Group #3913 — character table

	C₁	C₂	C₃	C₄	C₅	C₆	C₇	C₈	C₉	C₁₀	C₁₁	C₁₂	C₁₃	C₁₄	C₁₅
size	1	2	4	4	4	4	4	4	4	4	4	13	26	39	39
order	1	3	13	13	13	39	39	39	39	39	39	2	6	4	4
χ₁	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
χ₃	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	$- i$	$i$
χ₅	2	-1	2	2	2	-1	-1	-1	-1	-1	-1	2	-1	0	0
χ₆	2	-1	2	2	2	-1	-1	-1	-1	-1	-1	-2	1	0	0
χ₇	4	4	ζ²+ζ¹⁰+ζ⁵⁰+ζ⁶²+ζ⁹⁴+ζ¹⁰⁶+ζ¹⁴⁶+ζ¹⁵⁴	ζ¹⁴+ζ³⁴+ζ³⁸+ζ⁷⁰+ζ⁸⁶+ζ¹¹⁸+ζ¹²²+ζ¹⁴²	ζ²²+ζ⁴⁶+ζ⁵⁸+ζ⁷⁴+ζ⁸²+ζ⁹⁸+ζ¹¹⁰+ζ¹³⁴	ζ²+ζ¹⁰+ζ⁵⁰+ζ⁶²+ζ⁹⁴+ζ¹⁰⁶+ζ¹⁴⁶+ζ¹⁵⁴	ζ²+ζ¹⁰+ζ⁵⁰+ζ⁶²+ζ⁹⁴+ζ¹⁰⁶+ζ¹⁴⁶+ζ¹⁵⁴	ζ¹⁴+ζ³⁴+ζ³⁸+ζ⁷⁰+ζ⁸⁶+ζ¹¹⁸+ζ¹²²+ζ¹⁴²	ζ¹⁴+ζ³⁴+ζ³⁸+ζ⁷⁰+ζ⁸⁶+ζ¹¹⁸+ζ¹²²+ζ¹⁴²	ζ²²+ζ⁴⁶+ζ⁵⁸+ζ⁷⁴+ζ⁸²+ζ⁹⁸+ζ¹¹⁰+ζ¹³⁴	ζ²²+ζ⁴⁶+ζ⁵⁸+ζ⁷⁴+ζ⁸²+ζ⁹⁸+ζ¹¹⁰+ζ¹³⁴	0	0	0	0
χ₈	4	4	ζ¹⁴+ζ³⁴+ζ³⁸+ζ⁷⁰+ζ⁸⁶+ζ¹¹⁸+ζ¹²²+ζ¹⁴²	ζ²²+ζ⁴⁶+ζ⁵⁸+ζ⁷⁴+ζ⁸²+ζ⁹⁸+ζ¹¹⁰+ζ¹³⁴	ζ²+ζ¹⁰+ζ⁵⁰+ζ⁶²+ζ⁹⁴+ζ¹⁰⁶+ζ¹⁴⁶+ζ¹⁵⁴	ζ¹⁴+ζ³⁴+ζ³⁸+ζ⁷⁰+ζ⁸⁶+ζ¹¹⁸+ζ¹²²+ζ¹⁴²	ζ¹⁴+ζ³⁴+ζ³⁸+ζ⁷⁰+ζ⁸⁶+ζ¹¹⁸+ζ¹²²+ζ¹⁴²	ζ²²+ζ⁴⁶+ζ⁵⁸+ζ⁷⁴+ζ⁸²+ζ⁹⁸+ζ¹¹⁰+ζ¹³⁴	ζ²²+ζ⁴⁶+ζ⁵⁸+ζ⁷⁴+ζ⁸²+ζ⁹⁸+ζ¹¹⁰+ζ¹³⁴	ζ²+ζ¹⁰+ζ⁵⁰+ζ⁶²+ζ⁹⁴+ζ¹⁰⁶+ζ¹⁴⁶+ζ¹⁵⁴	ζ²+ζ¹⁰+ζ⁵⁰+ζ⁶²+ζ⁹⁴+ζ¹⁰⁶+ζ¹⁴⁶+ζ¹⁵⁴	0	0	0	0
χ₉	4	4	ζ²²+ζ⁴⁶+ζ⁵⁸+ζ⁷⁴+ζ⁸²+ζ⁹⁸+ζ¹¹⁰+ζ¹³⁴	ζ²+ζ¹⁰+ζ⁵⁰+ζ⁶²+ζ⁹⁴+ζ¹⁰⁶+ζ¹⁴⁶+ζ¹⁵⁴	ζ¹⁴+ζ³⁴+ζ³⁸+ζ⁷⁰+ζ⁸⁶+ζ¹¹⁸+ζ¹²²+ζ¹⁴²	ζ²²+ζ⁴⁶+ζ⁵⁸+ζ⁷⁴+ζ⁸²+ζ⁹⁸+ζ¹¹⁰+ζ¹³⁴	ζ²²+ζ⁴⁶+ζ⁵⁸+ζ⁷⁴+ζ⁸²+ζ⁹⁸+ζ¹¹⁰+ζ¹³⁴	ζ²+ζ¹⁰+ζ⁵⁰+ζ⁶²+ζ⁹⁴+ζ¹⁰⁶+ζ¹⁴⁶+ζ¹⁵⁴	ζ²+ζ¹⁰+ζ⁵⁰+ζ⁶²+ζ⁹⁴+ζ¹⁰⁶+ζ¹⁴⁶+ζ¹⁵⁴	ζ¹⁴+ζ³⁴+ζ³⁸+ζ⁷⁰+ζ⁸⁶+ζ¹¹⁸+ζ¹²²+ζ¹⁴²	ζ¹⁴+ζ³⁴+ζ³⁸+ζ⁷⁰+ζ⁸⁶+ζ¹¹⁸+ζ¹²²+ζ¹⁴²	0	0	0	0
χ₁₀	4	-2	ζ²+ζ¹⁰+ζ⁵⁰+ζ⁶²+ζ⁹⁴+ζ¹⁰⁶+ζ¹⁴⁶+ζ¹⁵⁴	ζ¹⁴+ζ³⁴+ζ³⁸+ζ⁷⁰+ζ⁸⁶+ζ¹¹⁸+ζ¹²²+ζ¹⁴²	ζ²²+ζ⁴⁶+ζ⁵⁸+ζ⁷⁴+ζ⁸²+ζ⁹⁸+ζ¹¹⁰+ζ¹³⁴	−ζ⁶²−ζ¹⁰⁶−ζ¹⁴⁶−ζ¹⁵⁴	−ζ²−ζ¹⁰−ζ⁵⁰−ζ⁹⁴	−ζ⁸⁶−ζ¹¹⁸−ζ¹²²−ζ¹⁴²	−ζ¹⁴−ζ³⁴−ζ³⁸−ζ⁷⁰	−ζ²²−ζ⁸²−ζ⁹⁸−ζ¹¹⁰	−ζ⁴⁶−ζ⁵⁸−ζ⁷⁴−ζ¹³⁴	0	0	0	0
χ₁₁	4	-2	ζ²+ζ¹⁰+ζ⁵⁰+ζ⁶²+ζ⁹⁴+ζ¹⁰⁶+ζ¹⁴⁶+ζ¹⁵⁴	ζ¹⁴+ζ³⁴+ζ³⁸+ζ⁷⁰+ζ⁸⁶+ζ¹¹⁸+ζ¹²²+ζ¹⁴²	ζ²²+ζ⁴⁶+ζ⁵⁸+ζ⁷⁴+ζ⁸²+ζ⁹⁸+ζ¹¹⁰+ζ¹³⁴	−ζ²−ζ¹⁰−ζ⁵⁰−ζ⁹⁴	−ζ⁶²−ζ¹⁰⁶−ζ¹⁴⁶−ζ¹⁵⁴	−ζ¹⁴−ζ³⁴−ζ³⁸−ζ⁷⁰	−ζ⁸⁶−ζ¹¹⁸−ζ¹²²−ζ¹⁴²	−ζ⁴⁶−ζ⁵⁸−ζ⁷⁴−ζ¹³⁴	−ζ²²−ζ⁸²−ζ⁹⁸−ζ¹¹⁰	0	0	0	0
χ₁₂	4	-2	ζ¹⁴+ζ³⁴+ζ³⁸+ζ⁷⁰+ζ⁸⁶+ζ¹¹⁸+ζ¹²²+ζ¹⁴²	ζ²²+ζ⁴⁶+ζ⁵⁸+ζ⁷⁴+ζ⁸²+ζ⁹⁸+ζ¹¹⁰+ζ¹³⁴	ζ²+ζ¹⁰+ζ⁵⁰+ζ⁶²+ζ⁹⁴+ζ¹⁰⁶+ζ¹⁴⁶+ζ¹⁵⁴	−ζ⁸⁶−ζ¹¹⁸−ζ¹²²−ζ¹⁴²	−ζ¹⁴−ζ³⁴−ζ³⁸−ζ⁷⁰	−ζ⁴⁶−ζ⁵⁸−ζ⁷⁴−ζ¹³⁴	−ζ²²−ζ⁸²−ζ⁹⁸−ζ¹¹⁰	−ζ⁶²−ζ¹⁰⁶−ζ¹⁴⁶−ζ¹⁵⁴	−ζ²−ζ¹⁰−ζ⁵⁰−ζ⁹⁴	0	0	0	0
χ₁₃	4	-2	ζ¹⁴+ζ³⁴+ζ³⁸+ζ⁷⁰+ζ⁸⁶+ζ¹¹⁸+ζ¹²²+ζ¹⁴²	ζ²²+ζ⁴⁶+ζ⁵⁸+ζ⁷⁴+ζ⁸²+ζ⁹⁸+ζ¹¹⁰+ζ¹³⁴	ζ²+ζ¹⁰+ζ⁵⁰+ζ⁶²+ζ⁹⁴+ζ¹⁰⁶+ζ¹⁴⁶+ζ¹⁵⁴	−ζ¹⁴−ζ³⁴−ζ³⁸−ζ⁷⁰	−ζ⁸⁶−ζ¹¹⁸−ζ¹²²−ζ¹⁴²	−ζ²²−ζ⁸²−ζ⁹⁸−ζ¹¹⁰	−ζ⁴⁶−ζ⁵⁸−ζ⁷⁴−ζ¹³⁴	−ζ²−ζ¹⁰−ζ⁵⁰−ζ⁹⁴	−ζ⁶²−ζ¹⁰⁶−ζ¹⁴⁶−ζ¹⁵⁴	0	0	0	0
χ₁₄	4	-2	ζ²²+ζ⁴⁶+ζ⁵⁸+ζ⁷⁴+ζ⁸²+ζ⁹⁸+ζ¹¹⁰+ζ¹³⁴	ζ²+ζ¹⁰+ζ⁵⁰+ζ⁶²+ζ⁹⁴+ζ¹⁰⁶+ζ¹⁴⁶+ζ¹⁵⁴	ζ¹⁴+ζ³⁴+ζ³⁸+ζ⁷⁰+ζ⁸⁶+ζ¹¹⁸+ζ¹²²+ζ¹⁴²	−ζ²²−ζ⁸²−ζ⁹⁸−ζ¹¹⁰	−ζ⁴⁶−ζ⁵⁸−ζ⁷⁴−ζ¹³⁴	−ζ⁶²−ζ¹⁰⁶−ζ¹⁴⁶−ζ¹⁵⁴	−ζ²−ζ¹⁰−ζ⁵⁰−ζ⁹⁴	−ζ¹⁴−ζ³⁴−ζ³⁸−ζ⁷⁰	−ζ⁸⁶−ζ¹¹⁸−ζ¹²²−ζ¹⁴²	0	0	0	0
χ₁₅	4	-2	ζ²²+ζ⁴⁶+ζ⁵⁸+ζ⁷⁴+ζ⁸²+ζ⁹⁸+ζ¹¹⁰+ζ¹³⁴	ζ²+ζ¹⁰+ζ⁵⁰+ζ⁶²+ζ⁹⁴+ζ¹⁰⁶+ζ¹⁴⁶+ζ¹⁵⁴	ζ¹⁴+ζ³⁴+ζ³⁸+ζ⁷⁰+ζ⁸⁶+ζ¹¹⁸+ζ¹²²+ζ¹⁴²	−ζ⁴⁶−ζ⁵⁸−ζ⁷⁴−ζ¹³⁴	−ζ²²−ζ⁸²−ζ⁹⁸−ζ¹¹⁰	−ζ²−ζ¹⁰−ζ⁵⁰−ζ⁹⁴	−ζ⁶²−ζ¹⁰⁶−ζ¹⁴⁶−ζ¹⁵⁴	−ζ⁸⁶−ζ¹¹⁸−ζ¹²²−ζ¹⁴²	−ζ¹⁴−ζ³⁴−ζ³⁸−ζ⁷⁰	0	0	0	0

Here ζ is a primitive root of unity of order 156 (ζ¹⁵⁶ = 1); i = ζ³⁹.

Character table — Group #3913