Group #10604912 — 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	C₃₁	C₃₂	C₃₃	C₃₄	C₃₅	C₃₆	C₃₇	C₃₈	C₃₉	C₄₀	C₄₁	C₄₂	C₄₃	C₄₄	C₄₅	C₄₆
size	1	1	1	1	2	2	4	4	4	4	4	4	4	4	4	4	8	8	8	8	8	8	8	8	8	8	8	8	8	8	10	10	10	10	20	20	40	40	40	40	40	40	40	40	40	40
order	1	2	2	2	2	2	4	4	5	10	10	10	10	10	10	10	2	2	10	10	10	10	10	10	10	10	20	20	20	20	2	2	4	4	2	4	4	4	4	4	4	4	8	8	8	8
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	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	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	1	1	1	1	1	1	-1	-1	-1	-1	-1	-1	-1	-1	$i$	$i$	$- i$	$- i$	$i$	$i$	$- i$	$- i$
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	1	1	1	1	1	1	-1	-1	-1	-1	-1	-1	-1	-1	$- i$	$- i$	$i$	$i$	$- i$	$- i$	$i$	$i$
χ₅	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	1	-1	-1	-1	-1
χ₆	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	-1	1	1	1	1
χ₇	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	$i$	$i$	$- i$	$- i$	$- i$	$- i$	$i$	$i$
χ₈	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	$- i$	$- i$	$i$	$i$	$i$	$i$	$- i$	$- i$
χ₉	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	-1	1	-1	1	-1
χ₁₀	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	1	-1	1	-1	1
χ₁₁	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	$i$	$- i$	$- i$	$i$	$i$	$- i$	$- i$	$i$
χ₁₂	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	$- i$	$i$	$i$	$- i$	$- i$	$i$	$i$	$- i$
χ₁₃	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	-1	-1	1	-1	1
χ₁₄	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	1	1	-1	1	-1
χ₁₅	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	$i$	$- i$	$- i$	$i$	$- i$	$i$	$i$	$- i$
χ₁₆	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	$- i$	$i$	$i$	$- i$	$i$	$- i$	$- i$	$i$
χ₁₇	2	2	2	2	2	2	-2	-2	2	2	2	2	2	2	2	2	0	0	0	0	0	0	0	0	0	0	-2	-2	-2	-2	2	2	-2	-2	2	-2	0	0	0	0	0	0	0	0	0	0
χ₁₈	2	2	2	2	2	2	-2	-2	2	2	2	2	2	2	2	2	0	0	0	0	0	0	0	0	0	0	-2	-2	-2	-2	-2	-2	2	2	-2	2	0	0	0	0	0	0	0	0	0	0
χ₁₉	2	2	2	2	-2	-2	-2	2	2	2	2	-2	-2	-2	-2	2	0	0	0	0	0	0	0	0	0	0	-2	-2	2	2	2	2	-2	-2	-2	2	0	0	0	0	0	0	0	0	0	0
χ₂₀	2	2	2	2	-2	-2	-2	2	2	2	2	-2	-2	-2	-2	2	0	0	0	0	0	0	0	0	0	0	-2	-2	2	2	-2	-2	2	2	2	-2	0	0	0	0	0	0	0	0	0	0
χ₂₁	4	4	4	4	4	4	4	4	-1	-1	-1	-1	-1	-1	-1	-1	4	4	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₂	4	4	4	4	4	4	4	4	-1	-1	-1	-1	-1	-1	-1	-1	-4	-4	1	1	1	1	1	1	1	1	-1	-1	-1	-1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₃	4	4	4	4	4	4	-4	-4	-1	-1	-1	-1	-1	-1	-1	-1	0	0	$\sqrt{5}$	$\sqrt{5}$	$- \sqrt{5}$	$- \sqrt{5}$	$\sqrt{5}$	$\sqrt{5}$	$- \sqrt{5}$	$- \sqrt{5}$	1	1	1	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₄	4	4	4	4	4	4	-4	-4	-1	-1	-1	-1	-1	-1	-1	-1	0	0	$- \sqrt{5}$	$- \sqrt{5}$	$\sqrt{5}$	$\sqrt{5}$	$- \sqrt{5}$	$- \sqrt{5}$	$\sqrt{5}$	$\sqrt{5}$	1	1	1	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₅	4	4	4	4	-4	-4	4	-4	-1	-1	-1	1	1	1	1	-1	4	-4	-1	-1	-1	-1	1	1	1	1	-1	-1	1	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₆	4	4	4	4	-4	-4	4	-4	-1	-1	-1	1	1	1	1	-1	-4	4	1	1	1	1	-1	-1	-1	-1	-1	-1	1	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₇	4	4	4	4	-4	-4	-4	4	-1	-1	-1	1	1	1	1	-1	0	0	$\sqrt{5}$	$\sqrt{5}$	$- \sqrt{5}$	$- \sqrt{5}$	$- \sqrt{5}$	$- \sqrt{5}$	$\sqrt{5}$	$\sqrt{5}$	1	1	-1	-1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₈	4	4	4	4	-4	-4	-4	4	-1	-1	-1	1	1	1	1	-1	0	0	$- \sqrt{5}$	$- \sqrt{5}$	$\sqrt{5}$	$\sqrt{5}$	$\sqrt{5}$	$\sqrt{5}$	$- \sqrt{5}$	$- \sqrt{5}$	1	1	-1	-1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₉	4	4	-4	-4	0	0	0	0	4	4	-4	0	0	0	0	-4	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	$4 i$	$- 4 i$	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₀	4	4	-4	-4	0	0	0	0	4	4	-4	0	0	0	0	-4	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	$- 4 i$	$4 i$	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₁	4	-4	4	-4	4	-4	0	0	4	-4	-4	4	4	-4	-4	4	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₂	4	-4	4	-4	4	-4	0	0	-1	1	1	-1	-1	1	1	-1	0	0	−ζ²+ζ⁶−ζ¹⁴+ζ¹⁸	ζ²−ζ⁶+ζ¹⁴−ζ¹⁸	−ζ²−ζ⁶+ζ¹⁴+ζ¹⁸	ζ²+ζ⁶−ζ¹⁴−ζ¹⁸	−ζ²+ζ⁶−ζ¹⁴+ζ¹⁸	ζ²−ζ⁶+ζ¹⁴−ζ¹⁸	−ζ²−ζ⁶+ζ¹⁴+ζ¹⁸	ζ²+ζ⁶−ζ¹⁴−ζ¹⁸	$\sqrt{5}$	$- \sqrt{5}$	$\sqrt{5}$	$- \sqrt{5}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₃	4	-4	4	-4	4	-4	0	0	-1	1	1	-1	-1	1	1	-1	0	0	−ζ²−ζ⁶+ζ¹⁴+ζ¹⁸	ζ²+ζ⁶−ζ¹⁴−ζ¹⁸	ζ²−ζ⁶+ζ¹⁴−ζ¹⁸	−ζ²+ζ⁶−ζ¹⁴+ζ¹⁸	−ζ²−ζ⁶+ζ¹⁴+ζ¹⁸	ζ²+ζ⁶−ζ¹⁴−ζ¹⁸	ζ²−ζ⁶+ζ¹⁴−ζ¹⁸	−ζ²+ζ⁶−ζ¹⁴+ζ¹⁸	$- \sqrt{5}$	$\sqrt{5}$	$- \sqrt{5}$	$\sqrt{5}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₄	4	-4	4	-4	4	-4	0	0	-1	1	1	-1	-1	1	1	-1	0	0	ζ²−ζ⁶+ζ¹⁴−ζ¹⁸	−ζ²+ζ⁶−ζ¹⁴+ζ¹⁸	ζ²+ζ⁶−ζ¹⁴−ζ¹⁸	−ζ²−ζ⁶+ζ¹⁴+ζ¹⁸	ζ²−ζ⁶+ζ¹⁴−ζ¹⁸	−ζ²+ζ⁶−ζ¹⁴+ζ¹⁸	ζ²+ζ⁶−ζ¹⁴−ζ¹⁸	−ζ²−ζ⁶+ζ¹⁴+ζ¹⁸	$\sqrt{5}$	$- \sqrt{5}$	$\sqrt{5}$	$- \sqrt{5}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₅	4	-4	4	-4	4	-4	0	0	-1	1	1	-1	-1	1	1	-1	0	0	ζ²+ζ⁶−ζ¹⁴−ζ¹⁸	−ζ²−ζ⁶+ζ¹⁴+ζ¹⁸	−ζ²+ζ⁶−ζ¹⁴+ζ¹⁸	ζ²−ζ⁶+ζ¹⁴−ζ¹⁸	ζ²+ζ⁶−ζ¹⁴−ζ¹⁸	−ζ²−ζ⁶+ζ¹⁴+ζ¹⁸	−ζ²+ζ⁶−ζ¹⁴+ζ¹⁸	ζ²−ζ⁶+ζ¹⁴−ζ¹⁸	$- \sqrt{5}$	$\sqrt{5}$	$- \sqrt{5}$	$\sqrt{5}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₆	4	-4	4	-4	-4	4	0	0	4	-4	-4	-4	-4	4	4	4	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₇	4	-4	4	-4	-4	4	0	0	-1	1	1	1	1	-1	-1	-1	0	0	−ζ²+ζ⁶−ζ¹⁴+ζ¹⁸	ζ²−ζ⁶+ζ¹⁴−ζ¹⁸	−ζ²−ζ⁶+ζ¹⁴+ζ¹⁸	ζ²+ζ⁶−ζ¹⁴−ζ¹⁸	ζ²−ζ⁶+ζ¹⁴−ζ¹⁸	−ζ²+ζ⁶−ζ¹⁴+ζ¹⁸	ζ²+ζ⁶−ζ¹⁴−ζ¹⁸	−ζ²−ζ⁶+ζ¹⁴+ζ¹⁸	$\sqrt{5}$	$- \sqrt{5}$	$- \sqrt{5}$	$\sqrt{5}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₈	4	-4	4	-4	-4	4	0	0	-1	1	1	1	1	-1	-1	-1	0	0	−ζ²−ζ⁶+ζ¹⁴+ζ¹⁸	ζ²+ζ⁶−ζ¹⁴−ζ¹⁸	ζ²−ζ⁶+ζ¹⁴−ζ¹⁸	−ζ²+ζ⁶−ζ¹⁴+ζ¹⁸	ζ²+ζ⁶−ζ¹⁴−ζ¹⁸	−ζ²−ζ⁶+ζ¹⁴+ζ¹⁸	−ζ²+ζ⁶−ζ¹⁴+ζ¹⁸	ζ²−ζ⁶+ζ¹⁴−ζ¹⁸	$- \sqrt{5}$	$\sqrt{5}$	$\sqrt{5}$	$- \sqrt{5}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₉	4	-4	4	-4	-4	4	0	0	-1	1	1	1	1	-1	-1	-1	0	0	ζ²−ζ⁶+ζ¹⁴−ζ¹⁸	−ζ²+ζ⁶−ζ¹⁴+ζ¹⁸	ζ²+ζ⁶−ζ¹⁴−ζ¹⁸	−ζ²−ζ⁶+ζ¹⁴+ζ¹⁸	−ζ²+ζ⁶−ζ¹⁴+ζ¹⁸	ζ²−ζ⁶+ζ¹⁴−ζ¹⁸	−ζ²−ζ⁶+ζ¹⁴+ζ¹⁸	ζ²+ζ⁶−ζ¹⁴−ζ¹⁸	$\sqrt{5}$	$- \sqrt{5}$	$- \sqrt{5}$	$\sqrt{5}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₀	4	-4	4	-4	-4	4	0	0	-1	1	1	1	1	-1	-1	-1	0	0	ζ²+ζ⁶−ζ¹⁴−ζ¹⁸	−ζ²−ζ⁶+ζ¹⁴+ζ¹⁸	−ζ²+ζ⁶−ζ¹⁴+ζ¹⁸	ζ²−ζ⁶+ζ¹⁴−ζ¹⁸	−ζ²−ζ⁶+ζ¹⁴+ζ¹⁸	ζ²+ζ⁶−ζ¹⁴−ζ¹⁸	ζ²−ζ⁶+ζ¹⁴−ζ¹⁸	−ζ²+ζ⁶−ζ¹⁴+ζ¹⁸	$- \sqrt{5}$	$\sqrt{5}$	$\sqrt{5}$	$- \sqrt{5}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₁	4	-4	-4	4	0	0	0	0	4	-4	4	0	0	0	0	-4	0	0	0	0	0	0	0	0	0	0	0	0	0	0	4	-4	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₂	4	-4	-4	4	0	0	0	0	4	-4	4	0	0	0	0	-4	0	0	0	0	0	0	0	0	0	0	0	0	0	0	-4	4	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₃	8	8	-8	-8	0	0	0	0	-2	-2	2	$2 \sqrt{5}$	$- 2 \sqrt{5}$	$2 \sqrt{5}$	$- 2 \sqrt{5}$	2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₄	8	8	-8	-8	0	0	0	0	-2	-2	2	$- 2 \sqrt{5}$	$2 \sqrt{5}$	$- 2 \sqrt{5}$	$2 \sqrt{5}$	2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₅	8	-8	-8	8	0	0	0	0	-2	2	-2	$2 \sqrt{5}$	$- 2 \sqrt{5}$	$- 2 \sqrt{5}$	$2 \sqrt{5}$	2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₆	8	-8	-8	8	0	0	0	0	-2	2	-2	$- 2 \sqrt{5}$	$2 \sqrt{5}$	$2 \sqrt{5}$	$- 2 \sqrt{5}$	2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0

Character table — Group #10604912