Group #63421 — character table

	C₁	C₂	C₃	C₄	C₅	C₆	C₇	C₈	C₉	C₁₀	C₁₁	C₁₂	C₁₃	C₁₄	C₁₅	C₁₆	C₁₇	C₁₈	C₁₉	C₂₀	C₂₁	C₂₂	C₂₃	C₂₄	C₂₅	C₂₆	C₂₇	C₂₈	C₂₉	C₃₀
size	1	1	1	1	2	2	2	2	6	6	8	8	8	8	8	8	8	8	8	8	8	8	12	12	18	18	18	18	36	36
order	1	2	2	2	3	6	6	6	4	4	9	9	9	18	18	18	18	18	18	18	18	18	12	12	8	8	8	8	4	4
χ₁	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
χ₂	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
χ₃	1	-1	1	-1	1	-1	-1	1	1	-1	1	1	1	1	1	1	-1	-1	-1	-1	-1	-1	1	-1	$i$	$i$	$- i$	$- i$	$i$	$- i$
χ₄	1	-1	1	-1	1	-1	-1	1	1	-1	1	1	1	1	1	1	-1	-1	-1	-1	-1	-1	1	-1	$- i$	$- i$	$i$	$i$	$- i$	$i$
χ₅	2	2	2	2	2	2	2	2	2	2	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	2	2	0	0	0	0	0	0
χ₆	2	2	2	2	-1	-1	-1	-1	2	2	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	−ζ⁴−ζ⁶⁸	-1	-1	0	0	0	0	0	0
χ₇	2	2	2	2	-1	-1	-1	-1	2	2	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	-1	-1	0	0	0	0	0	0
χ₈	2	2	2	2	-1	-1	-1	-1	2	2	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	ζ⁴−ζ⁴⁴+ζ⁵²	-1	-1	0	0	0	0	0	0
χ₉	2	2	-2	-2	2	2	-2	-2	0	0	-1	-1	-1	1	1	1	1	-1	1	-1	1	-1	0	0	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	0	0
χ₁₀	2	2	-2	-2	2	2	-2	-2	0	0	-1	-1	-1	1	1	1	1	-1	1	-1	1	-1	0	0	$- \sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	0	0
χ₁₁	2	-2	2	-2	2	-2	-2	2	2	-2	-1	-1	-1	-1	-1	-1	1	1	1	1	1	1	2	-2	0	0	0	0	0	0
χ₁₂	2	-2	2	-2	-1	1	1	-1	2	-2	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	−ζ⁴⁴+ζ⁵²−ζ⁶⁸	−ζ⁴⁴+ζ⁵²−ζ⁶⁸	−ζ⁴+ζ⁴⁴−ζ⁵²	−ζ⁴+ζ⁴⁴−ζ⁵²	ζ⁴+ζ⁶⁸	ζ⁴+ζ⁶⁸	-1	1	0	0	0	0	0	0
χ₁₃	2	-2	2	-2	-1	1	1	-1	2	-2	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	−ζ⁴+ζ⁴⁴−ζ⁵²	−ζ⁴+ζ⁴⁴−ζ⁵²	ζ⁴+ζ⁶⁸	ζ⁴+ζ⁶⁸	−ζ⁴⁴+ζ⁵²−ζ⁶⁸	−ζ⁴⁴+ζ⁵²−ζ⁶⁸	-1	1	0	0	0	0	0	0
χ₁₄	2	-2	2	-2	-1	1	1	-1	2	-2	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	ζ⁴+ζ⁶⁸	ζ⁴+ζ⁶⁸	−ζ⁴⁴+ζ⁵²−ζ⁶⁸	−ζ⁴⁴+ζ⁵²−ζ⁶⁸	−ζ⁴+ζ⁴⁴−ζ⁵²	−ζ⁴+ζ⁴⁴−ζ⁵²	-1	1	0	0	0	0	0	0
χ₁₅	2	-2	-2	2	2	-2	2	-2	0	0	-1	-1	-1	1	1	1	-1	1	-1	1	-1	1	0	0	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	0	0
χ₁₆	2	-2	-2	2	2	-2	2	-2	0	0	-1	-1	-1	1	1	1	-1	1	-1	1	-1	1	0	0	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	0	0
χ₁₇	3	3	3	3	3	3	3	3	-1	-1	0	0	0	0	0	0	0	0	0	0	0	0	-1	-1	1	1	1	1	-1	-1
χ₁₈	3	3	3	3	3	3	3	3	-1	-1	0	0	0	0	0	0	0	0	0	0	0	0	-1	-1	-1	-1	-1	-1	1	1
χ₁₉	3	-3	3	-3	3	-3	-3	3	-1	1	0	0	0	0	0	0	0	0	0	0	0	0	-1	1	$i$	$i$	$- i$	$- i$	$- i$	$i$
χ₂₀	3	-3	3	-3	3	-3	-3	3	-1	1	0	0	0	0	0	0	0	0	0	0	0	0	-1	1	$- i$	$- i$	$i$	$i$	$i$	$- i$
χ₂₁	4	4	-4	-4	4	4	-4	-4	0	0	1	1	1	-1	-1	-1	-1	1	-1	1	-1	1	0	0	0	0	0	0	0	0
χ₂₂	4	4	-4	-4	-2	-2	2	2	0	0	−ζ⁴⁴+ζ⁵²−ζ⁶⁸	−ζ⁴+ζ⁴⁴−ζ⁵²	ζ⁴+ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	−ζ⁴⁴+ζ⁵²−ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴+ζ⁴⁴−ζ⁵²	−ζ⁴−ζ⁶⁸	ζ⁴+ζ⁶⁸	0	0	0	0	0	0	0	0
χ₂₃	4	4	-4	-4	-2	-2	2	2	0	0	ζ⁴+ζ⁶⁸	−ζ⁴⁴+ζ⁵²−ζ⁶⁸	−ζ⁴+ζ⁴⁴−ζ⁵²	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	ζ⁴+ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	−ζ⁴⁴+ζ⁵²−ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴+ζ⁴⁴−ζ⁵²	0	0	0	0	0	0	0	0
χ₂₄	4	4	-4	-4	-2	-2	2	2	0	0	−ζ⁴+ζ⁴⁴−ζ⁵²	ζ⁴+ζ⁶⁸	−ζ⁴⁴+ζ⁵²−ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴+ζ⁴⁴−ζ⁵²	−ζ⁴−ζ⁶⁸	ζ⁴+ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	−ζ⁴⁴+ζ⁵²−ζ⁶⁸	0	0	0	0	0	0	0	0
χ₂₅	4	-4	-4	4	4	-4	4	-4	0	0	1	1	1	-1	-1	-1	1	-1	1	-1	1	-1	0	0	0	0	0	0	0	0
χ₂₆	4	-4	-4	4	-2	2	-2	2	0	0	−ζ⁴⁴+ζ⁵²−ζ⁶⁸	−ζ⁴+ζ⁴⁴−ζ⁵²	ζ⁴+ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	−ζ⁴⁴+ζ⁵²−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	−ζ⁴+ζ⁴⁴−ζ⁵²	ζ⁴−ζ⁴⁴+ζ⁵²	ζ⁴+ζ⁶⁸	−ζ⁴−ζ⁶⁸	0	0	0	0	0	0	0	0
χ₂₇	4	-4	-4	4	-2	2	-2	2	0	0	ζ⁴+ζ⁶⁸	−ζ⁴⁴+ζ⁵²−ζ⁶⁸	−ζ⁴+ζ⁴⁴−ζ⁵²	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	ζ⁴+ζ⁶⁸	−ζ⁴−ζ⁶⁸	−ζ⁴⁴+ζ⁵²−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	−ζ⁴+ζ⁴⁴−ζ⁵²	ζ⁴−ζ⁴⁴+ζ⁵²	0	0	0	0	0	0	0	0
χ₂₈	4	-4	-4	4	-2	2	-2	2	0	0	−ζ⁴+ζ⁴⁴−ζ⁵²	ζ⁴+ζ⁶⁸	−ζ⁴⁴+ζ⁵²−ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	−ζ⁴+ζ⁴⁴−ζ⁵²	ζ⁴−ζ⁴⁴+ζ⁵²	ζ⁴+ζ⁶⁸	−ζ⁴−ζ⁶⁸	−ζ⁴⁴+ζ⁵²−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	0	0	0	0	0	0	0	0
χ₂₉	6	6	6	6	-3	-3	-3	-3	-2	-2	0	0	0	0	0	0	0	0	0	0	0	0	1	1	0	0	0	0	0	0
χ₃₀	6	-6	6	-6	-3	3	3	-3	-2	2	0	0	0	0	0	0	0	0	0	0	0	0	1	-1	0	0	0	0	0	0

Character table — Group #63421