Character table for $\He_3:Q_8$

The row representing the character 216.66.3a2 is highlighted below.

		1A	2A	3A1	3A-1	3B	3C	3D	3E	4A	4B	4C	6A1	6A-1	6B	6C	6D	6E	12A1	12A-1	12B1	12B5	12C1	12C5	12D1	12D5	12E1	12E5	12F1	12F-1	12G1	12G-1
	Size	1	1	1	1	6	6	6	6	2	18	18	1	1	6	6	6	6	2	2	6	6	6	6	6	6	6	6	18	18	18	18
	2 P	1A	1A	3A-1	3A1	3B	3C	3D	3E	2A	2A	2A	3A1	3A-1	3B	3C	3D	3E	6A1	6A-1	6B	6B	6C	6C	6D	6D	6E	6E	6A1	6A-1	6A1	6A-1
	3 P	1A	2A	1A	1A	1A	1A	1A	1A	4A	4B	4C	2A	2A	2A	2A	2A	2A	4A	4A	4A	4A	4A	4A	4A	4A	4A	4A	4B	4B	4C	4C
	Type
216.66.1a	R	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
216.66.1b	R	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$-1$	$-1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$-1$	$-1$	$-1$	$-1$	$-1$	$-1$	$-1$	$-1$	$-1$	$-1$	$-1$	$-1$	$1$	$1$
216.66.1c	R	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$-1$	$1$	$-1$	$1$	$1$	$1$	$1$	$1$	$1$	$-1$	$-1$	$-1$	$-1$	$-1$	$-1$	$-1$	$-1$	$-1$	$-1$	$1$	$1$	$-1$	$-1$
216.66.1d	R	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$-1$	$-1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$-1$	$-1$	$-1$	$-1$
216.66.2a	R	$2$	$2$	$2$	$2$	$-1$	$-1$	$-1$	$2$	$2$	$0$	$0$	$2$	$2$	$-1$	$-1$	$-1$	$2$	$2$	$2$	$-1$	$-1$	$-1$	$-1$	$-1$	$-1$	$2$	$2$	$0$	$0$	$0$	$0$
216.66.2b	R	$2$	$2$	$2$	$2$	$-1$	$-1$	$2$	$-1$	$2$	$0$	$0$	$2$	$2$	$-1$	$-1$	$2$	$-1$	$2$	$2$	$-1$	$-1$	$-1$	$-1$	$2$	$2$	$-1$	$-1$	$0$	$0$	$0$	$0$
216.66.2c	R	$2$	$2$	$2$	$2$	$-1$	$2$	$-1$	$-1$	$2$	$0$	$0$	$2$	$2$	$-1$	$2$	$-1$	$-1$	$2$	$2$	$2$	$-1$	$2$	$-1$	$-1$	$-1$	$-1$	$-1$	$0$	$0$	$0$	$0$
216.66.2d	R	$2$	$2$	$2$	$2$	$2$	$-1$	$-1$	$-1$	$2$	$0$	$0$	$2$	$2$	$2$	$-1$	$-1$	$-1$	$2$	$2$	$-1$	$2$	$-1$	$2$	$-1$	$-1$	$-1$	$-1$	$0$	$0$	$0$	$0$
216.66.2e	R	$2$	$2$	$2$	$2$	$-1$	$-1$	$-1$	$2$	$-2$	$0$	$0$	$2$	$2$	$-1$	$-1$	$-1$	$2$	$-2$	$-2$	$1$	$1$	$1$	$1$	$1$	$1$	$-2$	$-2$	$0$	$0$	$0$	$0$
216.66.2f	R	$2$	$2$	$2$	$2$	$-1$	$-1$	$2$	$-1$	$-2$	$0$	$0$	$2$	$2$	$-1$	$-1$	$2$	$-1$	$-2$	$-2$	$1$	$1$	$1$	$1$	$-2$	$-2$	$1$	$1$	$0$	$0$	$0$	$0$
216.66.2g	R	$2$	$2$	$2$	$2$	$-1$	$2$	$-1$	$-1$	$-2$	$0$	$0$	$2$	$2$	$-1$	$2$	$-1$	$-1$	$-2$	$-2$	$-2$	$1$	$-2$	$1$	$1$	$1$	$1$	$1$	$0$	$0$	$0$	$0$
216.66.2h	R	$2$	$2$	$2$	$2$	$2$	$-1$	$-1$	$-1$	$-2$	$0$	$0$	$2$	$2$	$2$	$-1$	$-1$	$-1$	$-2$	$-2$	$1$	$-2$	$1$	$-2$	$1$	$1$	$1$	$1$	$0$	$0$	$0$	$0$
216.66.2i	S	$2$	$-2$	$2$	$2$	$2$	$2$	$2$	$2$	$0$	$0$	$0$	$-2$	$-2$	$-2$	$-2$	$-2$	$-2$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$
216.66.2j1	S	$2$	$-2$	$2$	$2$	$-1$	$-1$	$-1$	$2$	$0$	$0$	$0$	$-2$	$-2$	$1$	$1$	$1$	$-2$	$0$	$0$	$-{\zeta }_{12}^{-1}-{\zeta }_{12}$	${\zeta }_{12}^{-1}+{\zeta }_{12}$	${\zeta }_{12}^{-1}+{\zeta }_{12}$	$-{\zeta }_{12}^{-1}-{\zeta }_{12}$	${\zeta }_{12}^{-1}+{\zeta }_{12}$	$-{\zeta }_{12}^{-1}-{\zeta }_{12}$	$0$	$0$	$0$	$0$	$0$	$0$
216.66.2j2	S	$2$	$-2$	$2$	$2$	$-1$	$-1$	$-1$	$2$	$0$	$0$	$0$	$-2$	$-2$	$1$	$1$	$1$	$-2$	$0$	$0$	${\zeta }_{12}^{-1}+{\zeta }_{12}$	$-{\zeta }_{12}^{-1}-{\zeta }_{12}$	$-{\zeta }_{12}^{-1}-{\zeta }_{12}$	${\zeta }_{12}^{-1}+{\zeta }_{12}$	$-{\zeta }_{12}^{-1}-{\zeta }_{12}$	${\zeta }_{12}^{-1}+{\zeta }_{12}$	$0$	$0$	$0$	$0$	$0$	$0$
216.66.2k1	S	$2$	$-2$	$2$	$2$	$-1$	$-1$	$2$	$-1$	$0$	$0$	$0$	$-2$	$-2$	$1$	$1$	$-2$	$1$	$0$	$0$	$-{\zeta }_{12}^{-1}-{\zeta }_{12}$	$-{\zeta }_{12}^{-1}-{\zeta }_{12}$	${\zeta }_{12}^{-1}+{\zeta }_{12}$	${\zeta }_{12}^{-1}+{\zeta }_{12}$	$0$	$0$	${\zeta }_{12}^{-1}+{\zeta }_{12}$	$-{\zeta }_{12}^{-1}-{\zeta }_{12}$	$0$	$0$	$0$	$0$
216.66.2k2	S	$2$	$-2$	$2$	$2$	$-1$	$-1$	$2$	$-1$	$0$	$0$	$0$	$-2$	$-2$	$1$	$1$	$-2$	$1$	$0$	$0$	${\zeta }_{12}^{-1}+{\zeta }_{12}$	${\zeta }_{12}^{-1}+{\zeta }_{12}$	$-{\zeta }_{12}^{-1}-{\zeta }_{12}$	$-{\zeta }_{12}^{-1}-{\zeta }_{12}$	$0$	$0$	$-{\zeta }_{12}^{-1}-{\zeta }_{12}$	${\zeta }_{12}^{-1}+{\zeta }_{12}$	$0$	$0$	$0$	$0$
216.66.2l1	S	$2$	$-2$	$2$	$2$	$-1$	$2$	$-1$	$-1$	$0$	$0$	$0$	$-2$	$-2$	$1$	$-2$	$1$	$1$	$0$	$0$	$0$	$-{\zeta }_{12}^{-1}-{\zeta }_{12}$	$0$	${\zeta }_{12}^{-1}+{\zeta }_{12}$	${\zeta }_{12}^{-1}+{\zeta }_{12}$	$-{\zeta }_{12}^{-1}-{\zeta }_{12}$	$-{\zeta }_{12}^{-1}-{\zeta }_{12}$	${\zeta }_{12}^{-1}+{\zeta }_{12}$	$0$	$0$	$0$	$0$
216.66.2l2	S	$2$	$-2$	$2$	$2$	$-1$	$2$	$-1$	$-1$	$0$	$0$	$0$	$-2$	$-2$	$1$	$-2$	$1$	$1$	$0$	$0$	$0$	${\zeta }_{12}^{-1}+{\zeta }_{12}$	$0$	$-{\zeta }_{12}^{-1}-{\zeta }_{12}$	$-{\zeta }_{12}^{-1}-{\zeta }_{12}$	${\zeta }_{12}^{-1}+{\zeta }_{12}$	${\zeta }_{12}^{-1}+{\zeta }_{12}$	$-{\zeta }_{12}^{-1}-{\zeta }_{12}$	$0$	$0$	$0$	$0$
216.66.2m1	S	$2$	$-2$	$2$	$2$	$2$	$-1$	$-1$	$-1$	$0$	$0$	$0$	$-2$	$-2$	$-2$	$1$	$1$	$1$	$0$	$0$	$-{\zeta }_{12}^{-1}-{\zeta }_{12}$	$0$	${\zeta }_{12}^{-1}+{\zeta }_{12}$	$0$	$-{\zeta }_{12}^{-1}-{\zeta }_{12}$	${\zeta }_{12}^{-1}+{\zeta }_{12}$	$-{\zeta }_{12}^{-1}-{\zeta }_{12}$	${\zeta }_{12}^{-1}+{\zeta }_{12}$	$0$	$0$	$0$	$0$
216.66.2m2	S	$2$	$-2$	$2$	$2$	$2$	$-1$	$-1$	$-1$	$0$	$0$	$0$	$-2$	$-2$	$-2$	$1$	$1$	$1$	$0$	$0$	${\zeta }_{12}^{-1}+{\zeta }_{12}$	$0$	$-{\zeta }_{12}^{-1}-{\zeta }_{12}$	$0$	${\zeta }_{12}^{-1}+{\zeta }_{12}$	$-{\zeta }_{12}^{-1}-{\zeta }_{12}$	${\zeta }_{12}^{-1}+{\zeta }_{12}$	$-{\zeta }_{12}^{-1}-{\zeta }_{12}$	$0$	$0$	$0$	$0$
216.66.3a1	C	$3$	$3$	$3{\zeta }_3^{-1}$	$3{\zeta }_3$	$0$	$0$	$0$	$0$	$3$	$1$	$1$	$3{\zeta }_3$	$3{\zeta }_3^{-1}$	$0$	$0$	$0$	$0$	$3{\zeta }_3^{-1}$	$3{\zeta }_3$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	${\zeta }_3^{-1}$	${\zeta }_3$	${\zeta }_3^{-1}$	${\zeta }_3$
216.66.3a2	C	$3$	$3$	$3{\zeta }_3$	$3{\zeta }_3^{-1}$	$0$	$0$	$0$	$0$	$3$	$1$	$1$	$3{\zeta }_3^{-1}$	$3{\zeta }_3$	$0$	$0$	$0$	$0$	$3{\zeta }_3$	$3{\zeta }_3^{-1}$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	${\zeta }_3$	${\zeta }_3^{-1}$	${\zeta }_3$	${\zeta }_3^{-1}$
216.66.3b1	C	$3$	$3$	$3{\zeta }_3^{-1}$	$3{\zeta }_3$	$0$	$0$	$0$	$0$	$3$	$-1$	$-1$	$3{\zeta }_3$	$3{\zeta }_3^{-1}$	$0$	$0$	$0$	$0$	$3{\zeta }_3^{-1}$	$3{\zeta }_3$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$-{\zeta }_3^{-1}$	$-{\zeta }_3$	$-{\zeta }_3^{-1}$	$-{\zeta }_3$
216.66.3b2	C	$3$	$3$	$3{\zeta }_3$	$3{\zeta }_3^{-1}$	$0$	$0$	$0$	$0$	$3$	$-1$	$-1$	$3{\zeta }_3^{-1}$	$3{\zeta }_3$	$0$	$0$	$0$	$0$	$3{\zeta }_3$	$3{\zeta }_3^{-1}$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$-{\zeta }_3$	$-{\zeta }_3^{-1}$	$-{\zeta }_3$	$-{\zeta }_3^{-1}$
216.66.3c1	C	$3$	$3$	$3{\zeta }_3^{-1}$	$3{\zeta }_3$	$0$	$0$	$0$	$0$	$-3$	$-1$	$1$	$3{\zeta }_3$	$3{\zeta }_3^{-1}$	$0$	$0$	$0$	$0$	$-3{\zeta }_3^{-1}$	$-3{\zeta }_3$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$-{\zeta }_3^{-1}$	$-{\zeta }_3$	${\zeta }_3^{-1}$	${\zeta }_3$
216.66.3c2	C	$3$	$3$	$3{\zeta }_3$	$3{\zeta }_3^{-1}$	$0$	$0$	$0$	$0$	$-3$	$-1$	$1$	$3{\zeta }_3^{-1}$	$3{\zeta }_3$	$0$	$0$	$0$	$0$	$-3{\zeta }_3$	$-3{\zeta }_3^{-1}$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$-{\zeta }_3$	$-{\zeta }_3^{-1}$	${\zeta }_3$	${\zeta }_3^{-1}$
216.66.3d1	C	$3$	$3$	$3{\zeta }_3^{-1}$	$3{\zeta }_3$	$0$	$0$	$0$	$0$	$-3$	$1$	$-1$	$3{\zeta }_3$	$3{\zeta }_3^{-1}$	$0$	$0$	$0$	$0$	$-3{\zeta }_3^{-1}$	$-3{\zeta }_3$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	${\zeta }_3^{-1}$	${\zeta }_3$	$-{\zeta }_3^{-1}$	$-{\zeta }_3$
216.66.3d2	C	$3$	$3$	$3{\zeta }_3$	$3{\zeta }_3^{-1}$	$0$	$0$	$0$	$0$	$-3$	$1$	$-1$	$3{\zeta }_3^{-1}$	$3{\zeta }_3$	$0$	$0$	$0$	$0$	$-3{\zeta }_3$	$-3{\zeta }_3^{-1}$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	${\zeta }_3$	${\zeta }_3^{-1}$	$-{\zeta }_3$	$-{\zeta }_3^{-1}$
216.66.6a1	C	$6$	$-6$	$6{\zeta }_3^{-1}$	$6{\zeta }_3$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$-6{\zeta }_3$	$-6{\zeta }_3^{-1}$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$
216.66.6a2	C	$6$	$-6$	$6{\zeta }_3$	$6{\zeta }_3^{-1}$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$-6{\zeta }_3^{-1}$	$-6{\zeta }_3$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$