Character table for $C_3^4:(S_3\times \SD_{16})$

The column representing the conjugacy class 3A is highlighted below.

		1A	2A	2B	2C	2D	2E	3A	3B	3C	3D	3E	4A	4B	4C	4D	6A	6B	6C	6D	6E	6F	6G	6H	6I	6J	8A1	8A-1	8B1	8B-1	12A	12B	24A1	24A-1
	Size	1	27	27	36	81	108	8	18	24	48	144	162	324	486	972	72	162	216	216	216	216	216	216	432	432	162	162	486	486	324	648	324	324
	2 P	1A	1A	1A	1A	1A	1A	3A	3B	3C	3D	3E	2D	2D	2D	2D	3A	3B	3C	3C	3A	3B	3C	3A	3D	3E	4A	4A	4A	4A	6B	6B	12A	12A
	3 P	1A	2A	2B	2C	2D	2E	1A	1A	1A	1A	1A	4A	4B	4C	4D	2C	2D	2A	2C	2B	2C	2E	2E	2E	2C	8A1	8A-1	8B1	8B-1	4A	4B	8A1	8A-1
	Type
7776.cw.1a	R	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
7776.cw.1b	R	$1$	$-1$	$-1$	$-1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$-1$	$-1$	$1$	$-1$	$1$	$-1$	$-1$	$-1$	$-1$	$1$	$1$	$1$	$-1$	$1$	$1$	$-1$	$-1$	$1$	$-1$	$1$	$1$
7776.cw.1c	R	$1$	$-1$	$-1$	$-1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$-1$	$-1$	$-1$	$1$	$-1$	$-1$	$-1$	$-1$	$1$	$1$	$1$	$-1$	$-1$	$-1$	$1$	$1$	$1$	$1$	$-1$	$-1$
7776.cw.1d	R	$1$	$-1$	$-1$	$1$	$1$	$-1$	$1$	$1$	$1$	$1$	$1$	$1$	$-1$	$-1$	$1$	$1$	$1$	$-1$	$1$	$-1$	$1$	$-1$	$-1$	$-1$	$1$	$-1$	$-1$	$1$	$1$	$1$	$-1$	$-1$	$-1$
7776.cw.1e	R	$1$	$-1$	$-1$	$1$	$1$	$-1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$-1$	$-1$	$1$	$1$	$-1$	$1$	$-1$	$1$	$-1$	$-1$	$-1$	$1$	$1$	$1$	$-1$	$-1$	$1$	$1$	$1$	$1$
7776.cw.1f	R	$1$	$1$	$1$	$-1$	$1$	$-1$	$1$	$1$	$1$	$1$	$1$	$1$	$-1$	$1$	$-1$	$-1$	$1$	$1$	$-1$	$1$	$-1$	$-1$	$-1$	$-1$	$-1$	$1$	$1$	$1$	$1$	$1$	$-1$	$1$	$1$
7776.cw.1g	R	$1$	$1$	$1$	$-1$	$1$	$-1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$-1$	$1$	$1$	$-1$	$1$	$-1$	$-1$	$-1$	$-1$	$-1$	$-1$	$-1$	$-1$	$-1$	$1$	$1$	$-1$	$-1$
7776.cw.1h	R	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$-1$	$1$	$-1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$-1$	$-1$	$-1$	$-1$	$1$	$-1$	$-1$	$-1$
7776.cw.2a	R	$2$	$0$	$0$	$2$	$2$	$0$	$2$	$-1$	$2$	$2$	$-1$	$2$	$2$	$0$	$0$	$2$	$-1$	$0$	$2$	$0$	$-1$	$0$	$0$	$0$	$-1$	$2$	$2$	$0$	$0$	$-1$	$-1$	$-1$	$-1$
7776.cw.2b	R	$2$	$-2$	$-2$	$0$	$2$	$0$	$2$	$2$	$2$	$2$	$2$	$-2$	$0$	$2$	$0$	$0$	$2$	$-2$	$0$	$-2$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$-2$	$0$	$0$	$0$
7776.cw.2c	R	$2$	$2$	$2$	$0$	$2$	$0$	$2$	$2$	$2$	$2$	$2$	$-2$	$0$	$-2$	$0$	$0$	$2$	$2$	$0$	$2$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$-2$	$0$	$0$	$0$
7776.cw.2d	R	$2$	$0$	$0$	$-2$	$2$	$0$	$2$	$-1$	$2$	$2$	$-1$	$2$	$-2$	$0$	$0$	$-2$	$-1$	$0$	$-2$	$0$	$1$	$0$	$0$	$0$	$1$	$2$	$2$	$0$	$0$	$-1$	$1$	$-1$	$-1$
7776.cw.2e	R	$2$	$0$	$0$	$-2$	$2$	$0$	$2$	$-1$	$2$	$2$	$-1$	$2$	$2$	$0$	$0$	$-2$	$-1$	$0$	$-2$	$0$	$1$	$0$	$0$	$0$	$1$	$-2$	$-2$	$0$	$0$	$-1$	$-1$	$1$	$1$
7776.cw.2f	R	$2$	$0$	$0$	$2$	$2$	$0$	$2$	$-1$	$2$	$2$	$-1$	$2$	$-2$	$0$	$0$	$2$	$-1$	$0$	$2$	$0$	$-1$	$0$	$0$	$0$	$-1$	$-2$	$-2$	$0$	$0$	$-1$	$1$	$1$	$1$
7776.cw.2g1	C	$2$	$-2$	$2$	$0$	$-2$	$0$	$2$	$2$	$2$	$2$	$2$	$0$	$0$	$0$	$0$	$0$	$-2$	$-2$	$0$	$2$	$0$	$0$	$0$	$0$	$0$	$-{\zeta }_8-{\zeta }_8^3$	${\zeta }_8+{\zeta }_8^3$	$-{\zeta }_8-{\zeta }_8^3$	${\zeta }_8+{\zeta }_8^3$	$0$	$0$	$-{\zeta }_8-{\zeta }_8^3$	${\zeta }_8+{\zeta }_8^3$
7776.cw.2g2	C	$2$	$-2$	$2$	$0$	$-2$	$0$	$2$	$2$	$2$	$2$	$2$	$0$	$0$	$0$	$0$	$0$	$-2$	$-2$	$0$	$2$	$0$	$0$	$0$	$0$	$0$	${\zeta }_8+{\zeta }_8^3$	$-{\zeta }_8-{\zeta }_8^3$	${\zeta }_8+{\zeta }_8^3$	$-{\zeta }_8-{\zeta }_8^3$	$0$	$0$	${\zeta }_8+{\zeta }_8^3$	$-{\zeta }_8-{\zeta }_8^3$
7776.cw.2h1	C	$2$	$2$	$-2$	$0$	$-2$	$0$	$2$	$2$	$2$	$2$	$2$	$0$	$0$	$0$	$0$	$0$	$-2$	$2$	$0$	$-2$	$0$	$0$	$0$	$0$	$0$	$-{\zeta }_8-{\zeta }_8^3$	${\zeta }_8+{\zeta }_8^3$	${\zeta }_8+{\zeta }_8^3$	$-{\zeta }_8-{\zeta }_8^3$	$0$	$0$	$-{\zeta }_8-{\zeta }_8^3$	${\zeta }_8+{\zeta }_8^3$
7776.cw.2h2	C	$2$	$2$	$-2$	$0$	$-2$	$0$	$2$	$2$	$2$	$2$	$2$	$0$	$0$	$0$	$0$	$0$	$-2$	$2$	$0$	$-2$	$0$	$0$	$0$	$0$	$0$	${\zeta }_8+{\zeta }_8^3$	$-{\zeta }_8-{\zeta }_8^3$	$-{\zeta }_8-{\zeta }_8^3$	${\zeta }_8+{\zeta }_8^3$	$0$	$0$	${\zeta }_8+{\zeta }_8^3$	$-{\zeta }_8-{\zeta }_8^3$
7776.cw.4a	R	$4$	$0$	$0$	$0$	$4$	$0$	$4$	$-2$	$4$	$4$	$-2$	$-4$	$0$	$0$	$0$	$0$	$-2$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$2$	$0$	$0$	$0$
7776.cw.4b1	C	$4$	$0$	$0$	$0$	$-4$	$0$	$4$	$-2$	$4$	$4$	$-2$	$0$	$0$	$0$	$0$	$0$	$2$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$-2{\zeta }_8-2{\zeta }_8^3$	$2{\zeta }_8+2{\zeta }_8^3$	$0$	$0$	$0$	$0$	${\zeta }_8+{\zeta }_8^3$	$-{\zeta }_8-{\zeta }_8^3$
7776.cw.4b2	C	$4$	$0$	$0$	$0$	$-4$	$0$	$4$	$-2$	$4$	$4$	$-2$	$0$	$0$	$0$	$0$	$0$	$2$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$2{\zeta }_8+2{\zeta }_8^3$	$-2{\zeta }_8-2{\zeta }_8^3$	$0$	$0$	$0$	$0$	$-{\zeta }_8-{\zeta }_8^3$	${\zeta }_8+{\zeta }_8^3$
7776.cw.8a	R	$8$	$8$	$0$	$2$	$0$	$2$	$8$	$8$	$-1$	$-1$	$-1$	$0$	$0$	$0$	$0$	$2$	$0$	$-1$	$-1$	$0$	$2$	$-1$	$2$	$-1$	$-1$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$
7776.cw.8b	R	$8$	$8$	$0$	$-2$	$0$	$-2$	$8$	$8$	$-1$	$-1$	$-1$	$0$	$0$	$0$	$0$	$-2$	$0$	$-1$	$1$	$0$	$-2$	$1$	$-2$	$1$	$1$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$
7776.cw.8c	R	$8$	$-8$	$0$	$-2$	$0$	$2$	$8$	$8$	$-1$	$-1$	$-1$	$0$	$0$	$0$	$0$	$-2$	$0$	$1$	$1$	$0$	$-2$	$-1$	$2$	$-1$	$1$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$
7776.cw.8d	R	$8$	$-8$	$0$	$2$	$0$	$-2$	$8$	$8$	$-1$	$-1$	$-1$	$0$	$0$	$0$	$0$	$2$	$0$	$1$	$-1$	$0$	$2$	$1$	$-2$	$1$	$-1$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$
7776.cw.16a	R	$16$	$0$	$0$	$4$	$0$	$0$	$16$	$-8$	$-2$	$-2$	$1$	$0$	$0$	$0$	$0$	$4$	$0$	$0$	$-2$	$0$	$-2$	$0$	$0$	$0$	$1$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$
7776.cw.16b	R	$16$	$0$	$0$	$-4$	$0$	$0$	$16$	$-8$	$-2$	$-2$	$1$	$0$	$0$	$0$	$0$	$-4$	$0$	$0$	$2$	$0$	$2$	$0$	$0$	$0$	$-1$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$
7776.cw.24a	R	$24$	$0$	$8$	$6$	$0$	$2$	$-3$	$0$	$6$	$-3$	$0$	$0$	$0$	$0$	$0$	$-3$	$0$	$0$	$0$	$-1$	$0$	$2$	$-1$	$-1$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$
7776.cw.24b	R	$24$	$0$	$-8$	$-6$	$0$	$2$	$-3$	$0$	$6$	$-3$	$0$	$0$	$0$	$0$	$0$	$3$	$0$	$0$	$0$	$1$	$0$	$2$	$-1$	$-1$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$
7776.cw.24c	R	$24$	$0$	$-8$	$6$	$0$	$-2$	$-3$	$0$	$6$	$-3$	$0$	$0$	$0$	$0$	$0$	$-3$	$0$	$0$	$0$	$1$	$0$	$-2$	$1$	$1$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$
7776.cw.24d	R	$24$	$0$	$8$	$-6$	$0$	$-2$	$-3$	$0$	$6$	$-3$	$0$	$0$	$0$	$0$	$0$	$3$	$0$	$0$	$0$	$-1$	$0$	$-2$	$1$	$1$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$
7776.cw.48a	R	$48$	$0$	$0$	$0$	$0$	$4$	$-6$	$0$	$-6$	$3$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$-2$	$-2$	$1$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$
7776.cw.48b	R	$48$	$0$	$0$	$0$	$0$	$-4$	$-6$	$0$	$-6$	$3$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$2$	$2$	$-1$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$