	$-2$	$-2$	$0$	$-3$	$0$	$0$	$0$	$0$	$-2{\zeta }_5^{-1}-2{\zeta }_5$	$-2{\zeta }_5^{-2}-2{\zeta }_5^2$	$0$	$0$	$1$	$-2{\zeta }_5^{-1}-2{\zeta }_5$	$-2{\zeta }_5^{-2}-2{\zeta }_5^2$	$0$	$0$	$0$	${\zeta }_5^{-2}+{\zeta }_5^2$	${\zeta }_5^{-1}+{\zeta }_5$	$0$	$0$
1440.5848.6a2	R	$6$	$6$	$0$	$-2$	$-2$	$0$	$-3$	$0$	$0$	$0$	$0$	$-2{\zeta }_5^{-2}-2{\zeta }_5^2$	$-2{\zeta }_5^{-1}-2{\zeta }_5$	$0$	$0$	$1$	$-2{\zeta }_5^{-2}-2{\zeta }_5^2$	$-2{\zeta }_5^{-1}-2{\zeta }_5$	$0$	$0$	$0$	${\zeta }_5^{-1}+{\zeta }_5$	${\zeta }_5^{-2}+{\zeta }_5^2$	$0$	$0$
1440.5848.8a	R	$8$	$8$	$0$	$0$	$0$	$0$	$-4$	$2$	$-1$	$0$	$0$	$-2$	$-2$	$2$	$0$	$0$	$-2$	$-2$	$0$	$0$	$0$	$1$	$1$	$0$	$0$
1440.5848.9a1	R	$9$	$-3$	$-3$	$-3$	$1$	$1$	$0$	$0$	$0$	$3$	$-1$	$-3{\zeta }_5^{-1}-3{\zeta }_5$	$-3{\zeta }_5^{-2}-3{\zeta }_5^2$	$0$	$0$	$0$	${\zeta }_5^{-1}+{\zeta }_5$	${\zeta }_5^{-2}+{\zeta }_5^2$	${\zeta }_5^{-2}+{\zeta }_5^2$	${\zeta }_5^{-1}+{\zeta }_5$	$0$	$0$	$0$	$-{\zeta }_5^{-2}-{\zeta }_5^2$	$-{\zeta }_5^{-1}-{\zeta }_5$
1440.5848.9a2	R	$9$	$-3$	$-3$	$-3$	$1$	$1$	$0$	$0$	$0$	$3$	$-1$	$-3{\zeta }_5^{-2}-3{\zeta }_5^2$	$-3{\zeta }_5^{-1}-3{\zeta }_5$	$0$	$0$	$0$	${\zeta }_5^{-2}+{\zeta }_5^2$	${\zeta }_5^{-1}+{\zeta }_5$	${\zeta }_5^{-1}+{\zeta }_5$	${\zeta }_5^{-2}+{\zeta }_5^2$	$0$	$0$	$0$	$-{\zeta }_5^{-1}-{\zeta }_5$	$-{\zeta }_5^{-2}-{\zeta }_5^2$
1440.5848.9b1	R	$9$	$-3$	$3$	$-3$	$1$	$-1$	$0$	$0$	$0$	$-3$	$1$	$-3{\zeta }_5^{-1}-3{\zeta }_5$	$-3{\zeta }_5^{-2}-3{\zeta }_5^2$	$0$	$0$	$0$	${\zeta }_5^{-1}+{\zeta }_5$	${\zeta }_5^{-2}+{\zeta }_5^2$	$-{\zeta }_5^{-2}-{\zeta }_5^2$	$-{\zeta }_5^{-1}-{\zeta }_5$	$0$	$0$	$0$	${\zeta }_5^{-2}+{\zeta }_5^2$	${\zeta }_5^{-1}+{\zeta }_5$
1440.5848.9b2	R	$9$	$-3$	$3$	$-3$	$1$	$-1$	$0$	$0$	$0$	$-3$	$1$	$-3{\zeta }_5^{-2}-3{\zeta }_5^2$	$-3{\zeta }_5^{-1}-3{\zeta }_5$	$0$	$0$	$0$	${\zeta }_5^{-2}+{\zeta }_5^2$	${\zeta }_5^{-1}+{\zeta }_5$	$-{\zeta }_5^{-1}-{\zeta }_5$	$-{\zeta }_5^{-2}-{\zeta }_5^2$	$0$	$0$	$0$	${\zeta }_5^{-1}+{\zeta }_5$	${\zeta }_5^{-2}+{\zeta }_5^2$
1440.5848.10a	R	$10$	$10$	$0$	$2$	$2$	$0$	$-5$	$-2$	$1$	$0$	$0$	$0$	$0$	$-2$	$0$	$-1$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$
1440.5848.12a	R	$12$	$-4$	$4$	$0$	$0$	$0$	$0$	$3$	$0$	$-4$	$0$	$-3$	$-3$	$-1$	$1$	$0$	$1$	$1$	$-1$	$-1$	$-1$	$0$	$0$	$1$	$1$
1440.5848.12b	R	$12$	$-4$	$-4$	$0$	$0$	$0$	$0$	$3$	$0$	$4$	$0$	$-3$	$-3$	$-1$	$-1$	$0$	$1$	$1$	$1$	$1$	$1$	$0$	$0$	$-1$	$-1$
1440.5848.15a	R	$15$	$-5$	$5$	$3$	$-1$	$1$	$0$	$-3$	$0$	$-5$	$-1$	$0$	$0$	$1$	$-1$	$0$	$0$	$0$	$0$	$0$	$1$	$0$	$0$	$0$	$0$
1440.5848.15b	R	$15$	$-5$	$-5$	$3$	$-1$	$-1$	$0$	$-3$	$0$	$5$	$1$	$0$	$0$	$1$	$1$	$0$	$0$	$0$	$0$	$0$	$-1$	$0$	$0$	$0$	$0$