Character table for $D_{12}:S_4$

The row representing the character 576.5065.2f1 is highlighted below.

		1A	2A	2B	2C	2D	2E	2F	3A	3B	3C	4A	4B	4C	6A	6B	6C	6D	6E	6F1	6F-1	6G1	6G-1	8A1	8A3	8B1	8B3	12A	12B	12C	12D1	12D-1	12E1	12E-1
	Size	1	1	3	3	12	24	36	2	8	16	2	6	24	2	6	6	8	16	24	24	48	48	36	36	36	36	4	12	16	16	16	24	24
	2 P	1A	1A	1A	1A	1A	1A	1A	3A	3B	3C	2A	2A	2C	3A	3A	3A	3B	3C	3A	3A	3B	3B	4B	4B	4A	4A	6A	6A	6D	6E	6E	6C	6C
	3 P	1A	2A	2B	2C	2D	2E	2F	1A	1A	1A	4A	4B	4C	2A	2B	2C	2A	2A	2E	2E	2D	2D	8A3	8A1	8B3	8B1	4A	4B	4A	4A	4A	4C	4C
	Type
576.5065.1a	R	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
576.5065.1b	R	$1$	$1$	$1$	$1$	$-1$	$-1$	$-1$	$1$	$1$	$1$	$1$	$1$	$-1$	$1$	$1$	$1$	$1$	$1$	$-1$	$-1$	$-1$	$-1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$-1$	$-1$
576.5065.1c	R	$1$	$1$	$1$	$1$	$-1$	$1$	$-1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$-1$	$-1$	$-1$	$-1$	$-1$	$-1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
576.5065.1d	R	$1$	$1$	$1$	$1$	$1$	$-1$	$1$	$1$	$1$	$1$	$1$	$1$	$-1$	$1$	$1$	$1$	$1$	$1$	$-1$	$-1$	$1$	$1$	$-1$	$-1$	$-1$	$-1$	$1$	$1$	$1$	$1$	$1$	$-1$	$-1$
576.5065.2a	R	$2$	$2$	$2$	$2$	$0$	$2$	$0$	$-1$	$2$	$-1$	$2$	$2$	$2$	$-1$	$-1$	$-1$	$2$	$-1$	$-1$	$-1$	$0$	$0$	$0$	$0$	$0$	$0$	$-1$	$-1$	$2$	$-1$	$-1$	$-1$	$-1$
576.5065.2b	R	$2$	$2$	$2$	$2$	$2$	$0$	$2$	$2$	$-1$	$-1$	$2$	$2$	$0$	$2$	$2$	$2$	$-1$	$-1$	$0$	$0$	$-1$	$-1$	$0$	$0$	$0$	$0$	$2$	$2$	$-1$	$-1$	$-1$	$0$	$0$
576.5065.2c	R	$2$	$2$	$2$	$2$	$0$	$0$	$0$	$2$	$2$	$2$	$-2$	$-2$	$0$	$2$	$2$	$2$	$2$	$2$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$-2$	$-2$	$-2$	$-2$	$-2$	$0$	$0$
576.5065.2d	R	$2$	$2$	$2$	$2$	$-2$	$0$	$-2$	$2$	$-1$	$-1$	$2$	$2$	$0$	$2$	$2$	$2$	$-1$	$-1$	$0$	$0$	$1$	$1$	$0$	$0$	$0$	$0$	$2$	$2$	$-1$	$-1$	$-1$	$0$	$0$
576.5065.2e	R	$2$	$2$	$2$	$2$	$0$	$-2$	$0$	$-1$	$2$	$-1$	$2$	$2$	$-2$	$-1$	$-1$	$-1$	$2$	$-1$	$1$	$1$	$0$	$0$	$0$	$0$	$0$	$0$	$-1$	$-1$	$2$	$-1$	$-1$	$1$	$1$
576.5065.2f1	R	$2$	$-2$	$-2$	$2$	$0$	$0$	$0$	$2$	$2$	$2$	$0$	$0$	$0$	$-2$	$-2$	$2$	$-2$	$-2$	$0$	$0$	$0$	$0$	$-{\zeta }_8^{-1}-{\zeta }_8$	${\zeta }_8^{-1}+{\zeta }_8$	$-{\zeta }_8^{-1}-{\zeta }_8$	${\zeta }_8^{-1}+{\zeta }_8$	$0$	$0$	$0$	$0$	$0$	$0$	$0$
576.5065.2f2	R	$2$	$-2$	$-2$	$2$	$0$	$0$	$0$	$2$	$2$	$2$	$0$	$0$	$0$	$-2$	$-2$	$2$	$-2$	$-2$	$0$	$0$	$0$	$0$	${\zeta }_8^{-1}+{\zeta }_8$	$-{\zeta }_8^{-1}-{\zeta }_8$	${\zeta }_8^{-1}+{\zeta }_8$	$-{\zeta }_8^{-1}-{\zeta }_8$	$0$	$0$	$0$	$0$	$0$	$0$	$0$
576.5065.2g1	C	$2$	$2$	$2$	$2$	$0$	$0$	$0$	$-1$	$2$	$-1$	$-2$	$-2$	$0$	$-1$	$-1$	$-1$	$2$	$-1$	$-1-2{\zeta }_3$	$1+2{\zeta }_3$	$0$	$0$	$0$	$0$	$0$	$0$	$1$	$1$	$-2$	$1$	$1$	$-1-2{\zeta }_3$	$1+2{\zeta }_3$
576.5065.2g2	C	$2$	$2$	$2$	$2$	$0$	$0$	$0$	$-1$	$2$	$-1$	$-2$	$-2$	$0$	$-1$	$-1$	$-1$	$2$	$-1$	$1+2{\zeta }_3$	$-1-2{\zeta }_3$	$0$	$0$	$0$	$0$	$0$	$0$	$1$	$1$	$-2$	$1$	$1$	$1+2{\zeta }_3$	$-1-2{\zeta }_3$
576.5065.2h1	C	$2$	$2$	$2$	$2$	$0$	$0$	$0$	$2$	$-1$	$-1$	$-2$	$-2$	$0$	$2$	$2$	$2$	$-1$	$-1$	$0$	$0$	$-1-2{\zeta }_3$	$1+2{\zeta }_3$	$0$	$0$	$0$	$0$	$-2$	$-2$	$1$	$1$	$1$	$0$	$0$
576.5065.2h2	C	$2$	$2$	$2$	$2$	$0$	$0$	$0$	$2$	$-1$	$-1$	$-2$	$-2$	$0$	$2$	$2$	$2$	$-1$	$-1$	$0$	$0$	$1+2{\zeta }_3$	$-1-2{\zeta }_3$	$0$	$0$	$0$	$0$	$-2$	$-2$	$1$	$1$	$1$	$0$	$0$
576.5065.3a	R	$3$	$3$	$-1$	$-1$	$3$	$1$	$-1$	$3$	$0$	$0$	$3$	$-1$	$-1$	$3$	$-1$	$-1$	$0$	$0$	$1$	$1$	$0$	$0$	$-1$	$-1$	$1$	$1$	$3$	$-1$	$0$	$0$	$0$	$-1$	$-1$
576.5065.3b	R	$3$	$3$	$-1$	$-1$	$3$	$-1$	$-1$	$3$	$0$	$0$	$3$	$-1$	$1$	$3$	$-1$	$-1$	$0$	$0$	$-1$	$-1$	$0$	$0$	$1$	$1$	$-1$	$-1$	$3$	$-1$	$0$	$0$	$0$	$1$	$1$
576.5065.3c	R	$3$	$3$	$-1$	$-1$	$-3$	$-1$	$1$	$3$	$0$	$0$	$3$	$-1$	$1$	$3$	$-1$	$-1$	$0$	$0$	$-1$	$-1$	$0$	$0$	$-1$	$-1$	$1$	$1$	$3$	$-1$	$0$	$0$	$0$	$1$	$1$
576.5065.3d	R	$3$	$3$	$-1$	$-1$	$-3$	$1$	$1$	$3$	$0$	$0$	$3$	$-1$	$-1$	$3$	$-1$	$-1$	$0$	$0$	$1$	$1$	$0$	$0$	$1$	$1$	$-1$	$-1$	$3$	$-1$	$0$	$0$	$0$	$-1$	$-1$
576.5065.4a	R	$4$	$4$	$4$	$4$	$0$	$0$	$0$	$-2$	$-2$	$1$	$4$	$4$	$0$	$-2$	$-2$	$-2$	$-2$	$1$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$-2$	$-2$	$-2$	$1$	$1$	$0$	$0$
576.5065.4b	R	$4$	$-4$	$-4$	$4$	$0$	$0$	$0$	$-2$	$4$	$-2$	$0$	$0$	$0$	$2$	$2$	$-2$	$-4$	$2$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$
576.5065.4c	R	$4$	$-4$	$-4$	$4$	$0$	$0$	$0$	$4$	$-2$	$-2$	$0$	$0$	$0$	$-4$	$-4$	$4$	$2$	$2$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$
576.5065.4d	S	$4$	$4$	$4$	$4$	$0$	$0$	$0$	$-2$	$-2$	$1$	$-4$	$-4$	$0$	$-2$	$-2$	$-2$	$-2$	$1$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$2$	$2$	$2$	$-1$	$-1$	$0$	$0$
576.5065.4e1	C	$4$	$-4$	$-4$	$4$	$0$	$0$	$0$	$-2$	$-2$	$1$	$0$	$0$	$0$	$2$	$2$	$-2$	$2$	$-1$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$-3i$	$3i$	$0$	$0$
576.5065.4e2	C	$4$	$-4$	$-4$	$4$	$0$	$0$	$0$	$-2$	$-2$	$1$	$0$	$0$	$0$	$2$	$2$	$-2$	$2$	$-1$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$3i$	$-3i$	$0$	$0$
576.5065.6a	R	$6$	$6$	$-2$	$-2$	$0$	$0$	$0$	$6$	$0$	$0$	$-6$	$2$	$0$	$6$	$-2$	$-2$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$-6$	$2$	$0$	$0$	$0$	$0$	$0$
576.5065.6b	R	$6$	$6$	$-2$	$-2$	$0$	$2$	$0$	$-3$	$0$	$0$	$6$	$-2$	$-2$	$-3$	$1$	$1$	$0$	$0$	$-1$	$-1$	$0$	$0$	$0$	$0$	$0$	$0$	$-3$	$1$	$0$	$0$	$0$	$1$	$1$
576.5065.6c	R	$6$	$6$	$-2$	$-2$	$0$	$-2$	$0$	$-3$	$0$	$0$	$6$	$-2$	$2$	$-3$	$1$	$1$	$0$	$0$	$1$	$1$	$0$	$0$	$0$	$0$	$0$	$0$	$-3$	$1$	$0$	$0$	$0$	$-1$	$-1$
576.5065.6d1	R	$6$	$-6$	$2$	$-2$	$0$	$0$	$0$	$6$	$0$	$0$	$0$	$0$	$0$	$-6$	$2$	$-2$	$0$	$0$	$0$	$0$	$0$	$0$	$-{\zeta }_8^{-1}-{\zeta }_8$	${\zeta }_8^{-1}+{\zeta }_8$	${\zeta }_8^{-1}+{\zeta }_8$	$-{\zeta }_8^{-1}-{\zeta }_8$	$0$	$0$	$0$	$0$	$0$	$0$	$0$
576.5065.6d2	R	$6$	$-6$	$2$	$-2$	$0$	$0$	$0$	$6$	$0$	$0$	$0$	$0$	$0$	$-6$	$2$	$-2$	$0$	$0$	$0$	$0$	$0$	$0$	${\zeta }_8^{-1}+{\zeta }_8$	$-{\zeta }_8^{-1}-{\zeta }_8$	$-{\zeta }_8^{-1}-{\zeta }_8$	${\zeta }_8^{-1}+{\zeta }_8$	$0$	$0$	$0$	$0$	$0$	$0$	$0$
576.5065.6e1	C	$6$	$6$	$-2$	$-2$	$0$	$0$	$0$	$-3$	$0$	$0$	$-6$	$2$	$0$	$-3$	$1$	$1$	$0$	$0$	$-1-2{\zeta }_3$	$1+2{\zeta }_3$	$0$	$0$	$0$	$0$	$0$	$0$	$3$	$-1$	$0$	$0$	$0$	$1+2{\zeta }_3$	$-1-2{\zeta }_3$
576.5065.6e2	C	$6$	$6$	$-2$	$-2$	$0$	$0$	$0$	$-3$	$0$	$0$	$-6$	$2$	$0$	$-3$	$1$	$1$	$0$	$0$	$1+2{\zeta }_3$	$-1-2{\zeta }_3$	$0$	$0$	$0$	$0$	$0$	$0$	$3$	$-1$	$0$	$0$	$0$	$-1-2{\zeta }_3$	$1+2{\zeta }_3$
576.5065.12a	R	$12$	$-12$	$4$	$-4$	$0$	$0$	$0$	$-6$	$0$	$0$	$0$	$0$	$0$	$6$	$-2$	$2$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$