nLab character table of 2I

linear representation theory of binary icosahedral group $2 I$

$\,$

group order: ${\vert 2I\vert} = 120$

conjugacy classes:	1	2	3	4	5A	5B	6	10A	10B
their cardinality:	1	1	20	30	12	12	20	12	12

let $\phi \coloneqq \tfrac{1}{2}( 1 + \sqrt{5} )$ (the golden ratio)

character table over the complex numbers $\mathbb{C}$

irrep	1	2	3	4	5A	5B	6	10A	10B
$\rho_1$	1	1	1	1	1	1	1	1	1
$\rho_2$	2	-2	-1	0	$\phi - 1$	$-\phi$	1	$\phi$	$1 - \phi$
$\rho_3$	2	-2	-1	0	$-\phi$	$\phi - 1$	1	$1-\phi$	$\phi$
$\rho_4$	3	3	0	-1	$1 - \phi$	$\phi$	0	$\phi$	$1-\phi$
$\rho_5$	3	3	0	-1	$\phi$	$1-\phi$	0	$1-\phi$	$\phi$
$\rho_6$	4	4	1	0	-1	-1	1	-1	-1
$\rho_7$	4	-4	1	0	-1	-1	-1	1	1
$\rho_8$	5	5	-1	1	0	0	-1	0	0
$\rho_9$	6	-6	0	0	1	1	0	-1	-1

References

• GroupNames, SL(2,5)

• Bockland, Character tables and McKay quivers (pdf)

category: character tables