Finite Group Databasebeta

← Group #3689

Character table — Group #3689

Order 144.

	C₁	C₂	C₃	C₄	C₅	C₆	C₇	C₈	C₉	C₁₀	C₁₁	C₁₂	C₁₃	C₁₄	C₁₅
size	1	1	2	2	6	8	8	8	8	8	8	12	18	18	36
order	1	2	3	6	4	9	9	9	18	18	18	12	8	8	2
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	2	2	2	2	2	-1	-1	-1	-1	-1	-1	2	0	0	0
χ₄	2	2	-1	-1	2	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	-1	0	0	0
χ₅	2	2	-1	-1	2	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	-1	0	0	0
χ₆	2	2	-1	-1	2	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	-1	0	0	0
χ₇	2	-2	2	-2	0	-1	-1	-1	1	1	1	0	$- i \sqrt{2}$	$i \sqrt{2}$	0
χ₈	2	-2	2	-2	0	-1	-1	-1	1	1	1	0	$i \sqrt{2}$	$- i \sqrt{2}$	0
χ₉	3	3	3	3	-1	0	0	0	0	0	0	-1	1	1	-1
χ₁₀	3	3	3	3	-1	0	0	0	0	0	0	-1	-1	-1	1
χ₁₁	4	-4	4	-4	0	1	1	1	-1	-1	-1	0	0	0	0
χ₁₂	4	-4	-2	2	0	−ζ⁴⁴+ζ⁵²−ζ⁶⁸	−ζ⁴+ζ⁴⁴−ζ⁵²	ζ⁴+ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	0	0	0	0
χ₁₃	4	-4	-2	2	0	ζ⁴+ζ⁶⁸	−ζ⁴⁴+ζ⁵²−ζ⁶⁸	−ζ⁴+ζ⁴⁴−ζ⁵²	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	0	0	0	0
χ₁₄	4	-4	-2	2	0	−ζ⁴+ζ⁴⁴−ζ⁵²	ζ⁴+ζ⁶⁸	−ζ⁴⁴+ζ⁵²−ζ⁶⁸	ζ⁴−ζ⁴⁴+ζ⁵²	−ζ⁴−ζ⁶⁸	ζ⁴⁴−ζ⁵²+ζ⁶⁸	0	0	0	0
χ₁₅	6	6	-3	-3	-2	0	0	0	0	0	0	1	0	0	0

Here ζ is a primitive root of unity of order 72 (ζ⁷² = 1); i = ζ¹⁸.