Character table for $\He_3:F_9$

The column representing the conjugacy class 8A-1 is highlighted below.

		1A	2A	3A	3B	3C1	3C-1	3D	3E	3F	3G	3H	3I	3J	3K	3L	4A1	4A-1	6A	8A1	8A-1	8A3	8A-3	12A1	12A-1
	Size	1	81	2	8	8	8	24	24	24	24	24	24	24	24	24	81	81	162	243	243	243	243	162	162
	2 P	1A	1A	3A	3B	3C-1	3C1	3D	3E	3F	3G	3H	3I	3J	3K	3L	2A	2A	3A	4A1	4A-1	4A-1	4A1	6A	6A
	3 P	1A	2A	1A	1A	1A	1A	1A	1A	1A	1A	1A	1A	1A	1A	1A	4A-1	4A1	2A	8A3	8A-3	8A1	8A-1	4A1	4A-1
	Type
1944.3475.1a	R	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
1944.3475.1b	R	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$-1$	$-1$	$-1$	$-1$	$1$	$1$
1944.3475.1c1	C	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$-1$	$-1$	$1$	$-i$	$i$	$i$	$-i$	$-1$	$-1$
1944.3475.1c2	C	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$-1$	$-1$	$1$	$i$	$-i$	$-i$	$i$	$-1$	$-1$
1944.3475.1d1	C	$1$	$-1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$-{\zeta }_8^2$	${\zeta }_8^2$	$-1$	${\zeta }_8^3$	$-{\zeta }_8$	${\zeta }_8$	$-{\zeta }_8^3$	${\zeta }_8^2$	$-{\zeta }_8^2$
1944.3475.1d2	C	$1$	$-1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	${\zeta }_8^2$	$-{\zeta }_8^2$	$-1$	$-{\zeta }_8$	${\zeta }_8^3$	$-{\zeta }_8^3$	${\zeta }_8$	$-{\zeta }_8^2$	${\zeta }_8^2$
1944.3475.1d3	C	$1$	$-1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$-{\zeta }_8^2$	${\zeta }_8^2$	$-1$	$-{\zeta }_8^3$	${\zeta }_8$	$-{\zeta }_8$	${\zeta }_8^3$	${\zeta }_8^2$	$-{\zeta }_8^2$
1944.3475.1d4	C	$1$	$-1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	${\zeta }_8^2$	$-{\zeta }_8^2$	$-1$	${\zeta }_8$	$-{\zeta }_8^3$	${\zeta }_8^3$	$-{\zeta }_8$	$-{\zeta }_8^2$	${\zeta }_8^2$
1944.3475.6a	R	$6$	$-2$	$-3$	$6$	$-3$	$-3$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$2$	$2$	$1$	$0$	$0$	$0$	$0$	$-1$	$-1$
1944.3475.6b	S	$6$	$-2$	$-3$	$6$	$-3$	$-3$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$-2$	$-2$	$1$	$0$	$0$	$0$	$0$	$1$	$1$
1944.3475.6c1	C	$6$	$2$	$-3$	$6$	$-3$	$-3$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$-2i$	$2i$	$-1$	$0$	$0$	$0$	$0$	$-i$	$i$
1944.3475.6c2	C	$6$	$2$	$-3$	$6$	$-3$	$-3$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$2i$	$-2i$	$-1$	$0$	$0$	$0$	$0$	$i$	$-i$
1944.3475.8a	R	$8$	$0$	$8$	$-1$	$-1$	$-1$	$-1$	$-1$	$-1$	$-1$	$-1$	$-1$	$-1$	$-1$	$8$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$
1944.3475.8b	R	$8$	$0$	$8$	$-1$	$-1$	$-1$	$-1$	$-1$	$-1$	$-1$	$-1$	$-1$	$-1$	$8$	$-1$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$
1944.3475.8c	R	$8$	$0$	$8$	$-1$	$-1$	$-1$	$-1$	$-1$	$-1$	$-1$	$-1$	$-1$	$8$	$-1$	$-1$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$
1944.3475.8d	R	$8$	$0$	$8$	$-1$	$-1$	$-1$	$-1$	$-1$	$-1$	$-1$	$-1$	$8$	$-1$	$-1$	$-1$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$
1944.3475.8e	R	$8$	$0$	$8$	$-1$	$-1$	$-1$	$-1$	$-1$	$-1$	$-1$	$8$	$-1$	$-1$	$-1$	$-1$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$
1944.3475.8f	R	$8$	$0$	$8$	$-1$	$-1$	$-1$	$-1$	$-1$	$-1$	$8$	$-1$	$-1$	$-1$	$-1$	$-1$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$
1944.3475.8g	R	$8$	$0$	$8$	$-1$	$-1$	$-1$	$-1$	$-1$	$8$	$-1$	$-1$	$-1$	$-1$	$-1$	$-1$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$
1944.3475.8h	R	$8$	$0$	$8$	$-1$	$-1$	$-1$	$-1$	$8$	$-1$	$-1$	$-1$	$-1$	$-1$	$-1$	$-1$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$
1944.3475.8i	R	$8$	$0$	$8$	$-1$	$-1$	$-1$	$8$	$-1$	$-1$	$-1$	$-1$	$-1$	$-1$	$-1$	$-1$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$
1944.3475.8j	R	$8$	$0$	$8$	$8$	$8$	$8$	$-1$	$-1$	$-1$	$-1$	$-1$	$-1$	$-1$	$-1$	$-1$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$
1944.3475.24a1	C	$24$	$0$	$-12$	$-3$	$-3-9{\zeta }_3$	$6+9{\zeta }_3$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$
1944.3475.24a2	C	$24$	$0$	$-12$	$-3$	$6+9{\zeta }_3$	$-3-9{\zeta }_3$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$