nLab character table of GL(2,3)

linear representation theory of the finite general linear group GL(2,3)

$\,$

group order: ${\vert GL(2,3)\vert} = 48$

conjugacy classes:	1	2A	2B	3	4	6	8A	8B
their cardinality:	1	1	12	8	6	8	6	6

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

irrep	1	2A	2B	3	4	6	8A	8B
$\rho_1$	1	1	1	1	1	1	1	1
$\rho_2$	1	1	-1	1	1	1	-1	-1
$\rho_3$	2	2	0	-1	2	-1	0	0
$\rho_4$	2	-2	0	-1	0	1	$-\sqrt{-2}$	$\sqrt{-2}$
$\rho_5$	2	-2	0	-1	0	1	$\sqrt{-2}$	$-\sqrt{-2}$
$\rho_6$	3	3	-1	0	-1	0	1	1
$\rho_7$	3	3	1	0	-1	0	-1	-1
$\rho_8$	4	-4	0	1	0	-1	0	0

character table over the rational numbers $\mathbb{Q}$ and real numbers $\mathbb{R}$

irrep	1	2A	2B	3	4	6	8A	8B
$\rho_1$	1	1	1	1	1	1	1	1
$\rho_2$	1	1	-1	1	1	1	-1	-1
$\rho_3$	2	2	0	-1	2	-1	0	0
$\rho_4 \oplus \rho_5$	4	-4	0	-2	0	2	0	0
$\rho_6$	3	3	-1	0	-1	0	1	1
$\rho_7$	3	3	1	0	-1	0	-1	-1
$\rho_8$	4	-4	0	1	0	-1	0	0

References

• GroupNames, GL(2,3)

category: character tables