Finite Group Databasebeta

← Group #238043

Character table — Group #238043

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111222222222222224444444488888888888888881616161616161616161616161616161616161616
order12222222222244444422244444222244444444444444444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ511111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ91111-1-1-1-1-1-111-1-111111-1111-1-1-111-1-111-1-11111-1-1-1-111-1-111-1-111-1-111-1-111-1-1
χ101111-1-1-1-1-1-111-1-111111-1111-1-1-111-1-111-1-11111-1-1-1-1-1-111-1-111-1-11111-1-1-1-111
χ111111-1-1-1-1-1-111-1-111111-1111-1-1-111-1-111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-111
χ121111-1-1-1-1-1-111-1-111111-1111-1-1-111-1-111-1-1-1-1-1-11111-1-11111-1-1-1-111-1-11111-1-1
χ131111-1-1-1-1-1-111-1-111111-1111-1-1-1-1-111-1-1111111-1-1-1-111-1-111-1-1-1-111-1-111-1-111
χ141111-1-1-1-1-1-111-1-111111-1111-1-1-1-1-111-1-1111111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1
χ151111-1-1-1-1-1-111-1-111111-1111-1-1-1-1-111-1-111-1-1-1-1111111-1-1-1-111-1-11111-1-111-1-1
χ161111-1-1-1-1-1-111-1-111111-1111-1-1-1-1-111-1-111-1-1-1-11111-1-11111-1-111-1-111-1-1-1-111
χ17222222222222-2-2-2-2-2-2222-2-2-2-2-200000000000000002-22-20000000000000000
χ18222222222222-2-2-2-2-2-2222-2-2-2-2-20000000000000000-22-220000000000000000
χ1922222222-2-2222222-2-2-2-2-22-22-2-20000000022-2-222-2-200000000000000000000
χ2022222222-2-2222222-2-2-2-2-22-22-2-200000000-2-222-2-22200000000000000000000
χ2122222222-2-222-2-2-2-222-2-2-2-22-222000000000000000000002-22-2000000000000
χ2222222222-2-222-2-2-2-222-2-2-2-22-22200000000000000000000-22-22000000000000
χ23222222-2-222-2-22222222-2-2-2-2-22-20000000000000000000000002i−2i2i−2i00000000
χ24222222-2-222-2-22222222-2-2-2-2-22-2000000000000000000000000−2i2i−2i2i00000000
χ25222222-2-222-2-2-2-2-2-2-2-22-2-2222-222222-2-2-2-20000000000000000000000000000
χ26222222-2-222-2-2-2-2-2-2-2-22-2-2222-22-2-2-2-222220000000000000000000000000000
χ27222222-2-2-2-2-2-22222-2-2-222-22-2-22000000000000000000000000000000002i−2i2i−2i
χ28222222-2-2-2-2-2-22222-2-2-222-22-2-2200000000000000000000000000000000−2i2i−2i2i
χ29222222-2-2-2-2-2-2-2-2-2-222-2222-222-200000000000000000000000000002i−2i2i−2i0000
χ30222222-2-2-2-2-2-2-2-2-2-222-2222-222-20000000000000000000000000000−2i2i−2i2i0000
χ312222-2-22222-2-222-2-222-2-222-2-2-2200000000000000000000000000002i−2i−2i2i0000
χ322222-2-22222-2-222-2-222-2-222-2-2-220000000000000000000000000000−2i2i2i−2i0000
χ332222-2-22222-2-2-2-222-2-2-2-22-2222-2000000000000000000000000000000002i−2i−2i2i
χ342222-2-22222-2-2-2-222-2-2-2-22-2222-200000000000000000000000000000000−2i2i2i−2i
χ352222-2-222-2-2-2-222-2-2-2-222-222-22-222-2-2-2-2220000000000000000000000000000
χ362222-2-222-2-2-2-222-2-2-2-222-222-22-2-2-22222-2-20000000000000000000000000000
χ372222-2-222-2-2-2-2-2-2222222-2-2-22-220000000000000000000000002i−2i−2i2i00000000
χ382222-2-222-2-2-2-2-2-2222222-2-2-22-22000000000000000000000000−2i2i2i−2i00000000
χ392222-2-2-2-2222222-2-222-22-2-222-2-2000000000000000000002-2-22000000000000
χ402222-2-2-2-2222222-2-222-22-2-222-2-200000000000000000000-222-2000000000000
χ412222-2-2-2-22222-2-222-2-2-22-22-2-2220000000022-2-2-2-22200000000000000000000
χ422222-2-2-2-22222-2-222-2-2-22-22-2-22200000000-2-22222-2-200000000000000000000
χ432222-2-2-2-2-2-22222-2-2-2-22-22-2-222200000000000000002-2-220000000000000000
χ442222-2-2-2-2-2-22222-2-2-2-22-22-2-22220000000000000000-222-20000000000000000
χ4544-4-400004-4004i−4i004i−4i00000000000000002-22i−2i2i−2i2-200000000000000000000
χ4644-4-400004-4004i−4i004i−4i0000000000000000-22−2i2i−2i2i-2200000000000000000000
χ4744-4-400004-400−4i4i00−4i4i00000000000000002-2−2i2i−2i2i2-200000000000000000000
χ4844-4-400004-400−4i4i00−4i4i0000000000000000-222i−2i2i−2i-2200000000000000000000
χ4944-4-40000-44004i−4i00−4i4i00000000000000002-2−2i2i2i−2i-2200000000000000000000
χ5044-4-40000-44004i−4i00−4i4i0000000000000000-222i−2i−2i2i2-200000000000000000000
χ5144-4-40000-4400−4i4i004i−4i00000000000000002-22i−2i−2i2i-2200000000000000000000
χ5244-4-40000-4400−4i4i004i−4i0000000000000000-22−2i2i2i−2i2-200000000000000000000
χ534-4-444-44-4004-4000000000000002-22-22-22-20000000000000000000000000000
χ544-4-444-44-4004-400000000000000-22-22-22-220000000000000000000000000000
χ554-4-444-4-4400-44000000000000002-22-2-22-220000000000000000000000000000
χ564-4-444-4-4400-4400000000000000-22-222-22-20000000000000000000000000000
χ574-4-44-444-400-44000000000000002-2-22-222-20000000000000000000000000000
χ584-4-44-444-400-4400000000000000-222-22-2-220000000000000000000000000000
χ594-4-44-44-44004-4000000000000002-2-222-2-220000000000000000000000000000
χ604-4-44-44-44004-400000000000000-222-2-222-20000000000000000000000000000
χ618-88-800000000008i−8i0000000000000000000000000000000000000000000000
χ628-88-80000000000−8i8i0000000000000000000000000000000000000000000000

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