Group #64847 — 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
size	1	1	2	2	2	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	10	10	20	20	20	40	40	40	40
order	1	2	4	8	8	5	10	16	16	20	20	40	40	40	40	80	80	80	80	80	80	80	80	2	4	8	16	16	4	4	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
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
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	$i$	$- i$	$i$	$- i$
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	$- i$	$i$	$- i$	$i$
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
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
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	$i$	$- i$	$- i$	$i$
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	$- i$	$i$	$i$	$- i$
χ₉	2	2	2	-2	-2	2	2	0	0	2	2	-2	-2	-2	-2	0	0	0	0	0	0	0	0	2	2	-2	0	0	0	0	0	0
χ₁₀	2	2	2	-2	-2	2	2	0	0	2	2	-2	-2	-2	-2	0	0	0	0	0	0	0	0	-2	-2	2	0	0	0	0	0	0
χ₁₁	2	2	-2	0	0	2	2	$i \sqrt{2}$	$- i \sqrt{2}$	-2	-2	0	0	0	0	$i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	2	-2	0	$i \sqrt{2}$	$- i \sqrt{2}$	0	0	0	0
χ₁₂	2	2	-2	0	0	2	2	$i \sqrt{2}$	$- i \sqrt{2}$	-2	-2	0	0	0	0	$i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	-2	2	0	$- i \sqrt{2}$	$i \sqrt{2}$	0	0	0	0
χ₁₃	2	2	-2	0	0	2	2	$- i \sqrt{2}$	$i \sqrt{2}$	-2	-2	0	0	0	0	$- i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	2	-2	0	$- i \sqrt{2}$	$i \sqrt{2}$	0	0	0	0
χ₁₄	2	2	-2	0	0	2	2	$- i \sqrt{2}$	$i \sqrt{2}$	-2	-2	0	0	0	0	$- i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	-2	2	0	$i \sqrt{2}$	$- i \sqrt{2}$	0	0	0	0
χ₁₅	4	4	4	4	4	-1	-1	4	4	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	0	0	0	0	0	0	0	0	0
χ₁₆	4	4	4	4	4	-1	-1	-4	-4	-1	-1	-1	-1	-1	-1	1	1	1	1	1	1	1	1	0	0	0	0	0	0	0	0	0
χ₁₇	4	4	4	-4	-4	-1	-1	0	0	-1	-1	1	1	1	1	$i \sqrt{5}$	$i \sqrt{5}$	$- i \sqrt{5}$	$- i \sqrt{5}$	$i \sqrt{5}$	$i \sqrt{5}$	$- i \sqrt{5}$	$- i \sqrt{5}$	0	0	0	0	0	0	0	0	0
χ₁₈	4	4	4	-4	-4	-1	-1	0	0	-1	-1	1	1	1	1	$- i \sqrt{5}$	$- i \sqrt{5}$	$i \sqrt{5}$	$i \sqrt{5}$	$- i \sqrt{5}$	$- i \sqrt{5}$	$i \sqrt{5}$	$i \sqrt{5}$	0	0	0	0	0	0	0	0	0
χ₁₉	4	4	-4	0	0	-1	-1	$2 i \sqrt{2}$	$- 2 i \sqrt{2}$	1	1	$i \sqrt{5}$	$i \sqrt{5}$	$- i \sqrt{5}$	$- i \sqrt{5}$	ζ¹⁴+ζ⁴²+ζ⁴⁶+ζ⁵⁸	ζ¹⁴+ζ⁴²+ζ⁴⁶+ζ⁵⁸	ζ²⁶+ζ⁶²+ζ⁷⁴+ζ⁷⁸	ζ²⁶+ζ⁶²+ζ⁷⁴+ζ⁷⁸	−ζ¹⁴−ζ⁴²−ζ⁴⁶−ζ⁵⁸	−ζ¹⁴−ζ⁴²−ζ⁴⁶−ζ⁵⁸	−ζ²⁶−ζ⁶²−ζ⁷⁴−ζ⁷⁸	−ζ²⁶−ζ⁶²−ζ⁷⁴−ζ⁷⁸	0	0	0	0	0	0	0	0	0
χ₂₀	4	4	-4	0	0	-1	-1	$2 i \sqrt{2}$	$- 2 i \sqrt{2}$	1	1	$- i \sqrt{5}$	$- i \sqrt{5}$	$i \sqrt{5}$	$i \sqrt{5}$	ζ²⁶+ζ⁶²+ζ⁷⁴+ζ⁷⁸	ζ²⁶+ζ⁶²+ζ⁷⁴+ζ⁷⁸	ζ¹⁴+ζ⁴²+ζ⁴⁶+ζ⁵⁸	ζ¹⁴+ζ⁴²+ζ⁴⁶+ζ⁵⁸	−ζ²⁶−ζ⁶²−ζ⁷⁴−ζ⁷⁸	−ζ²⁶−ζ⁶²−ζ⁷⁴−ζ⁷⁸	−ζ¹⁴−ζ⁴²−ζ⁴⁶−ζ⁵⁸	−ζ¹⁴−ζ⁴²−ζ⁴⁶−ζ⁵⁸	0	0	0	0	0	0	0	0	0
χ₂₁	4	4	-4	0	0	-1	-1	$- 2 i \sqrt{2}$	$2 i \sqrt{2}$	1	1	$i \sqrt{5}$	$i \sqrt{5}$	$- i \sqrt{5}$	$- i \sqrt{5}$	−ζ¹⁴−ζ⁴²−ζ⁴⁶−ζ⁵⁸	−ζ¹⁴−ζ⁴²−ζ⁴⁶−ζ⁵⁸	−ζ²⁶−ζ⁶²−ζ⁷⁴−ζ⁷⁸	−ζ²⁶−ζ⁶²−ζ⁷⁴−ζ⁷⁸	ζ¹⁴+ζ⁴²+ζ⁴⁶+ζ⁵⁸	ζ¹⁴+ζ⁴²+ζ⁴⁶+ζ⁵⁸	ζ²⁶+ζ⁶²+ζ⁷⁴+ζ⁷⁸	ζ²⁶+ζ⁶²+ζ⁷⁴+ζ⁷⁸	0	0	0	0	0	0	0	0	0
χ₂₂	4	4	-4	0	0	-1	-1	$- 2 i \sqrt{2}$	$2 i \sqrt{2}$	1	1	$- i \sqrt{5}$	$- i \sqrt{5}$	$i \sqrt{5}$	$i \sqrt{5}$	−ζ²⁶−ζ⁶²−ζ⁷⁴−ζ⁷⁸	−ζ²⁶−ζ⁶²−ζ⁷⁴−ζ⁷⁸	−ζ¹⁴−ζ⁴²−ζ⁴⁶−ζ⁵⁸	−ζ¹⁴−ζ⁴²−ζ⁴⁶−ζ⁵⁸	ζ²⁶+ζ⁶²+ζ⁷⁴+ζ⁷⁸	ζ²⁶+ζ⁶²+ζ⁷⁴+ζ⁷⁸	ζ¹⁴+ζ⁴²+ζ⁴⁶+ζ⁵⁸	ζ¹⁴+ζ⁴²+ζ⁴⁶+ζ⁵⁸	0	0	0	0	0	0	0	0	0
χ₂₃	4	-4	0	$2 i \sqrt{2}$	$- 2 i \sqrt{2}$	4	-4	0	0	0	0	$2 i \sqrt{2}$	$- 2 i \sqrt{2}$	$2 i \sqrt{2}$	$- 2 i \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₄	4	-4	0	$2 i \sqrt{2}$	$- 2 i \sqrt{2}$	-1	1	0	0	$i \sqrt{5}$	$- i \sqrt{5}$	ζ¹⁴+ζ⁴²+ζ⁴⁶+ζ⁵⁸	−ζ¹⁴−ζ⁴²−ζ⁴⁶−ζ⁵⁸	ζ²⁶+ζ⁶²+ζ⁷⁴+ζ⁷⁸	−ζ²⁶−ζ⁶²−ζ⁷⁴−ζ⁷⁸	−ζ²⁹−ζ⁴⁷+ζ⁶¹+ζ⁶³	ζ²⁹+ζ⁴⁷−ζ⁶¹−ζ⁶³	−ζ¹³+ζ³¹+ζ⁷⁷−ζ⁷⁹	ζ¹³−ζ³¹−ζ⁷⁷+ζ⁷⁹	ζ⁹−ζ²⁷−ζ⁴¹+ζ⁴³	−ζ⁹+ζ²⁷+ζ⁴¹−ζ⁴³	ζ¹¹−ζ⁵⁷−ζ⁵⁹+ζ⁷³	−ζ¹¹+ζ⁵⁷+ζ⁵⁹−ζ⁷³	0	0	0	0	0	0	0	0	0
χ₂₅	4	-4	0	$2 i \sqrt{2}$	$- 2 i \sqrt{2}$	-1	1	0	0	$i \sqrt{5}$	$- i \sqrt{5}$	ζ¹⁴+ζ⁴²+ζ⁴⁶+ζ⁵⁸	−ζ¹⁴−ζ⁴²−ζ⁴⁶−ζ⁵⁸	ζ²⁶+ζ⁶²+ζ⁷⁴+ζ⁷⁸	−ζ²⁶−ζ⁶²−ζ⁷⁴−ζ⁷⁸	ζ²⁹+ζ⁴⁷−ζ⁶¹−ζ⁶³	−ζ²⁹−ζ⁴⁷+ζ⁶¹+ζ⁶³	ζ¹³−ζ³¹−ζ⁷⁷+ζ⁷⁹	−ζ¹³+ζ³¹+ζ⁷⁷−ζ⁷⁹	−ζ⁹+ζ²⁷+ζ⁴¹−ζ⁴³	ζ⁹−ζ²⁷−ζ⁴¹+ζ⁴³	−ζ¹¹+ζ⁵⁷+ζ⁵⁹−ζ⁷³	ζ¹¹−ζ⁵⁷−ζ⁵⁹+ζ⁷³	0	0	0	0	0	0	0	0	0
χ₂₆	4	-4	0	$2 i \sqrt{2}$	$- 2 i \sqrt{2}$	-1	1	0	0	$- i \sqrt{5}$	$i \sqrt{5}$	ζ²⁶+ζ⁶²+ζ⁷⁴+ζ⁷⁸	−ζ²⁶−ζ⁶²−ζ⁷⁴−ζ⁷⁸	ζ¹⁴+ζ⁴²+ζ⁴⁶+ζ⁵⁸	−ζ¹⁴−ζ⁴²−ζ⁴⁶−ζ⁵⁸	−ζ¹³+ζ³¹+ζ⁷⁷−ζ⁷⁹	ζ¹³−ζ³¹−ζ⁷⁷+ζ⁷⁹	ζ²⁹+ζ⁴⁷−ζ⁶¹−ζ⁶³	−ζ²⁹−ζ⁴⁷+ζ⁶¹+ζ⁶³	ζ¹¹−ζ⁵⁷−ζ⁵⁹+ζ⁷³	−ζ¹¹+ζ⁵⁷+ζ⁵⁹−ζ⁷³	−ζ⁹+ζ²⁷+ζ⁴¹−ζ⁴³	ζ⁹−ζ²⁷−ζ⁴¹+ζ⁴³	0	0	0	0	0	0	0	0	0
χ₂₇	4	-4	0	$2 i \sqrt{2}$	$- 2 i \sqrt{2}$	-1	1	0	0	$- i \sqrt{5}$	$i \sqrt{5}$	ζ²⁶+ζ⁶²+ζ⁷⁴+ζ⁷⁸	−ζ²⁶−ζ⁶²−ζ⁷⁴−ζ⁷⁸	ζ¹⁴+ζ⁴²+ζ⁴⁶+ζ⁵⁸	−ζ¹⁴−ζ⁴²−ζ⁴⁶−ζ⁵⁸	ζ¹³−ζ³¹−ζ⁷⁷+ζ⁷⁹	−ζ¹³+ζ³¹+ζ⁷⁷−ζ⁷⁹	−ζ²⁹−ζ⁴⁷+ζ⁶¹+ζ⁶³	ζ²⁹+ζ⁴⁷−ζ⁶¹−ζ⁶³	−ζ¹¹+ζ⁵⁷+ζ⁵⁹−ζ⁷³	ζ¹¹−ζ⁵⁷−ζ⁵⁹+ζ⁷³	ζ⁹−ζ²⁷−ζ⁴¹+ζ⁴³	−ζ⁹+ζ²⁷+ζ⁴¹−ζ⁴³	0	0	0	0	0	0	0	0	0
χ₂₈	4	-4	0	$- 2 i \sqrt{2}$	$2 i \sqrt{2}$	4	-4	0	0	0	0	$- 2 i \sqrt{2}$	$2 i \sqrt{2}$	$- 2 i \sqrt{2}$	$2 i \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₉	4	-4	0	$- 2 i \sqrt{2}$	$2 i \sqrt{2}$	-1	1	0	0	$i \sqrt{5}$	$- i \sqrt{5}$	−ζ¹⁴−ζ⁴²−ζ⁴⁶−ζ⁵⁸	ζ¹⁴+ζ⁴²+ζ⁴⁶+ζ⁵⁸	−ζ²⁶−ζ⁶²−ζ⁷⁴−ζ⁷⁸	ζ²⁶+ζ⁶²+ζ⁷⁴+ζ⁷⁸	ζ⁹−ζ²⁷−ζ⁴¹+ζ⁴³	−ζ⁹+ζ²⁷+ζ⁴¹−ζ⁴³	ζ¹¹−ζ⁵⁷−ζ⁵⁹+ζ⁷³	−ζ¹¹+ζ⁵⁷+ζ⁵⁹−ζ⁷³	ζ²⁹+ζ⁴⁷−ζ⁶¹−ζ⁶³	−ζ²⁹−ζ⁴⁷+ζ⁶¹+ζ⁶³	ζ¹³−ζ³¹−ζ⁷⁷+ζ⁷⁹	−ζ¹³+ζ³¹+ζ⁷⁷−ζ⁷⁹	0	0	0	0	0	0	0	0	0
χ₃₀	4	-4	0	$- 2 i \sqrt{2}$	$2 i \sqrt{2}$	-1	1	0	0	$i \sqrt{5}$	$- i \sqrt{5}$	−ζ¹⁴−ζ⁴²−ζ⁴⁶−ζ⁵⁸	ζ¹⁴+ζ⁴²+ζ⁴⁶+ζ⁵⁸	−ζ²⁶−ζ⁶²−ζ⁷⁴−ζ⁷⁸	ζ²⁶+ζ⁶²+ζ⁷⁴+ζ⁷⁸	−ζ⁹+ζ²⁷+ζ⁴¹−ζ⁴³	ζ⁹−ζ²⁷−ζ⁴¹+ζ⁴³	−ζ¹¹+ζ⁵⁷+ζ⁵⁹−ζ⁷³	ζ¹¹−ζ⁵⁷−ζ⁵⁹+ζ⁷³	−ζ²⁹−ζ⁴⁷+ζ⁶¹+ζ⁶³	ζ²⁹+ζ⁴⁷−ζ⁶¹−ζ⁶³	−ζ¹³+ζ³¹+ζ⁷⁷−ζ⁷⁹	ζ¹³−ζ³¹−ζ⁷⁷+ζ⁷⁹	0	0	0	0	0	0	0	0	0
χ₃₁	4	-4	0	$- 2 i \sqrt{2}$	$2 i \sqrt{2}$	-1	1	0	0	$- i \sqrt{5}$	$i \sqrt{5}$	−ζ²⁶−ζ⁶²−ζ⁷⁴−ζ⁷⁸	ζ²⁶+ζ⁶²+ζ⁷⁴+ζ⁷⁸	−ζ¹⁴−ζ⁴²−ζ⁴⁶−ζ⁵⁸	ζ¹⁴+ζ⁴²+ζ⁴⁶+ζ⁵⁸	ζ¹¹−ζ⁵⁷−ζ⁵⁹+ζ⁷³	−ζ¹¹+ζ⁵⁷+ζ⁵⁹−ζ⁷³	−ζ⁹+ζ²⁷+ζ⁴¹−ζ⁴³	ζ⁹−ζ²⁷−ζ⁴¹+ζ⁴³	ζ¹³−ζ³¹−ζ⁷⁷+ζ⁷⁹	−ζ¹³+ζ³¹+ζ⁷⁷−ζ⁷⁹	−ζ²⁹−ζ⁴⁷+ζ⁶¹+ζ⁶³	ζ²⁹+ζ⁴⁷−ζ⁶¹−ζ⁶³	0	0	0	0	0	0	0	0	0
χ₃₂	4	-4	0	$- 2 i \sqrt{2}$	$2 i \sqrt{2}$	-1	1	0	0	$- i \sqrt{5}$	$i \sqrt{5}$	−ζ²⁶−ζ⁶²−ζ⁷⁴−ζ⁷⁸	ζ²⁶+ζ⁶²+ζ⁷⁴+ζ⁷⁸	−ζ¹⁴−ζ⁴²−ζ⁴⁶−ζ⁵⁸	ζ¹⁴+ζ⁴²+ζ⁴⁶+ζ⁵⁸	−ζ¹¹+ζ⁵⁷+ζ⁵⁹−ζ⁷³	ζ¹¹−ζ⁵⁷−ζ⁵⁹+ζ⁷³	ζ⁹−ζ²⁷−ζ⁴¹+ζ⁴³	−ζ⁹+ζ²⁷+ζ⁴¹−ζ⁴³	−ζ¹³+ζ³¹+ζ⁷⁷−ζ⁷⁹	ζ¹³−ζ³¹−ζ⁷⁷+ζ⁷⁹	ζ²⁹+ζ⁴⁷−ζ⁶¹−ζ⁶³	−ζ²⁹−ζ⁴⁷+ζ⁶¹+ζ⁶³	0	0	0	0	0	0	0	0	0

Character table — Group #64847