Group #13014251 — 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	C₄₇	C₄₈	C₄₉	C₅₀	C₅₁	C₅₂	C₅₃
size	1	1	2	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	16	16	16	16	16	16	16	16	16	16	40	40	40	40	80	80	80	80	80	80	80	80	80	80
order	1	2	2	4	4	2	4	5	10	10	10	10	10	10	10	8	8	20	20	20	20	40	40	40	40	40	40	40	40	4	4	20	20	20	20	20	20	20	20	2	4	8	8	8	8	8	8	8	8	16	16	16	16
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	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	-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	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	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	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	-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	-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	-1	-1	-1	-1	-1	1	1	$- i$	$- i$	$i$	$i$	$i$	$i$	$- i$	$- i$
χ₉	2	2	2	2	2	2	2	2	2	2	2	2	2	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	0	0	0	0	0	0	0	0	0	0
χ₁₀	2	2	2	2	2	2	2	2	2	2	2	2	2	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	0	0	0	0	0	0	0	0	0	0
χ₁₁	2	2	2	-2	-2	2	-2	2	2	2	2	2	2	2	2	0	0	-2	-2	-2	-2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	$2 i$	$- 2 i$	0	0	$1 + i$	$- 1 - i$	$1 - i$	$- 1 + i$	0	0	0	0
χ₁₂	2	2	2	-2	-2	2	-2	2	2	2	2	2	2	2	2	0	0	-2	-2	-2	-2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	$2 i$	$- 2 i$	0	0	$- 1 - i$	$1 + i$	$- 1 + i$	$1 - i$	0	0	0	0
χ₁₃	2	2	2	-2	-2	2	-2	2	2	2	2	2	2	2	2	0	0	-2	-2	-2	-2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	$- 2 i$	$2 i$	0	0	$1 - i$	$- 1 + i$	$1 + i$	$- 1 - i$	0	0	0	0
χ₁₄	2	2	2	-2	-2	2	-2	2	2	2	2	2	2	2	2	0	0	-2	-2	-2	-2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	$- 2 i$	$2 i$	0	0	$- 1 + i$	$1 - i$	$- 1 - i$	$1 + i$	0	0	0	0
χ₁₅	2	2	2	-2	-2	-2	2	2	-2	-2	-2	-2	2	2	2	0	0	2	2	-2	-2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	2	-2	0	0	0	0	0	0	0	0	$i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$
χ₁₆	2	2	2	-2	-2	-2	2	2	-2	-2	-2	-2	2	2	2	0	0	2	2	-2	-2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	2	-2	0	0	0	0	0	0	0	0	$- i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$
χ₁₇	2	2	2	-2	-2	-2	2	2	-2	-2	-2	-2	2	2	2	0	0	2	2	-2	-2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	-2	2	0	0	0	0	0	0	0	0	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$
χ₁₈	2	2	2	-2	-2	-2	2	2	-2	-2	-2	-2	2	2	2	0	0	2	2	-2	-2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	-2	2	0	0	0	0	0	0	0	0	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$
χ₁₉	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	4	4	-1	-1	-1	-1	-1	-1	-1	-1	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₀	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	-4	-4	1	1	1	1	1	1	1	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₁	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	$\sqrt{5}$	$\sqrt{5}$	$\sqrt{5}$	$\sqrt{5}$	$- \sqrt{5}$	$- \sqrt{5}$	$- \sqrt{5}$	$- \sqrt{5}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₂	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	$- \sqrt{5}$	$- \sqrt{5}$	$- \sqrt{5}$	$- \sqrt{5}$	$\sqrt{5}$	$\sqrt{5}$	$\sqrt{5}$	$\sqrt{5}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₃	4	4	4	4	4	-4	-4	4	-4	-4	-4	-4	4	4	4	0	0	-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	0	0
χ₂₄	4	4	4	4	4	-4	-4	-1	1	1	1	1	-1	-1	-1	0	0	1	1	-1	-1	$\sqrt{5}$	$\sqrt{5}$	$\sqrt{5}$	$\sqrt{5}$	$- \sqrt{5}$	$- \sqrt{5}$	$- \sqrt{5}$	$- \sqrt{5}$	0	0	−ζ⁴+ζ¹²−ζ²⁸+ζ³⁶	−ζ⁴+ζ¹²−ζ²⁸+ζ³⁶	ζ⁴−ζ¹²+ζ²⁸−ζ³⁶	ζ⁴−ζ¹²+ζ²⁸−ζ³⁶	−ζ⁴−ζ¹²+ζ²⁸+ζ³⁶	−ζ⁴−ζ¹²+ζ²⁸+ζ³⁶	ζ⁴+ζ¹²−ζ²⁸−ζ³⁶	ζ⁴+ζ¹²−ζ²⁸−ζ³⁶	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₅	4	4	4	4	4	-4	-4	-1	1	1	1	1	-1	-1	-1	0	0	1	1	-1	-1	$\sqrt{5}$	$\sqrt{5}$	$\sqrt{5}$	$\sqrt{5}$	$- \sqrt{5}$	$- \sqrt{5}$	$- \sqrt{5}$	$- \sqrt{5}$	0	0	ζ⁴−ζ¹²+ζ²⁸−ζ³⁶	ζ⁴−ζ¹²+ζ²⁸−ζ³⁶	−ζ⁴+ζ¹²−ζ²⁸+ζ³⁶	−ζ⁴+ζ¹²−ζ²⁸+ζ³⁶	ζ⁴+ζ¹²−ζ²⁸−ζ³⁶	ζ⁴+ζ¹²−ζ²⁸−ζ³⁶	−ζ⁴−ζ¹²+ζ²⁸+ζ³⁶	−ζ⁴−ζ¹²+ζ²⁸+ζ³⁶	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₆	4	4	4	4	4	-4	-4	-1	1	1	1	1	-1	-1	-1	0	0	1	1	-1	-1	$- \sqrt{5}$	$- \sqrt{5}$	$- \sqrt{5}$	$- \sqrt{5}$	$\sqrt{5}$	$\sqrt{5}$	$\sqrt{5}$	$\sqrt{5}$	0	0	−ζ⁴−ζ¹²+ζ²⁸+ζ³⁶	−ζ⁴−ζ¹²+ζ²⁸+ζ³⁶	ζ⁴+ζ¹²−ζ²⁸−ζ³⁶	ζ⁴+ζ¹²−ζ²⁸−ζ³⁶	ζ⁴−ζ¹²+ζ²⁸−ζ³⁶	ζ⁴−ζ¹²+ζ²⁸−ζ³⁶	−ζ⁴+ζ¹²−ζ²⁸+ζ³⁶	−ζ⁴+ζ¹²−ζ²⁸+ζ³⁶	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₇	4	4	4	4	4	-4	-4	-1	1	1	1	1	-1	-1	-1	0	0	1	1	-1	-1	$- \sqrt{5}$	$- \sqrt{5}$	$- \sqrt{5}$	$- \sqrt{5}$	$\sqrt{5}$	$\sqrt{5}$	$\sqrt{5}$	$\sqrt{5}$	0	0	ζ⁴+ζ¹²−ζ²⁸−ζ³⁶	ζ⁴+ζ¹²−ζ²⁸−ζ³⁶	−ζ⁴−ζ¹²+ζ²⁸+ζ³⁶	−ζ⁴−ζ¹²+ζ²⁸+ζ³⁶	−ζ⁴+ζ¹²−ζ²⁸+ζ³⁶	−ζ⁴+ζ¹²−ζ²⁸+ζ³⁶	ζ⁴−ζ¹²+ζ²⁸−ζ³⁶	ζ⁴−ζ¹²+ζ²⁸−ζ³⁶	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₈	4	4	-4	4	-4	0	0	4	0	0	0	0	4	-4	-4	0	0	0	0	-4	4	0	0	0	0	0	0	0	0	$2 i$	$- 2 i$	$2 i$	$- 2 i$	$2 i$	$- 2 i$	$2 i$	$- 2 i$	$2 i$	$- 2 i$	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₉	4	4	-4	4	-4	0	0	4	0	0	0	0	4	-4	-4	0	0	0	0	-4	4	0	0	0	0	0	0	0	0	$- 2 i$	$2 i$	$- 2 i$	$2 i$	$- 2 i$	$2 i$	$- 2 i$	$2 i$	$- 2 i$	$2 i$	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₀	4	4	-4	4	-4	0	0	-1	$\sqrt{5}$	$\sqrt{5}$	$- \sqrt{5}$	$- \sqrt{5}$	-1	1	1	0	0	$\sqrt{5}$	$- \sqrt{5}$	1	-1	−ζ⁴+ζ¹²−ζ²⁸+ζ³⁶	−ζ⁴+ζ¹²−ζ²⁸+ζ³⁶	ζ⁴−ζ¹²+ζ²⁸−ζ³⁶	ζ⁴−ζ¹²+ζ²⁸−ζ³⁶	−ζ⁴−ζ¹²+ζ²⁸+ζ³⁶	−ζ⁴−ζ¹²+ζ²⁸+ζ³⁶	ζ⁴+ζ¹²−ζ²⁸−ζ³⁶	ζ⁴+ζ¹²−ζ²⁸−ζ³⁶	$2 i$	$- 2 i$	ζ⁶−ζ¹⁴−ζ²²−ζ³⁸	−ζ⁶+ζ¹⁴+ζ²²+ζ³⁸	−ζ⁶+ζ¹⁴−ζ²²−ζ³⁸	ζ⁶−ζ¹⁴+ζ²²+ζ³⁸	−ζ⁶−ζ¹⁴−ζ²²+ζ³⁸	ζ⁶+ζ¹⁴+ζ²²−ζ³⁸	−ζ⁶−ζ¹⁴+ζ²²−ζ³⁸	ζ⁶+ζ¹⁴−ζ²²+ζ³⁸	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₁	4	4	-4	4	-4	0	0	-1	$\sqrt{5}$	$\sqrt{5}$	$- \sqrt{5}$	$- \sqrt{5}$	-1	1	1	0	0	$\sqrt{5}$	$- \sqrt{5}$	1	-1	−ζ⁴+ζ¹²−ζ²⁸+ζ³⁶	−ζ⁴+ζ¹²−ζ²⁸+ζ³⁶	ζ⁴−ζ¹²+ζ²⁸−ζ³⁶	ζ⁴−ζ¹²+ζ²⁸−ζ³⁶	−ζ⁴−ζ¹²+ζ²⁸+ζ³⁶	−ζ⁴−ζ¹²+ζ²⁸+ζ³⁶	ζ⁴+ζ¹²−ζ²⁸−ζ³⁶	ζ⁴+ζ¹²−ζ²⁸−ζ³⁶	$- 2 i$	$2 i$	−ζ⁶+ζ¹⁴+ζ²²+ζ³⁸	ζ⁶−ζ¹⁴−ζ²²−ζ³⁸	ζ⁶−ζ¹⁴+ζ²²+ζ³⁸	−ζ⁶+ζ¹⁴−ζ²²−ζ³⁸	ζ⁶+ζ¹⁴+ζ²²−ζ³⁸	−ζ⁶−ζ¹⁴−ζ²²+ζ³⁸	ζ⁶+ζ¹⁴−ζ²²+ζ³⁸	−ζ⁶−ζ¹⁴+ζ²²−ζ³⁸	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₂	4	4	-4	4	-4	0	0	-1	$\sqrt{5}$	$\sqrt{5}$	$- \sqrt{5}$	$- \sqrt{5}$	-1	1	1	0	0	$\sqrt{5}$	$- \sqrt{5}$	1	-1	ζ⁴−ζ¹²+ζ²⁸−ζ³⁶	ζ⁴−ζ¹²+ζ²⁸−ζ³⁶	−ζ⁴+ζ¹²−ζ²⁸+ζ³⁶	−ζ⁴+ζ¹²−ζ²⁸+ζ³⁶	ζ⁴+ζ¹²−ζ²⁸−ζ³⁶	ζ⁴+ζ¹²−ζ²⁸−ζ³⁶	−ζ⁴−ζ¹²+ζ²⁸+ζ³⁶	−ζ⁴−ζ¹²+ζ²⁸+ζ³⁶	$2 i$	$- 2 i$	−ζ⁶+ζ¹⁴−ζ²²−ζ³⁸	ζ⁶−ζ¹⁴+ζ²²+ζ³⁸	ζ⁶−ζ¹⁴−ζ²²−ζ³⁸	−ζ⁶+ζ¹⁴+ζ²²+ζ³⁸	−ζ⁶−ζ¹⁴+ζ²²−ζ³⁸	ζ⁶+ζ¹⁴−ζ²²+ζ³⁸	−ζ⁶−ζ¹⁴−ζ²²+ζ³⁸	ζ⁶+ζ¹⁴+ζ²²−ζ³⁸	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₃	4	4	-4	4	-4	0	0	-1	$\sqrt{5}$	$\sqrt{5}$	$- \sqrt{5}$	$- \sqrt{5}$	-1	1	1	0	0	$\sqrt{5}$	$- \sqrt{5}$	1	-1	ζ⁴−ζ¹²+ζ²⁸−ζ³⁶	ζ⁴−ζ¹²+ζ²⁸−ζ³⁶	−ζ⁴+ζ¹²−ζ²⁸+ζ³⁶	−ζ⁴+ζ¹²−ζ²⁸+ζ³⁶	ζ⁴+ζ¹²−ζ²⁸−ζ³⁶	ζ⁴+ζ¹²−ζ²⁸−ζ³⁶	−ζ⁴−ζ¹²+ζ²⁸+ζ³⁶	−ζ⁴−ζ¹²+ζ²⁸+ζ³⁶	$- 2 i$	$2 i$	ζ⁶−ζ¹⁴+ζ²²+ζ³⁸	−ζ⁶+ζ¹⁴−ζ²²−ζ³⁸	−ζ⁶+ζ¹⁴+ζ²²+ζ³⁸	ζ⁶−ζ¹⁴−ζ²²−ζ³⁸	ζ⁶+ζ¹⁴−ζ²²+ζ³⁸	−ζ⁶−ζ¹⁴+ζ²²−ζ³⁸	ζ⁶+ζ¹⁴+ζ²²−ζ³⁸	−ζ⁶−ζ¹⁴−ζ²²+ζ³⁸	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₄	4	4	-4	4	-4	0	0	-1	$- \sqrt{5}$	$- \sqrt{5}$	$\sqrt{5}$	$\sqrt{5}$	-1	1	1	0	0	$- \sqrt{5}$	$\sqrt{5}$	1	-1	−ζ⁴−ζ¹²+ζ²⁸+ζ³⁶	−ζ⁴−ζ¹²+ζ²⁸+ζ³⁶	ζ⁴+ζ¹²−ζ²⁸−ζ³⁶	ζ⁴+ζ¹²−ζ²⁸−ζ³⁶	ζ⁴−ζ¹²+ζ²⁸−ζ³⁶	ζ⁴−ζ¹²+ζ²⁸−ζ³⁶	−ζ⁴+ζ¹²−ζ²⁸+ζ³⁶	−ζ⁴+ζ¹²−ζ²⁸+ζ³⁶	$2 i$	$- 2 i$	−ζ⁶−ζ¹⁴−ζ²²+ζ³⁸	ζ⁶+ζ¹⁴+ζ²²−ζ³⁸	−ζ⁶−ζ¹⁴+ζ²²−ζ³⁸	ζ⁶+ζ¹⁴−ζ²²+ζ³⁸	−ζ⁶+ζ¹⁴−ζ²²−ζ³⁸	ζ⁶−ζ¹⁴+ζ²²+ζ³⁸	ζ⁶−ζ¹⁴−ζ²²−ζ³⁸	−ζ⁶+ζ¹⁴+ζ²²+ζ³⁸	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₅	4	4	-4	4	-4	0	0	-1	$- \sqrt{5}$	$- \sqrt{5}$	$\sqrt{5}$	$\sqrt{5}$	-1	1	1	0	0	$- \sqrt{5}$	$\sqrt{5}$	1	-1	−ζ⁴−ζ¹²+ζ²⁸+ζ³⁶	−ζ⁴−ζ¹²+ζ²⁸+ζ³⁶	ζ⁴+ζ¹²−ζ²⁸−ζ³⁶	ζ⁴+ζ¹²−ζ²⁸−ζ³⁶	ζ⁴−ζ¹²+ζ²⁸−ζ³⁶	ζ⁴−ζ¹²+ζ²⁸−ζ³⁶	−ζ⁴+ζ¹²−ζ²⁸+ζ³⁶	−ζ⁴+ζ¹²−ζ²⁸+ζ³⁶	$- 2 i$	$2 i$	ζ⁶+ζ¹⁴+ζ²²−ζ³⁸	−ζ⁶−ζ¹⁴−ζ²²+ζ³⁸	ζ⁶+ζ¹⁴−ζ²²+ζ³⁸	−ζ⁶−ζ¹⁴+ζ²²−ζ³⁸	ζ⁶−ζ¹⁴+ζ²²+ζ³⁸	−ζ⁶+ζ¹⁴−ζ²²−ζ³⁸	−ζ⁶+ζ¹⁴+ζ²²+ζ³⁸	ζ⁶−ζ¹⁴−ζ²²−ζ³⁸	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₆	4	4	-4	4	-4	0	0	-1	$- \sqrt{5}$	$- \sqrt{5}$	$\sqrt{5}$	$\sqrt{5}$	-1	1	1	0	0	$- \sqrt{5}$	$\sqrt{5}$	1	-1	ζ⁴+ζ¹²−ζ²⁸−ζ³⁶	ζ⁴+ζ¹²−ζ²⁸−ζ³⁶	−ζ⁴−ζ¹²+ζ²⁸+ζ³⁶	−ζ⁴−ζ¹²+ζ²⁸+ζ³⁶	−ζ⁴+ζ¹²−ζ²⁸+ζ³⁶	−ζ⁴+ζ¹²−ζ²⁸+ζ³⁶	ζ⁴−ζ¹²+ζ²⁸−ζ³⁶	ζ⁴−ζ¹²+ζ²⁸−ζ³⁶	$2 i$	$- 2 i$	−ζ⁶−ζ¹⁴+ζ²²−ζ³⁸	ζ⁶+ζ¹⁴−ζ²²+ζ³⁸	−ζ⁶−ζ¹⁴−ζ²²+ζ³⁸	ζ⁶+ζ¹⁴+ζ²²−ζ³⁸	ζ⁶−ζ¹⁴−ζ²²−ζ³⁸	−ζ⁶+ζ¹⁴+ζ²²+ζ³⁸	−ζ⁶+ζ¹⁴−ζ²²−ζ³⁸	ζ⁶−ζ¹⁴+ζ²²+ζ³⁸	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₇	4	4	-4	4	-4	0	0	-1	$- \sqrt{5}$	$- \sqrt{5}$	$\sqrt{5}$	$\sqrt{5}$	-1	1	1	0	0	$- \sqrt{5}$	$\sqrt{5}$	1	-1	ζ⁴+ζ¹²−ζ²⁸−ζ³⁶	ζ⁴+ζ¹²−ζ²⁸−ζ³⁶	−ζ⁴−ζ¹²+ζ²⁸+ζ³⁶	−ζ⁴−ζ¹²+ζ²⁸+ζ³⁶	−ζ⁴+ζ¹²−ζ²⁸+ζ³⁶	−ζ⁴+ζ¹²−ζ²⁸+ζ³⁶	ζ⁴−ζ¹²+ζ²⁸−ζ³⁶	ζ⁴−ζ¹²+ζ²⁸−ζ³⁶	$- 2 i$	$2 i$	ζ⁶+ζ¹⁴−ζ²²+ζ³⁸	−ζ⁶−ζ¹⁴+ζ²²−ζ³⁸	ζ⁶+ζ¹⁴+ζ²²−ζ³⁸	−ζ⁶−ζ¹⁴−ζ²²+ζ³⁸	−ζ⁶+ζ¹⁴+ζ²²+ζ³⁸	ζ⁶−ζ¹⁴−ζ²²−ζ³⁸	ζ⁶−ζ¹⁴+ζ²²+ζ³⁸	−ζ⁶+ζ¹⁴−ζ²²−ζ³⁸	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₈	4	4	-4	-4	4	0	0	4	0	0	0	0	4	-4	-4	0	0	0	0	4	-4	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	$2 i$	$- 2 i$	0	0	0	0	0	0	0	0
χ₃₉	4	4	-4	-4	4	0	0	4	0	0	0	0	4	-4	-4	0	0	0	0	4	-4	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	$- 2 i$	$2 i$	0	0	0	0	0	0	0	0
χ₄₀	8	8	8	-8	-8	8	-8	-2	-2	-2	-2	-2	-2	-2	-2	0	0	2	2	2	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	0	0
χ₄₁	8	8	8	-8	-8	-8	8	-2	2	2	2	2	-2	-2	-2	0	0	-2	-2	2	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	0	0
χ₄₂	8	8	-8	-8	8	0	0	-2	$2 \sqrt{5}$	$2 \sqrt{5}$	$- 2 \sqrt{5}$	$- 2 \sqrt{5}$	-2	2	2	0	0	$- 2 \sqrt{5}$	$2 \sqrt{5}$	-2	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	0	0
χ₄₃	8	8	-8	-8	8	0	0	-2	$- 2 \sqrt{5}$	$- 2 \sqrt{5}$	$2 \sqrt{5}$	$2 \sqrt{5}$	-2	2	2	0	0	$2 \sqrt{5}$	$- 2 \sqrt{5}$	-2	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	0	0
χ₄₄	8	-8	0	0	0	0	0	8	0	0	0	0	-8	0	0	$2 i \sqrt{2}$	$- 2 i \sqrt{2}$	0	0	0	0	$2 i \sqrt{2}$	$- 2 i \sqrt{2}$	$2 i \sqrt{2}$	$- 2 i \sqrt{2}$	$2 i \sqrt{2}$	$- 2 i \sqrt{2}$	$2 i \sqrt{2}$	$- 2 i \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₅	8	-8	0	0	0	0	0	8	0	0	0	0	-8	0	0	$- 2 i \sqrt{2}$	$2 i \sqrt{2}$	0	0	0	0	$- 2 i \sqrt{2}$	$2 i \sqrt{2}$	$- 2 i \sqrt{2}$	$2 i \sqrt{2}$	$- 2 i \sqrt{2}$	$2 i \sqrt{2}$	$- 2 i \sqrt{2}$	$2 i \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₆	8	-8	0	0	0	0	0	-2	−2ζ⁴+2ζ¹²−2ζ²⁸+2ζ³⁶	2ζ⁴−2ζ¹²+2ζ²⁸−2ζ³⁶	−2ζ⁴−2ζ¹²+2ζ²⁸+2ζ³⁶	2ζ⁴+2ζ¹²−2ζ²⁸−2ζ³⁶	2	$2 \sqrt{5}$	$- 2 \sqrt{5}$	$2 i \sqrt{2}$	$- 2 i \sqrt{2}$	0	0	0	0	ζ⁷+ζ¹³−ζ²¹+ζ²³+ζ²⁹−ζ³¹+ζ³⁷+ζ³⁹	−ζ⁷−ζ¹³+ζ²¹−ζ²³−ζ²⁹+ζ³¹−ζ³⁷−ζ³⁹	ζ⁷+ζ¹³+ζ²¹+ζ²³−ζ²⁹+ζ³¹+ζ³⁷−ζ³⁹	−ζ⁷−ζ¹³−ζ²¹−ζ²³+ζ²⁹−ζ³¹−ζ³⁷+ζ³⁹	ζ⁷−ζ¹³+ζ²¹−ζ²³+ζ²⁹+ζ³¹+ζ³⁷+ζ³⁹	−ζ⁷+ζ¹³−ζ²¹+ζ²³−ζ²⁹−ζ³¹−ζ³⁷−ζ³⁹	−ζ⁷+ζ¹³+ζ²¹+ζ²³+ζ²⁹+ζ³¹−ζ³⁷+ζ³⁹	ζ⁷−ζ¹³−ζ²¹−ζ²³−ζ²⁹−ζ³¹+ζ³⁷−ζ³⁹	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₇	8	-8	0	0	0	0	0	-2	−2ζ⁴+2ζ¹²−2ζ²⁸+2ζ³⁶	2ζ⁴−2ζ¹²+2ζ²⁸−2ζ³⁶	−2ζ⁴−2ζ¹²+2ζ²⁸+2ζ³⁶	2ζ⁴+2ζ¹²−2ζ²⁸−2ζ³⁶	2	$2 \sqrt{5}$	$- 2 \sqrt{5}$	$- 2 i \sqrt{2}$	$2 i \sqrt{2}$	0	0	0	0	−ζ⁷−ζ¹³+ζ²¹−ζ²³−ζ²⁹+ζ³¹−ζ³⁷−ζ³⁹	ζ⁷+ζ¹³−ζ²¹+ζ²³+ζ²⁹−ζ³¹+ζ³⁷+ζ³⁹	−ζ⁷−ζ¹³−ζ²¹−ζ²³+ζ²⁹−ζ³¹−ζ³⁷+ζ³⁹	ζ⁷+ζ¹³+ζ²¹+ζ²³−ζ²⁹+ζ³¹+ζ³⁷−ζ³⁹	−ζ⁷+ζ¹³−ζ²¹+ζ²³−ζ²⁹−ζ³¹−ζ³⁷−ζ³⁹	ζ⁷−ζ¹³+ζ²¹−ζ²³+ζ²⁹+ζ³¹+ζ³⁷+ζ³⁹	ζ⁷−ζ¹³−ζ²¹−ζ²³−ζ²⁹−ζ³¹+ζ³⁷−ζ³⁹	−ζ⁷+ζ¹³+ζ²¹+ζ²³+ζ²⁹+ζ³¹−ζ³⁷+ζ³⁹	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₈	8	-8	0	0	0	0	0	-2	−2ζ⁴−2ζ¹²+2ζ²⁸+2ζ³⁶	2ζ⁴+2ζ¹²−2ζ²⁸−2ζ³⁶	2ζ⁴−2ζ¹²+2ζ²⁸−2ζ³⁶	−2ζ⁴+2ζ¹²−2ζ²⁸+2ζ³⁶	2	$- 2 \sqrt{5}$	$2 \sqrt{5}$	$2 i \sqrt{2}$	$- 2 i \sqrt{2}$	0	0	0	0	ζ⁷−ζ¹³+ζ²¹−ζ²³+ζ²⁹+ζ³¹+ζ³⁷+ζ³⁹	−ζ⁷+ζ¹³−ζ²¹+ζ²³−ζ²⁹−ζ³¹−ζ³⁷−ζ³⁹	−ζ⁷+ζ¹³+ζ²¹+ζ²³+ζ²⁹+ζ³¹−ζ³⁷+ζ³⁹	ζ⁷−ζ¹³−ζ²¹−ζ²³−ζ²⁹−ζ³¹+ζ³⁷−ζ³⁹	ζ⁷+ζ¹³+ζ²¹+ζ²³−ζ²⁹+ζ³¹+ζ³⁷−ζ³⁹	−ζ⁷−ζ¹³−ζ²¹−ζ²³+ζ²⁹−ζ³¹−ζ³⁷+ζ³⁹	ζ⁷+ζ¹³−ζ²¹+ζ²³+ζ²⁹−ζ³¹+ζ³⁷+ζ³⁹	−ζ⁷−ζ¹³+ζ²¹−ζ²³−ζ²⁹+ζ³¹−ζ³⁷−ζ³⁹	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₉	8	-8	0	0	0	0	0	-2	−2ζ⁴−2ζ¹²+2ζ²⁸+2ζ³⁶	2ζ⁴+2ζ¹²−2ζ²⁸−2ζ³⁶	2ζ⁴−2ζ¹²+2ζ²⁸−2ζ³⁶	−2ζ⁴+2ζ¹²−2ζ²⁸+2ζ³⁶	2	$- 2 \sqrt{5}$	$2 \sqrt{5}$	$- 2 i \sqrt{2}$	$2 i \sqrt{2}$	0	0	0	0	−ζ⁷+ζ¹³−ζ²¹+ζ²³−ζ²⁹−ζ³¹−ζ³⁷−ζ³⁹	ζ⁷−ζ¹³+ζ²¹−ζ²³+ζ²⁹+ζ³¹+ζ³⁷+ζ³⁹	ζ⁷−ζ¹³−ζ²¹−ζ²³−ζ²⁹−ζ³¹+ζ³⁷−ζ³⁹	−ζ⁷+ζ¹³+ζ²¹+ζ²³+ζ²⁹+ζ³¹−ζ³⁷+ζ³⁹	−ζ⁷−ζ¹³−ζ²¹−ζ²³+ζ²⁹−ζ³¹−ζ³⁷+ζ³⁹	ζ⁷+ζ¹³+ζ²¹+ζ²³−ζ²⁹+ζ³¹+ζ³⁷−ζ³⁹	−ζ⁷−ζ¹³+ζ²¹−ζ²³−ζ²⁹+ζ³¹−ζ³⁷−ζ³⁹	ζ⁷+ζ¹³−ζ²¹+ζ²³+ζ²⁹−ζ³¹+ζ³⁷+ζ³⁹	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₅₀	8	-8	0	0	0	0	0	-2	2ζ⁴−2ζ¹²+2ζ²⁸−2ζ³⁶	−2ζ⁴+2ζ¹²−2ζ²⁸+2ζ³⁶	2ζ⁴+2ζ¹²−2ζ²⁸−2ζ³⁶	−2ζ⁴−2ζ¹²+2ζ²⁸+2ζ³⁶	2	$2 \sqrt{5}$	$- 2 \sqrt{5}$	$2 i \sqrt{2}$	$- 2 i \sqrt{2}$	0	0	0	0	ζ⁷+ζ¹³+ζ²¹+ζ²³−ζ²⁹+ζ³¹+ζ³⁷−ζ³⁹	−ζ⁷−ζ¹³−ζ²¹−ζ²³+ζ²⁹−ζ³¹−ζ³⁷+ζ³⁹	ζ⁷+ζ¹³−ζ²¹+ζ²³+ζ²⁹−ζ³¹+ζ³⁷+ζ³⁹	−ζ⁷−ζ¹³+ζ²¹−ζ²³−ζ²⁹+ζ³¹−ζ³⁷−ζ³⁹	−ζ⁷+ζ¹³+ζ²¹+ζ²³+ζ²⁹+ζ³¹−ζ³⁷+ζ³⁹	ζ⁷−ζ¹³−ζ²¹−ζ²³−ζ²⁹−ζ³¹+ζ³⁷−ζ³⁹	ζ⁷−ζ¹³+ζ²¹−ζ²³+ζ²⁹+ζ³¹+ζ³⁷+ζ³⁹	−ζ⁷+ζ¹³−ζ²¹+ζ²³−ζ²⁹−ζ³¹−ζ³⁷−ζ³⁹	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₅₁	8	-8	0	0	0	0	0	-2	2ζ⁴−2ζ¹²+2ζ²⁸−2ζ³⁶	−2ζ⁴+2ζ¹²−2ζ²⁸+2ζ³⁶	2ζ⁴+2ζ¹²−2ζ²⁸−2ζ³⁶	−2ζ⁴−2ζ¹²+2ζ²⁸+2ζ³⁶	2	$2 \sqrt{5}$	$- 2 \sqrt{5}$	$- 2 i \sqrt{2}$	$2 i \sqrt{2}$	0	0	0	0	−ζ⁷−ζ¹³−ζ²¹−ζ²³+ζ²⁹−ζ³¹−ζ³⁷+ζ³⁹	ζ⁷+ζ¹³+ζ²¹+ζ²³−ζ²⁹+ζ³¹+ζ³⁷−ζ³⁹	−ζ⁷−ζ¹³+ζ²¹−ζ²³−ζ²⁹+ζ³¹−ζ³⁷−ζ³⁹	ζ⁷+ζ¹³−ζ²¹+ζ²³+ζ²⁹−ζ³¹+ζ³⁷+ζ³⁹	ζ⁷−ζ¹³−ζ²¹−ζ²³−ζ²⁹−ζ³¹+ζ³⁷−ζ³⁹	−ζ⁷+ζ¹³+ζ²¹+ζ²³+ζ²⁹+ζ³¹−ζ³⁷+ζ³⁹	−ζ⁷+ζ¹³−ζ²¹+ζ²³−ζ²⁹−ζ³¹−ζ³⁷−ζ³⁹	ζ⁷−ζ¹³+ζ²¹−ζ²³+ζ²⁹+ζ³¹+ζ³⁷+ζ³⁹	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₅₂	8	-8	0	0	0	0	0	-2	2ζ⁴+2ζ¹²−2ζ²⁸−2ζ³⁶	−2ζ⁴−2ζ¹²+2ζ²⁸+2ζ³⁶	−2ζ⁴+2ζ¹²−2ζ²⁸+2ζ³⁶	2ζ⁴−2ζ¹²+2ζ²⁸−2ζ³⁶	2	$- 2 \sqrt{5}$	$2 \sqrt{5}$	$2 i \sqrt{2}$	$- 2 i \sqrt{2}$	0	0	0	0	−ζ⁷+ζ¹³+ζ²¹+ζ²³+ζ²⁹+ζ³¹−ζ³⁷+ζ³⁹	ζ⁷−ζ¹³−ζ²¹−ζ²³−ζ²⁹−ζ³¹+ζ³⁷−ζ³⁹	ζ⁷−ζ¹³+ζ²¹−ζ²³+ζ²⁹+ζ³¹+ζ³⁷+ζ³⁹	−ζ⁷+ζ¹³−ζ²¹+ζ²³−ζ²⁹−ζ³¹−ζ³⁷−ζ³⁹	ζ⁷+ζ¹³−ζ²¹+ζ²³+ζ²⁹−ζ³¹+ζ³⁷+ζ³⁹	−ζ⁷−ζ¹³+ζ²¹−ζ²³−ζ²⁹+ζ³¹−ζ³⁷−ζ³⁹	ζ⁷+ζ¹³+ζ²¹+ζ²³−ζ²⁹+ζ³¹+ζ³⁷−ζ³⁹	−ζ⁷−ζ¹³−ζ²¹−ζ²³+ζ²⁹−ζ³¹−ζ³⁷+ζ³⁹	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₅₃	8	-8	0	0	0	0	0	-2	2ζ⁴+2ζ¹²−2ζ²⁸−2ζ³⁶	−2ζ⁴−2ζ¹²+2ζ²⁸+2ζ³⁶	−2ζ⁴+2ζ¹²−2ζ²⁸+2ζ³⁶	2ζ⁴−2ζ¹²+2ζ²⁸−2ζ³⁶	2	$- 2 \sqrt{5}$	$2 \sqrt{5}$	$- 2 i \sqrt{2}$	$2 i \sqrt{2}$	0	0	0	0	ζ⁷−ζ¹³−ζ²¹−ζ²³−ζ²⁹−ζ³¹+ζ³⁷−ζ³⁹	−ζ⁷+ζ¹³+ζ²¹+ζ²³+ζ²⁹+ζ³¹−ζ³⁷+ζ³⁹	−ζ⁷+ζ¹³−ζ²¹+ζ²³−ζ²⁹−ζ³¹−ζ³⁷−ζ³⁹	ζ⁷−ζ¹³+ζ²¹−ζ²³+ζ²⁹+ζ³¹+ζ³⁷+ζ³⁹	−ζ⁷−ζ¹³+ζ²¹−ζ²³−ζ²⁹+ζ³¹−ζ³⁷−ζ³⁹	ζ⁷+ζ¹³−ζ²¹+ζ²³+ζ²⁹−ζ³¹+ζ³⁷+ζ³⁹	−ζ⁷−ζ¹³−ζ²¹−ζ²³+ζ²⁹−ζ³¹−ζ³⁷+ζ³⁹	ζ⁷+ζ¹³+ζ²¹+ζ²³−ζ²⁹+ζ³¹+ζ³⁷−ζ³⁹	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 #13014251