Group #3648 — character table

	C₁	C₂	C₃	C₄	C₅	C₆	C₇	C₈	C₉	C₁₀	C₁₁	C₁₂	C₁₃	C₁₄	C₁₅	C₁₆	C₁₇
size	1	2	2	2	4	4	4	4	4	4	4	5	10	10	10	35	35
order	1	7	7	7	5	35	35	35	35	35	35	2	14	14	14	4	4
χ₁	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
χ₃	1	1	1	1	1	1	1	1	1	1	1	-1	-1	-1	-1	$i$	$- i$
χ₄	1	1	1	1	1	1	1	1	1	1	1	-1	-1	-1	-1	$- i$	$i$
χ₅	2	ζ²+ζ²⁶+ζ⁵⁴+ζ⁵⁸+ζ⁸²+ζ⁸⁶+ζ¹¹⁴+ζ¹³⁸	ζ¹⁸+ζ³⁸+ζ⁴⁶+ζ⁶⁶+ζ⁷⁴+ζ⁹⁴+ζ¹⁰²+ζ¹²²	ζ⁶+ζ²²+ζ³⁴+ζ⁶²+ζ⁷⁸+ζ¹⁰⁶+ζ¹¹⁸+ζ¹³⁴	2	ζ²+ζ²⁶+ζ⁵⁴+ζ⁵⁸+ζ⁸²+ζ⁸⁶+ζ¹¹⁴+ζ¹³⁸	ζ²+ζ²⁶+ζ⁵⁴+ζ⁵⁸+ζ⁸²+ζ⁸⁶+ζ¹¹⁴+ζ¹³⁸	ζ¹⁸+ζ³⁸+ζ⁴⁶+ζ⁶⁶+ζ⁷⁴+ζ⁹⁴+ζ¹⁰²+ζ¹²²	ζ¹⁸+ζ³⁸+ζ⁴⁶+ζ⁶⁶+ζ⁷⁴+ζ⁹⁴+ζ¹⁰²+ζ¹²²	ζ⁶+ζ²²+ζ³⁴+ζ⁶²+ζ⁷⁸+ζ¹⁰⁶+ζ¹¹⁸+ζ¹³⁴	ζ⁶+ζ²²+ζ³⁴+ζ⁶²+ζ⁷⁸+ζ¹⁰⁶+ζ¹¹⁸+ζ¹³⁴	2	ζ²+ζ²⁶+ζ⁵⁴+ζ⁵⁸+ζ⁸²+ζ⁸⁶+ζ¹¹⁴+ζ¹³⁸	ζ¹⁸+ζ³⁸+ζ⁴⁶+ζ⁶⁶+ζ⁷⁴+ζ⁹⁴+ζ¹⁰²+ζ¹²²	ζ⁶+ζ²²+ζ³⁴+ζ⁶²+ζ⁷⁸+ζ¹⁰⁶+ζ¹¹⁸+ζ¹³⁴	0	0
χ₆	2	ζ²+ζ²⁶+ζ⁵⁴+ζ⁵⁸+ζ⁸²+ζ⁸⁶+ζ¹¹⁴+ζ¹³⁸	ζ¹⁸+ζ³⁸+ζ⁴⁶+ζ⁶⁶+ζ⁷⁴+ζ⁹⁴+ζ¹⁰²+ζ¹²²	ζ⁶+ζ²²+ζ³⁴+ζ⁶²+ζ⁷⁸+ζ¹⁰⁶+ζ¹¹⁸+ζ¹³⁴	2	ζ²+ζ²⁶+ζ⁵⁴+ζ⁵⁸+ζ⁸²+ζ⁸⁶+ζ¹¹⁴+ζ¹³⁸	ζ²+ζ²⁶+ζ⁵⁴+ζ⁵⁸+ζ⁸²+ζ⁸⁶+ζ¹¹⁴+ζ¹³⁸	ζ¹⁸+ζ³⁸+ζ⁴⁶+ζ⁶⁶+ζ⁷⁴+ζ⁹⁴+ζ¹⁰²+ζ¹²²	ζ¹⁸+ζ³⁸+ζ⁴⁶+ζ⁶⁶+ζ⁷⁴+ζ⁹⁴+ζ¹⁰²+ζ¹²²	ζ⁶+ζ²²+ζ³⁴+ζ⁶²+ζ⁷⁸+ζ¹⁰⁶+ζ¹¹⁸+ζ¹³⁴	ζ⁶+ζ²²+ζ³⁴+ζ⁶²+ζ⁷⁸+ζ¹⁰⁶+ζ¹¹⁸+ζ¹³⁴	-2	−ζ²−ζ²⁶−ζ⁵⁴−ζ⁵⁸−ζ⁸²−ζ⁸⁶−ζ¹¹⁴−ζ¹³⁸	−ζ¹⁸−ζ³⁸−ζ⁴⁶−ζ⁶⁶−ζ⁷⁴−ζ⁹⁴−ζ¹⁰²−ζ¹²²	−ζ⁶−ζ²²−ζ³⁴−ζ⁶²−ζ⁷⁸−ζ¹⁰⁶−ζ¹¹⁸−ζ¹³⁴	0	0
χ₇	2	ζ¹⁸+ζ³⁸+ζ⁴⁶+ζ⁶⁶+ζ⁷⁴+ζ⁹⁴+ζ¹⁰²+ζ¹²²	ζ⁶+ζ²²+ζ³⁴+ζ⁶²+ζ⁷⁸+ζ¹⁰⁶+ζ¹¹⁸+ζ¹³⁴	ζ²+ζ²⁶+ζ⁵⁴+ζ⁵⁸+ζ⁸²+ζ⁸⁶+ζ¹¹⁴+ζ¹³⁸	2	ζ¹⁸+ζ³⁸+ζ⁴⁶+ζ⁶⁶+ζ⁷⁴+ζ⁹⁴+ζ¹⁰²+ζ¹²²	ζ¹⁸+ζ³⁸+ζ⁴⁶+ζ⁶⁶+ζ⁷⁴+ζ⁹⁴+ζ¹⁰²+ζ¹²²	ζ⁶+ζ²²+ζ³⁴+ζ⁶²+ζ⁷⁸+ζ¹⁰⁶+ζ¹¹⁸+ζ¹³⁴	ζ⁶+ζ²²+ζ³⁴+ζ⁶²+ζ⁷⁸+ζ¹⁰⁶+ζ¹¹⁸+ζ¹³⁴	ζ²+ζ²⁶+ζ⁵⁴+ζ⁵⁸+ζ⁸²+ζ⁸⁶+ζ¹¹⁴+ζ¹³⁸	ζ²+ζ²⁶+ζ⁵⁴+ζ⁵⁸+ζ⁸²+ζ⁸⁶+ζ¹¹⁴+ζ¹³⁸	2	ζ¹⁸+ζ³⁸+ζ⁴⁶+ζ⁶⁶+ζ⁷⁴+ζ⁹⁴+ζ¹⁰²+ζ¹²²	ζ⁶+ζ²²+ζ³⁴+ζ⁶²+ζ⁷⁸+ζ¹⁰⁶+ζ¹¹⁸+ζ¹³⁴	ζ²+ζ²⁶+ζ⁵⁴+ζ⁵⁸+ζ⁸²+ζ⁸⁶+ζ¹¹⁴+ζ¹³⁸	0	0
χ₈	2	ζ¹⁸+ζ³⁸+ζ⁴⁶+ζ⁶⁶+ζ⁷⁴+ζ⁹⁴+ζ¹⁰²+ζ¹²²	ζ⁶+ζ²²+ζ³⁴+ζ⁶²+ζ⁷⁸+ζ¹⁰⁶+ζ¹¹⁸+ζ¹³⁴	ζ²+ζ²⁶+ζ⁵⁴+ζ⁵⁸+ζ⁸²+ζ⁸⁶+ζ¹¹⁴+ζ¹³⁸	2	ζ¹⁸+ζ³⁸+ζ⁴⁶+ζ⁶⁶+ζ⁷⁴+ζ⁹⁴+ζ¹⁰²+ζ¹²²	ζ¹⁸+ζ³⁸+ζ⁴⁶+ζ⁶⁶+ζ⁷⁴+ζ⁹⁴+ζ¹⁰²+ζ¹²²	ζ⁶+ζ²²+ζ³⁴+ζ⁶²+ζ⁷⁸+ζ¹⁰⁶+ζ¹¹⁸+ζ¹³⁴	ζ⁶+ζ²²+ζ³⁴+ζ⁶²+ζ⁷⁸+ζ¹⁰⁶+ζ¹¹⁸+ζ¹³⁴	ζ²+ζ²⁶+ζ⁵⁴+ζ⁵⁸+ζ⁸²+ζ⁸⁶+ζ¹¹⁴+ζ¹³⁸	ζ²+ζ²⁶+ζ⁵⁴+ζ⁵⁸+ζ⁸²+ζ⁸⁶+ζ¹¹⁴+ζ¹³⁸	-2	−ζ¹⁸−ζ³⁸−ζ⁴⁶−ζ⁶⁶−ζ⁷⁴−ζ⁹⁴−ζ¹⁰²−ζ¹²²	−ζ⁶−ζ²²−ζ³⁴−ζ⁶²−ζ⁷⁸−ζ¹⁰⁶−ζ¹¹⁸−ζ¹³⁴	−ζ²−ζ²⁶−ζ⁵⁴−ζ⁵⁸−ζ⁸²−ζ⁸⁶−ζ¹¹⁴−ζ¹³⁸	0	0
χ₉	2	ζ⁶+ζ²²+ζ³⁴+ζ⁶²+ζ⁷⁸+ζ¹⁰⁶+ζ¹¹⁸+ζ¹³⁴	ζ²+ζ²⁶+ζ⁵⁴+ζ⁵⁸+ζ⁸²+ζ⁸⁶+ζ¹¹⁴+ζ¹³⁸	ζ¹⁸+ζ³⁸+ζ⁴⁶+ζ⁶⁶+ζ⁷⁴+ζ⁹⁴+ζ¹⁰²+ζ¹²²	2	ζ⁶+ζ²²+ζ³⁴+ζ⁶²+ζ⁷⁸+ζ¹⁰⁶+ζ¹¹⁸+ζ¹³⁴	ζ⁶+ζ²²+ζ³⁴+ζ⁶²+ζ⁷⁸+ζ¹⁰⁶+ζ¹¹⁸+ζ¹³⁴	ζ²+ζ²⁶+ζ⁵⁴+ζ⁵⁸+ζ⁸²+ζ⁸⁶+ζ¹¹⁴+ζ¹³⁸	ζ²+ζ²⁶+ζ⁵⁴+ζ⁵⁸+ζ⁸²+ζ⁸⁶+ζ¹¹⁴+ζ¹³⁸	ζ¹⁸+ζ³⁸+ζ⁴⁶+ζ⁶⁶+ζ⁷⁴+ζ⁹⁴+ζ¹⁰²+ζ¹²²	ζ¹⁸+ζ³⁸+ζ⁴⁶+ζ⁶⁶+ζ⁷⁴+ζ⁹⁴+ζ¹⁰²+ζ¹²²	2	ζ⁶+ζ²²+ζ³⁴+ζ⁶²+ζ⁷⁸+ζ¹⁰⁶+ζ¹¹⁸+ζ¹³⁴	ζ²+ζ²⁶+ζ⁵⁴+ζ⁵⁸+ζ⁸²+ζ⁸⁶+ζ¹¹⁴+ζ¹³⁸	ζ¹⁸+ζ³⁸+ζ⁴⁶+ζ⁶⁶+ζ⁷⁴+ζ⁹⁴+ζ¹⁰²+ζ¹²²	0	0
χ₁₀	2	ζ⁶+ζ²²+ζ³⁴+ζ⁶²+ζ⁷⁸+ζ¹⁰⁶+ζ¹¹⁸+ζ¹³⁴	ζ²+ζ²⁶+ζ⁵⁴+ζ⁵⁸+ζ⁸²+ζ⁸⁶+ζ¹¹⁴+ζ¹³⁸	ζ¹⁸+ζ³⁸+ζ⁴⁶+ζ⁶⁶+ζ⁷⁴+ζ⁹⁴+ζ¹⁰²+ζ¹²²	2	ζ⁶+ζ²²+ζ³⁴+ζ⁶²+ζ⁷⁸+ζ¹⁰⁶+ζ¹¹⁸+ζ¹³⁴	ζ⁶+ζ²²+ζ³⁴+ζ⁶²+ζ⁷⁸+ζ¹⁰⁶+ζ¹¹⁸+ζ¹³⁴	ζ²+ζ²⁶+ζ⁵⁴+ζ⁵⁸+ζ⁸²+ζ⁸⁶+ζ¹¹⁴+ζ¹³⁸	ζ²+ζ²⁶+ζ⁵⁴+ζ⁵⁸+ζ⁸²+ζ⁸⁶+ζ¹¹⁴+ζ¹³⁸	ζ¹⁸+ζ³⁸+ζ⁴⁶+ζ⁶⁶+ζ⁷⁴+ζ⁹⁴+ζ¹⁰²+ζ¹²²	ζ¹⁸+ζ³⁸+ζ⁴⁶+ζ⁶⁶+ζ⁷⁴+ζ⁹⁴+ζ¹⁰²+ζ¹²²	-2	−ζ⁶−ζ²²−ζ³⁴−ζ⁶²−ζ⁷⁸−ζ¹⁰⁶−ζ¹¹⁸−ζ¹³⁴	−ζ²−ζ²⁶−ζ⁵⁴−ζ⁵⁸−ζ⁸²−ζ⁸⁶−ζ¹¹⁴−ζ¹³⁸	−ζ¹⁸−ζ³⁸−ζ⁴⁶−ζ⁶⁶−ζ⁷⁴−ζ⁹⁴−ζ¹⁰²−ζ¹²²	0	0
χ₁₁	4	4	4	4	-1	-1	-1	-1	-1	-1	-1	0	0	0	0	0	0
χ₁₂	4	2ζ²+2ζ²⁶+2ζ⁵⁴+2ζ⁵⁸+2ζ⁸²+2ζ⁸⁶+2ζ¹¹⁴+2ζ¹³⁸	2ζ¹⁸+2ζ³⁸+2ζ⁴⁶+2ζ⁶⁶+2ζ⁷⁴+2ζ⁹⁴+2ζ¹⁰²+2ζ¹²²	2ζ⁶+2ζ²²+2ζ³⁴+2ζ⁶²+2ζ⁷⁸+2ζ¹⁰⁶+2ζ¹¹⁸+2ζ¹³⁴	-1	−ζ⁸²−ζ⁸⁶−ζ¹¹⁴−ζ¹³⁸	−ζ²−ζ²⁶−ζ⁵⁴−ζ⁵⁸	−ζ¹⁸−ζ⁶⁶−ζ⁹⁴−ζ¹⁰²	−ζ³⁸−ζ⁴⁶−ζ⁷⁴−ζ¹²²	−ζ⁶−ζ²²−ζ³⁴−ζ⁷⁸	−ζ⁶²−ζ¹⁰⁶−ζ¹¹⁸−ζ¹³⁴	0	0	0	0	0	0
χ₁₃	4	2ζ²+2ζ²⁶+2ζ⁵⁴+2ζ⁵⁸+2ζ⁸²+2ζ⁸⁶+2ζ¹¹⁴+2ζ¹³⁸	2ζ¹⁸+2ζ³⁸+2ζ⁴⁶+2ζ⁶⁶+2ζ⁷⁴+2ζ⁹⁴+2ζ¹⁰²+2ζ¹²²	2ζ⁶+2ζ²²+2ζ³⁴+2ζ⁶²+2ζ⁷⁸+2ζ¹⁰⁶+2ζ¹¹⁸+2ζ¹³⁴	-1	−ζ²−ζ²⁶−ζ⁵⁴−ζ⁵⁸	−ζ⁸²−ζ⁸⁶−ζ¹¹⁴−ζ¹³⁸	−ζ³⁸−ζ⁴⁶−ζ⁷⁴−ζ¹²²	−ζ¹⁸−ζ⁶⁶−ζ⁹⁴−ζ¹⁰²	−ζ⁶²−ζ¹⁰⁶−ζ¹¹⁸−ζ¹³⁴	−ζ⁶−ζ²²−ζ³⁴−ζ⁷⁸	0	0	0	0	0	0
χ₁₄	4	2ζ¹⁸+2ζ³⁸+2ζ⁴⁶+2ζ⁶⁶+2ζ⁷⁴+2ζ⁹⁴+2ζ¹⁰²+2ζ¹²²	2ζ⁶+2ζ²²+2ζ³⁴+2ζ⁶²+2ζ⁷⁸+2ζ¹⁰⁶+2ζ¹¹⁸+2ζ¹³⁴	2ζ²+2ζ²⁶+2ζ⁵⁴+2ζ⁵⁸+2ζ⁸²+2ζ⁸⁶+2ζ¹¹⁴+2ζ¹³⁸	-1	−ζ¹⁸−ζ⁶⁶−ζ⁹⁴−ζ¹⁰²	−ζ³⁸−ζ⁴⁶−ζ⁷⁴−ζ¹²²	−ζ⁶²−ζ¹⁰⁶−ζ¹¹⁸−ζ¹³⁴	−ζ⁶−ζ²²−ζ³⁴−ζ⁷⁸	−ζ⁸²−ζ⁸⁶−ζ¹¹⁴−ζ¹³⁸	−ζ²−ζ²⁶−ζ⁵⁴−ζ⁵⁸	0	0	0	0	0	0
χ₁₅	4	2ζ¹⁸+2ζ³⁸+2ζ⁴⁶+2ζ⁶⁶+2ζ⁷⁴+2ζ⁹⁴+2ζ¹⁰²+2ζ¹²²	2ζ⁶+2ζ²²+2ζ³⁴+2ζ⁶²+2ζ⁷⁸+2ζ¹⁰⁶+2ζ¹¹⁸+2ζ¹³⁴	2ζ²+2ζ²⁶+2ζ⁵⁴+2ζ⁵⁸+2ζ⁸²+2ζ⁸⁶+2ζ¹¹⁴+2ζ¹³⁸	-1	−ζ³⁸−ζ⁴⁶−ζ⁷⁴−ζ¹²²	−ζ¹⁸−ζ⁶⁶−ζ⁹⁴−ζ¹⁰²	−ζ⁶−ζ²²−ζ³⁴−ζ⁷⁸	−ζ⁶²−ζ¹⁰⁶−ζ¹¹⁸−ζ¹³⁴	−ζ²−ζ²⁶−ζ⁵⁴−ζ⁵⁸	−ζ⁸²−ζ⁸⁶−ζ¹¹⁴−ζ¹³⁸	0	0	0	0	0	0
χ₁₆	4	2ζ⁶+2ζ²²+2ζ³⁴+2ζ⁶²+2ζ⁷⁸+2ζ¹⁰⁶+2ζ¹¹⁸+2ζ¹³⁴	2ζ²+2ζ²⁶+2ζ⁵⁴+2ζ⁵⁸+2ζ⁸²+2ζ⁸⁶+2ζ¹¹⁴+2ζ¹³⁸	2ζ¹⁸+2ζ³⁸+2ζ⁴⁶+2ζ⁶⁶+2ζ⁷⁴+2ζ⁹⁴+2ζ¹⁰²+2ζ¹²²	-1	−ζ⁶−ζ²²−ζ³⁴−ζ⁷⁸	−ζ⁶²−ζ¹⁰⁶−ζ¹¹⁸−ζ¹³⁴	−ζ⁸²−ζ⁸⁶−ζ¹¹⁴−ζ¹³⁸	−ζ²−ζ²⁶−ζ⁵⁴−ζ⁵⁸	−ζ³⁸−ζ⁴⁶−ζ⁷⁴−ζ¹²²	−ζ¹⁸−ζ⁶⁶−ζ⁹⁴−ζ¹⁰²	0	0	0	0	0	0
χ₁₇	4	2ζ⁶+2ζ²²+2ζ³⁴+2ζ⁶²+2ζ⁷⁸+2ζ¹⁰⁶+2ζ¹¹⁸+2ζ¹³⁴	2ζ²+2ζ²⁶+2ζ⁵⁴+2ζ⁵⁸+2ζ⁸²+2ζ⁸⁶+2ζ¹¹⁴+2ζ¹³⁸	2ζ¹⁸+2ζ³⁸+2ζ⁴⁶+2ζ⁶⁶+2ζ⁷⁴+2ζ⁹⁴+2ζ¹⁰²+2ζ¹²²	-1	−ζ⁶²−ζ¹⁰⁶−ζ¹¹⁸−ζ¹³⁴	−ζ⁶−ζ²²−ζ³⁴−ζ⁷⁸	−ζ²−ζ²⁶−ζ⁵⁴−ζ⁵⁸	−ζ⁸²−ζ⁸⁶−ζ¹¹⁴−ζ¹³⁸	−ζ¹⁸−ζ⁶⁶−ζ⁹⁴−ζ¹⁰²	−ζ³⁸−ζ⁴⁶−ζ⁷⁴−ζ¹²²	0	0	0	0	0	0

Here ζ is a primitive root of unity of order 140 (ζ¹⁴⁰ = 1); i = ζ³⁵.

Character table — Group #3648