Character table for $C_3^3:S_3^2.S_4$

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

		1A	2A	2B	2C	2D	2E	3A	3B	3C	3D	3E	3F	3G	3H	3I	4A	4B	6A	6B	6C	6D	6E	6F	6G	6H	6I	6J	6K	6L	6M	6N	6O	6P	8A1	8A-1	8B1	8B-1	9A	12A	24A1	24A-1
	Size	1	27	27	81	108	324	2	24	24	48	72	144	144	432	432	486	1458	162	216	216	216	648	648	648	648	648	648	648	1296	1296	1296	1296	1296	486	486	1458	1458	864	972	972	972
	2 P	1A	1A	1A	1A	1A	1A	3A	3B	3C	3D	3E	3F	3G	3H	3I	2C	2C	3A	3A	3C	3B	3B	3B	3E	3E	3C	3C	3E	3F	3H	3G	3D	3I	4A	4A	4A	4A	9A	6A	12A	12A
	3 P	1A	2A	2B	2C	2D	2E	1A	1A	1A	1A	1A	1A	1A	1A	1A	4A	4B	2C	2D	2A	2B	2E	2D	2A	2B	2D	2E	2C	2C	2A	2D	2E	2B	8A1	8A-1	8B1	8B-1	3A	4A	8A1	8A-1
	Type
23328.du.1a	R	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
23328.du.1b	R	$1$	$-1$	$-1$	$1$	$-1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$-1$	$1$	$-1$	$-1$	$-1$	$1$	$-1$	$-1$	$-1$	$-1$	$1$	$1$	$1$	$-1$	$-1$	$1$	$-1$	$-1$	$-1$	$1$	$1$	$1$	$1$	$-1$	$-1$
23328.du.1c	R	$1$	$-1$	$-1$	$1$	$1$	$-1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$-1$	$1$	$1$	$-1$	$-1$	$-1$	$1$	$-1$	$-1$	$1$	$-1$	$1$	$1$	$-1$	$1$	$-1$	$-1$	$1$	$1$	$-1$	$-1$	$1$	$1$	$1$	$1$
23328.du.1d	R	$1$	$1$	$1$	$1$	$-1$	$-1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$-1$	$1$	$1$	$-1$	$-1$	$1$	$1$	$-1$	$-1$	$1$	$1$	$1$	$-1$	$-1$	$1$	$-1$	$-1$	$-1$	$-1$	$1$	$1$	$-1$	$-1$
23328.du.2a	R	$2$	$2$	$2$	$2$	$0$	$0$	$2$	$2$	$2$	$2$	$-1$	$-1$	$2$	$-1$	$-1$	$2$	$2$	$2$	$0$	$2$	$2$	$0$	$0$	$-1$	$-1$	$0$	$0$	$-1$	$-1$	$-1$	$0$	$0$	$-1$	$0$	$0$	$0$	$0$	$-1$	$2$	$0$	$0$
23328.du.2b	R	$2$	$-2$	$-2$	$2$	$0$	$0$	$2$	$2$	$2$	$2$	$-1$	$-1$	$2$	$-1$	$-1$	$2$	$-2$	$2$	$0$	$-2$	$-2$	$0$	$0$	$1$	$1$	$0$	$0$	$-1$	$-1$	$1$	$0$	$0$	$1$	$0$	$0$	$0$	$0$	$-1$	$2$	$0$	$0$
23328.du.2c1	C	$2$	$-2$	$2$	$-2$	$0$	$0$	$2$	$2$	$2$	$2$	$-1$	$-1$	$2$	$-1$	$-1$	$0$	$0$	$-2$	$0$	$-2$	$2$	$0$	$0$	$1$	$-1$	$0$	$0$	$1$	$1$	$1$	$0$	$0$	$-1$	$-{\zeta }_8-{\zeta }_8^3$	${\zeta }_8+{\zeta }_8^3$	$-{\zeta }_8-{\zeta }_8^3$	${\zeta }_8+{\zeta }_8^3$	$-1$	$0$	$-{\zeta }_8-{\zeta }_8^3$	${\zeta }_8+{\zeta }_8^3$
23328.du.2c2	C	$2$	$-2$	$2$	$-2$	$0$	$0$	$2$	$2$	$2$	$2$	$-1$	$-1$	$2$	$-1$	$-1$	$0$	$0$	$-2$	$0$	$-2$	$2$	$0$	$0$	$1$	$-1$	$0$	$0$	$1$	$1$	$1$	$0$	$0$	$-1$	${\zeta }_8+{\zeta }_8^3$	$-{\zeta }_8-{\zeta }_8^3$	${\zeta }_8+{\zeta }_8^3$	$-{\zeta }_8-{\zeta }_8^3$	$-1$	$0$	${\zeta }_8+{\zeta }_8^3$	$-{\zeta }_8-{\zeta }_8^3$
23328.du.2d1	C	$2$	$2$	$-2$	$-2$	$0$	$0$	$2$	$2$	$2$	$2$	$-1$	$-1$	$2$	$-1$	$-1$	$0$	$0$	$-2$	$0$	$2$	$-2$	$0$	$0$	$-1$	$1$	$0$	$0$	$1$	$1$	$-1$	$0$	$0$	$1$	$-{\zeta }_8-{\zeta }_8^3$	${\zeta }_8+{\zeta }_8^3$	${\zeta }_8+{\zeta }_8^3$	$-{\zeta }_8-{\zeta }_8^3$	$-1$	$0$	$-{\zeta }_8-{\zeta }_8^3$	${\zeta }_8+{\zeta }_8^3$
23328.du.2d2	C	$2$	$2$	$-2$	$-2$	$0$	$0$	$2$	$2$	$2$	$2$	$-1$	$-1$	$2$	$-1$	$-1$	$0$	$0$	$-2$	$0$	$2$	$-2$	$0$	$0$	$-1$	$1$	$0$	$0$	$1$	$1$	$-1$	$0$	$0$	$1$	${\zeta }_8+{\zeta }_8^3$	$-{\zeta }_8-{\zeta }_8^3$	$-{\zeta }_8-{\zeta }_8^3$	${\zeta }_8+{\zeta }_8^3$	$-1$	$0$	${\zeta }_8+{\zeta }_8^3$	$-{\zeta }_8-{\zeta }_8^3$
23328.du.3a	R	$3$	$3$	$3$	$3$	$1$	$1$	$3$	$3$	$3$	$3$	$0$	$0$	$3$	$0$	$0$	$-1$	$-1$	$3$	$1$	$3$	$3$	$1$	$1$	$0$	$0$	$1$	$1$	$0$	$0$	$0$	$1$	$1$	$0$	$-1$	$-1$	$-1$	$-1$	$0$	$-1$	$-1$	$-1$
23328.du.3b	R	$3$	$3$	$3$	$3$	$-1$	$-1$	$3$	$3$	$3$	$3$	$0$	$0$	$3$	$0$	$0$	$-1$	$-1$	$3$	$-1$	$3$	$3$	$-1$	$-1$	$0$	$0$	$-1$	$-1$	$0$	$0$	$0$	$-1$	$-1$	$0$	$1$	$1$	$1$	$1$	$0$	$-1$	$1$	$1$
23328.du.3c	R	$3$	$-3$	$-3$	$3$	$-1$	$1$	$3$	$3$	$3$	$3$	$0$	$0$	$3$	$0$	$0$	$-1$	$1$	$3$	$-1$	$-3$	$-3$	$1$	$-1$	$0$	$0$	$-1$	$1$	$0$	$0$	$0$	$-1$	$1$	$0$	$1$	$1$	$-1$	$-1$	$0$	$-1$	$1$	$1$
23328.du.3d	R	$3$	$-3$	$-3$	$3$	$1$	$-1$	$3$	$3$	$3$	$3$	$0$	$0$	$3$	$0$	$0$	$-1$	$1$	$3$	$1$	$-3$	$-3$	$-1$	$1$	$0$	$0$	$1$	$-1$	$0$	$0$	$0$	$1$	$-1$	$0$	$-1$	$-1$	$1$	$1$	$0$	$-1$	$-1$	$-1$
23328.du.4a	R	$4$	$-4$	$4$	$-4$	$0$	$0$	$4$	$4$	$4$	$4$	$1$	$1$	$4$	$1$	$1$	$0$	$0$	$-4$	$0$	$-4$	$4$	$0$	$0$	$-1$	$1$	$0$	$0$	$-1$	$-1$	$-1$	$0$	$0$	$1$	$0$	$0$	$0$	$0$	$1$	$0$	$0$	$0$
23328.du.4b	R	$4$	$4$	$-4$	$-4$	$0$	$0$	$4$	$4$	$4$	$4$	$1$	$1$	$4$	$1$	$1$	$0$	$0$	$-4$	$0$	$4$	$-4$	$0$	$0$	$1$	$-1$	$0$	$0$	$-1$	$-1$	$1$	$0$	$0$	$-1$	$0$	$0$	$0$	$0$	$1$	$0$	$0$	$0$
23328.du.8a	R	$8$	$0$	$8$	$0$	$2$	$2$	$8$	$-1$	$8$	$-1$	$2$	$2$	$-1$	$2$	$-1$	$0$	$0$	$0$	$2$	$0$	$-1$	$-1$	$-1$	$0$	$2$	$2$	$2$	$0$	$0$	$0$	$-1$	$-1$	$-1$	$0$	$0$	$0$	$0$	$-1$	$0$	$0$	$0$
23328.du.8b	R	$8$	$8$	$0$	$0$	$2$	$2$	$8$	$8$	$-1$	$-1$	$2$	$2$	$-1$	$-1$	$2$	$0$	$0$	$0$	$2$	$-1$	$0$	$2$	$2$	$2$	$0$	$-1$	$-1$	$0$	$0$	$-1$	$-1$	$-1$	$0$	$0$	$0$	$0$	$0$	$-1$	$0$	$0$	$0$
23328.du.8c	R	$8$	$0$	$8$	$0$	$-2$	$-2$	$8$	$-1$	$8$	$-1$	$2$	$2$	$-1$	$2$	$-1$	$0$	$0$	$0$	$-2$	$0$	$-1$	$1$	$1$	$0$	$2$	$-2$	$-2$	$0$	$0$	$0$	$1$	$1$	$-1$	$0$	$0$	$0$	$0$	$-1$	$0$	$0$	$0$
23328.du.8d	R	$8$	$8$	$0$	$0$	$-2$	$-2$	$8$	$8$	$-1$	$-1$	$2$	$2$	$-1$	$-1$	$2$	$0$	$0$	$0$	$-2$	$-1$	$0$	$-2$	$-2$	$2$	$0$	$1$	$1$	$0$	$0$	$-1$	$1$	$1$	$0$	$0$	$0$	$0$	$0$	$-1$	$0$	$0$	$0$
23328.du.8e	R	$8$	$-8$	$0$	$0$	$-2$	$2$	$8$	$8$	$-1$	$-1$	$2$	$2$	$-1$	$-1$	$2$	$0$	$0$	$0$	$-2$	$1$	$0$	$2$	$-2$	$-2$	$0$	$1$	$-1$	$0$	$0$	$1$	$1$	$-1$	$0$	$0$	$0$	$0$	$0$	$-1$	$0$	$0$	$0$
23328.du.8f	R	$8$	$-8$	$0$	$0$	$2$	$-2$	$8$	$8$	$-1$	$-1$	$2$	$2$	$-1$	$-1$	$2$	$0$	$0$	$0$	$2$	$1$	$0$	$-2$	$2$	$-2$	$0$	$-1$	$1$	$0$	$0$	$1$	$-1$	$1$	$0$	$0$	$0$	$0$	$0$	$-1$	$0$	$0$	$0$
23328.du.8g	R	$8$	$0$	$-8$	$0$	$-2$	$2$	$8$	$-1$	$8$	$-1$	$2$	$2$	$-1$	$2$	$-1$	$0$	$0$	$0$	$-2$	$0$	$1$	$-1$	$1$	$0$	$-2$	$-2$	$2$	$0$	$0$	$0$	$1$	$-1$	$1$	$0$	$0$	$0$	$0$	$-1$	$0$	$0$	$0$
23328.du.8h	R	$8$	$0$	$-8$	$0$	$2$	$-2$	$8$	$-1$	$8$	$-1$	$2$	$2$	$-1$	$2$	$-1$	$0$	$0$	$0$	$2$	$0$	$1$	$1$	$-1$	$0$	$-2$	$2$	$-2$	$0$	$0$	$0$	$-1$	$1$	$1$	$0$	$0$	$0$	$0$	$-1$	$0$	$0$	$0$
23328.du.16a	R	$16$	$0$	$0$	$0$	$0$	$4$	$16$	$-2$	$-2$	$7$	$4$	$4$	$-2$	$-2$	$-2$	$0$	$0$	$0$	$0$	$0$	$0$	$-2$	$0$	$0$	$0$	$0$	$-2$	$0$	$0$	$0$	$0$	$1$	$0$	$0$	$0$	$0$	$0$	$1$	$0$	$0$	$0$
23328.du.16b	R	$16$	$0$	$16$	$0$	$0$	$0$	$16$	$-2$	$16$	$-2$	$-2$	$-2$	$-2$	$-2$	$1$	$0$	$0$	$0$	$0$	$0$	$-2$	$0$	$0$	$0$	$-2$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$1$	$0$	$0$	$0$	$0$	$1$	$0$	$0$	$0$
23328.du.16c	R	$16$	$16$	$0$	$0$	$0$	$0$	$16$	$16$	$-2$	$-2$	$-2$	$-2$	$-2$	$1$	$-2$	$0$	$0$	$0$	$0$	$-2$	$0$	$0$	$0$	$-2$	$0$	$0$	$0$	$0$	$0$	$1$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$1$	$0$	$0$	$0$
23328.du.16d	R	$16$	$0$	$0$	$0$	$0$	$-4$	$16$	$-2$	$-2$	$7$	$4$	$4$	$-2$	$-2$	$-2$	$0$	$0$	$0$	$0$	$0$	$0$	$2$	$0$	$0$	$0$	$0$	$2$	$0$	$0$	$0$	$0$	$-1$	$0$	$0$	$0$	$0$	$0$	$1$	$0$	$0$	$0$
23328.du.16e	R	$16$	$-16$	$0$	$0$	$0$	$0$	$16$	$16$	$-2$	$-2$	$-2$	$-2$	$-2$	$1$	$-2$	$0$	$0$	$0$	$0$	$2$	$0$	$0$	$0$	$2$	$0$	$0$	$0$	$0$	$0$	$-1$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$1$	$0$	$0$	$0$
23328.du.16f	R	$16$	$0$	$-16$	$0$	$0$	$0$	$16$	$-2$	$16$	$-2$	$-2$	$-2$	$-2$	$-2$	$1$	$0$	$0$	$0$	$0$	$0$	$2$	$0$	$0$	$0$	$2$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$-1$	$0$	$0$	$0$	$0$	$1$	$0$	$0$	$0$
23328.du.18a	R	$18$	$0$	$0$	$2$	$6$	$0$	$-9$	$0$	$0$	$0$	$6$	$-3$	$0$	$0$	$0$	$2$	$0$	$-1$	$-3$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$2$	$-1$	$0$	$0$	$0$	$0$	$2$	$2$	$0$	$0$	$0$	$-1$	$-1$	$-1$
23328.du.18b	R	$18$	$0$	$0$	$2$	$-6$	$0$	$-9$	$0$	$0$	$0$	$6$	$-3$	$0$	$0$	$0$	$2$	$0$	$-1$	$3$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$2$	$-1$	$0$	$0$	$0$	$0$	$-2$	$-2$	$0$	$0$	$0$	$-1$	$1$	$1$
23328.du.32a	R	$32$	$0$	$0$	$0$	$0$	$0$	$32$	$-4$	$-4$	$14$	$-4$	$-4$	$-4$	$2$	$2$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$-1$	$0$	$0$	$0$
23328.du.36a	R	$36$	$0$	$0$	$4$	$0$	$0$	$-18$	$0$	$0$	$0$	$-6$	$3$	$0$	$0$	$0$	$4$	$0$	$-2$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$-2$	$1$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$-2$	$0$	$0$
23328.du.36b1	C	$36$	$0$	$0$	$-4$	$0$	$0$	$-18$	$0$	$0$	$0$	$-6$	$3$	$0$	$0$	$0$	$0$	$0$	$2$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$2$	$-1$	$0$	$0$	$0$	$0$	$-2{\zeta }_8-2{\zeta }_8^3$	$2{\zeta }_8+2{\zeta }_8^3$	$0$	$0$	$0$	$0$	${\zeta }_8+{\zeta }_8^3$	$-{\zeta }_8-{\zeta }_8^3$
23328.du.36b2	C	$36$	$0$	$0$	$-4$	$0$	$0$	$-18$	$0$	$0$	$0$	$-6$	$3$	$0$	$0$	$0$	$0$	$0$	$2$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$2$	$-1$	$0$	$0$	$0$	$0$	$2{\zeta }_8+2{\zeta }_8^3$	$-2{\zeta }_8-2{\zeta }_8^3$	$0$	$0$	$0$	$0$	$-{\zeta }_8-{\zeta }_8^3$	${\zeta }_8+{\zeta }_8^3$
23328.du.48a	R	$48$	$0$	$0$	$0$	$4$	$0$	$48$	$-6$	$-6$	$-6$	$0$	$0$	$3$	$0$	$0$	$0$	$0$	$0$	$4$	$0$	$0$	$0$	$-2$	$0$	$0$	$-2$	$0$	$0$	$0$	$0$	$1$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$
23328.du.48b	R	$48$	$0$	$0$	$0$	$-4$	$0$	$48$	$-6$	$-6$	$-6$	$0$	$0$	$3$	$0$	$0$	$0$	$0$	$0$	$-4$	$0$	$0$	$0$	$2$	$0$	$0$	$2$	$0$	$0$	$0$	$0$	$-1$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$
23328.du.54a	R	$54$	$0$	$0$	$6$	$6$	$0$	$-27$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$-2$	$0$	$-3$	$-3$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$-2$	$-2$	$0$	$0$	$0$	$1$	$1$	$1$
23328.du.54b	R	$54$	$0$	$0$	$6$	$-6$	$0$	$-27$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$-2$	$0$	$-3$	$3$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$2$	$2$	$0$	$0$	$0$	$1$	$-1$	$-1$
23328.du.72a	R	$72$	$0$	$0$	$-8$	$0$	$0$	$-36$	$0$	$0$	$0$	$6$	$-3$	$0$	$0$	$0$	$0$	$0$	$4$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$-2$	$1$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$