Finite Group Databasebeta

← Group #240804

Character table — Group #240804

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111222222222222224444444488888888888888881616161616161616161616161616161616161616
order12222222444444444424444444444444448888888822444444888888888888
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-1-1-11111-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-11111-1-1
χ91111-1-1111-1-1-1-111111-1-1-111-1-111111-1-1-1-11111-1-1-1-1111-1-1-11-111-1-11-111-1-11-1
χ101111-1-1111-1-1-1-111111-1-1-111-1-111111-1-1-1-11111-1-1-1-111-11-1-1-11-1-111-11-1-111-11
χ111111-1-1111-1-1-1-111111-1-1-111-1-111111-1-1-1-1-1-1-1-11111-1-11-1111-111-1-1-11-1-111-11
χ121111-1-1111-1-1-1-111111-1-1-111-1-111111-1-1-1-1-1-1-1-11111-1-1-1111-11-1-1111-111-1-11-1
χ131111-1-1111-1-1-1-111111-1-1-111-1-11-1-1-1-111111111-1-1-1-1-1-11-1111-1-1-111-1111-1-1-11
χ141111-1-1111-1-1-1-111111-1-1-111-1-11-1-1-1-111111111-1-1-1-1-1-1-1111-1111-1-11-1-1-1111-1
χ151111-1-1111-1-1-1-111111-1-1-111-1-11-1-1-1-11111-1-1-1-11111111-1-1-11-1-1-1111-1-1-1111-1
χ161111-1-1111-1-1-1-111111-1-1-111-1-11-1-1-1-11111-1-1-1-1111111-11-1-1-1111-1-1-1111-1-1-11
χ17222222222-2-2-2-222-22-2222-2-2-2-2-20000000000000000000000002-22-200000000
χ18222222222-2-2-2-222-22-2222-2-2-2-2-2000000000000000000000000-22-2200000000
χ1922222222-22222-2-22-222-2-2-2-2-2-2200000000000000002-2002-200000000000000
χ2022222222-22222-2-22-222-2-2-2-2-2-220000000000000000-2200-2200000000000000
χ2122222222-2-2-2-2-2-2-2-2-2-22-2-22222-20000000000000000000000000000002i−2i2i−2i00
χ2222222222-2-2-2-2-2-2-2-2-2-22-2-22222-2000000000000000000000000000000−2i2i−2i2i00
χ23222222-2-2222-2-2-2-2222-22-22-22-2-20000000000000000002200-2-2000000000000
χ24222222-2-2222-2-2-2-2222-22-22-22-2-2000000000000000000-2-20022000000000000
χ25222222-2-22-2-222-2-2-22-2-22-2-22-2222i2i−2i−2i2i2i−2i−2i0000000000000000000000000000
χ26222222-2-22-2-222-2-2-22-2-22-2-22-222−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000
χ27222222-2-2-222-2-2222-22-2-22-22-22-20000000000000000000000000000220000-2-2
χ28222222-2-2-222-2-2222-22-2-22-22-22-20000000000000000000000000000-2-2000022
χ29222222-2-2-2-2-22222-2-2-2-2-222-22-22000000002i2i−2i−2i2i2i−2i−2i00000000000000000000
χ30222222-2-2-2-2-22222-2-2-2-2-222-22-2200000000−2i−2i2i2i−2i−2i2i2i00000000000000000000
χ312222-2-2222222222-22-2-2-2-2-2-222-20000000000000000000000002-2-2200000000
χ322222-2-2222222222-22-2-2-2-2-2-222-2000000000000000000000000-222-200000000
χ332222-2-222-22222-2-2-2-2-2-22222-2-2-20000000000000000000000000000002i−2i−2i2i00
χ342222-2-222-22222-2-2-2-2-2-22222-2-2-2000000000000000000000000000000−2i2i2i−2i00
χ352222-2-222-2-2-2-2-2-2-22-22-222-2-222200000000000000002-200-2200000000000000
χ362222-2-222-2-2-2-2-2-2-22-22-222-2-22220000000000000000-22002-200000000000000
χ372222-2-2-2-2222-2-2-2-2-22-22-22-222-222i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ382222-2-2-2-2222-2-2-2-2-22-22-22-222-22−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ392222-2-2-2-22-2-222-2-22222-222-2-22-20000000000000000002-200-22000000000000
χ402222-2-2-2-22-2-222-2-22222-222-2-22-2000000000000000000-22002-2000000000000
χ412222-2-2-2-2-222-2-222-2-2-222-22-2-222000000002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ422222-2-2-2-2-222-2-222-2-2-222-22-2-22200000000−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ432222-2-2-2-2-2-2-222222-2222-2-222-2-200000000000000000000000000002-20000-22
χ442222-2-2-2-2-2-2-222222-2222-2-222-2-20000000000000000000000000000-2200002-2
χ4544-4-4004-4400004-40-40000000000000000022−2222−22000000000000000000000000
χ4644-4-4004-4400004-40-400000000000000000−2222−2222000000000000000000000000
χ4744-4-4004-4-40000-44040000000000000000000002i2−2i22i2−2i200000000000000000000
χ4844-4-4004-4-40000-4404000000000000000000000−2i22i2−2i22i200000000000000000000
χ4944-4-400-4440000-440-400000000000000000000022−22−222200000000000000000000
χ5044-4-400-4440000-440-4000000000000000000000−222222−2200000000000000000000
χ5144-4-400-44-400004-404000000000000000002i2−2i2−2i22i2000000000000000000000000
χ5244-4-400-44-400004-40400000000000000000−2i22i22i2−2i2000000000000000000000000
χ534-4-444-40004-4000040-4000000002i−2i2i−2i2i−2i2i−2i0000000000000000000000000000
χ544-4-444-40004-4000040-400000000−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000
χ554-4-444-4000-440000-404000000002-2-222-2-220000000000000000000000000000
χ564-4-444-4000-440000-40400000000-222-2-222-20000000000000000000000000000
χ574-4-44-440004-40000-404000000002-2-22-222-20000000000000000000000000000
χ584-4-44-440004-40000-40400000000-222-22-2-220000000000000000000000000000
χ594-4-44-44000-44000040-4000000002i−2i2i−2i−2i2i−2i2i0000000000000000000000000000
χ604-4-44-44000-44000040-400000000−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000
χ618-88-800000008i−8i0000000000000000000000000000000000000000000000000
χ628-88-80000000−8i8i0000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).