Finite Group Databasebeta

← Group #113286

Character table — Group #113286

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111222222222222224444444488888888888888881616161616161616161616161616161616161616
order12222244444444444422444444888888888888888822244444888888888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-111-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111-1-11-1-1-1-1-1-1-1-11111
χ511111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-111-1-1-1-1-1-1-1-1-11111
χ611111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1111-1-11-1-1-1-11111-1-1-1-1
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ91111-1-1-1-11111-1-1-1-1-1-11-11111-1-1iiii−i−i−i−iiiii−i−i−i−i1-111-11-1-111-1-1ii−i−iii−i−i
χ101111-1-1-1-11111-1-1-1-1-1-11-11111-1-1iiii−i−i−i−iiiii−i−i−i−i-11-1-11-11111-1-1−i−iii−i−iii
χ111111-1-1-1-11111-1-1-1-1-1-11-11111-1-1iiii−i−i−i−i−i−i−i−iiiii1-1-1-111-11-1-111ii−i−i−i−iii
χ121111-1-1-1-11111-1-1-1-1-1-11-11111-1-1iiii−i−i−i−i−i−i−i−iiiii-1111-1-11-1-1-111−i−iiiii−i−i
χ131111-1-1-1-11111-1-1-1-1-1-11-11111-1-1−i−i−i−iiiiiiiii−i−i−i−i1-1-1-111-11-1-111−i−iiiii−i−i
χ141111-1-1-1-11111-1-1-1-1-1-11-11111-1-1−i−i−i−iiiiiiiii−i−i−i−i-1111-1-11-1-1-111ii−i−i−i−iii
χ151111-1-1-1-11111-1-1-1-1-1-11-11111-1-1−i−i−i−iiiii−i−i−i−iiiii1-111-11-1-111-1-1−i−iii−i−iii
χ161111-1-1-1-11111-1-1-1-1-1-11-11111-1-1−i−i−i−iiiii−i−i−i−iiiii-11-1-11-11111-1-1ii−i−iii−i−i
χ172222222222-2-2-2-2-2-2-2-2-2-222-2-22200000000000000000000000000002i−2i2i−2i0000
χ182222222222-2-2-2-2-2-2-2-2-2-222-2-2220000000000000000000000000000−2i2i−2i2i0000
χ1922222222-2-22222-2-222-2-22-2-22-2-200000000000000002-2000-220000000000000
χ2022222222-2-22222-2-222-2-22-2-22-2-20000000000000000-220002-20000000000000
χ2122222222-2-2-2-2-2-222-2-2222-22-2-2-22i2i−2i−2i2i2i−2i−2i0000000000000000000000000000
χ2222222222-2-2-2-2-2-222-2-2222-22-2-2-2−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000
χ23222222-2-222222222-2-2-2-2-2-22-22-20000000000000000000000002-22-200000000
χ24222222-2-222222222-2-2-2-2-2-22-22-2000000000000000000000000-22-2200000000
χ25222222-2-222-2-2-2-2-2-22222-2-2-222-2000000000000000000000000000000002i−2i2i−2i
χ26222222-2-222-2-2-2-2-2-22222-2-2-222-200000000000000000000000000000000−2i2i−2i2i
χ27222222-2-2-2-22222-2-2-2-222-22-2-2-220000000000000000002-2-2002000000000000
χ28222222-2-2-2-22222-2-2-2-222-22-2-2-22000000000000000000-22200-2000000000000
χ29222222-2-2-2-2-2-2-2-22222-2-2-2222-220000000022-2-222-2-200000000000000000000
χ30222222-2-2-2-2-2-2-2-22222-2-2-2222-2200000000-2-222-2-22200000000000000000000
χ312222-2-2222222-2-2-2-222-22-2-22-2-220000000000000000000000002-2-2200000000
χ322222-2-2222222-2-2-2-222-22-2-22-2-22000000000000000000000000-222-200000000
χ332222-2-22222-2-22222-2-22-2-2-2-22-22000000000000000000000000000000002-2-22
χ342222-2-22222-2-22222-2-22-2-2-2-22-2200000000000000000000000000000000-222-2
χ352222-2-222-2-222-2-222222-2-22-2-22-20000000000000000002-2200-2000000000000
χ362222-2-222-2-222-2-222222-2-22-2-22-2000000000000000000-22-2002000000000000
χ372222-2-222-2-2-2-222-2-2-2-2-22-22222-2000000002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ382222-2-222-2-2-2-222-2-2-2-2-22-22222-200000000−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ392222-2-2-2-222-2-2222222-2222-2-2-2-200000000000000000000000000002-2-220000
χ402222-2-2-2-222-2-2222222-2222-2-2-2-20000000000000000000000000000-222-20000
χ412222-2-2-2-2-2-222-2-222-2-2-222-2-2222000000000000000022000-2-20000000000000
χ422222-2-2-2-2-2-222-2-222-2-2-222-2-22220000000000000000-2-2000220000000000000
χ432222-2-2-2-2-2-2-2-222-2-2222-22-22-22222-2-2-2-2220000000000000000000000000000
χ442222-2-2-2-2-2-2-2-222-2-2222-22-22-222-2-22222-2-20000000000000000000000000000
χ4544-4-400004i−4i004i−4i4-400000000002ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ30000000000000000000000000000
χ4644-4-400004i−4i004i−4i4-40000000000−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ30000000000000000000000000000
χ4744-4-400004i−4i00−4i4i-4400000000002ζ3−2ζ3−2ζ2ζ−2ζ32ζ32ζ−2ζ0000000000000000000000000000
χ4844-4-400004i−4i00−4i4i-440000000000−2ζ32ζ32ζ−2ζ2ζ3−2ζ3−2ζ2ζ0000000000000000000000000000
χ4944-4-40000−4i4i004i−4i-4400000000002ζ−2ζ−2ζ32ζ3−2ζ2ζ2ζ3−2ζ30000000000000000000000000000
χ5044-4-40000−4i4i004i−4i-440000000000−2ζ2ζ2ζ3−2ζ32ζ−2ζ−2ζ32ζ30000000000000000000000000000
χ5144-4-40000−4i4i00−4i4i4-400000000002ζ3−2ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ0000000000000000000000000000
χ5244-4-40000−4i4i00−4i4i4-40000000000−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ0000000000000000000000000000
χ534-44-4004i−4i004-400004i−4i00000000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ300000000000000000000
χ544-44-4004i−4i004-400004i−4i0000000000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ300000000000000000000
χ554-44-4004i−4i00-440000−4i4i00000000000000002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ00000000000000000000
χ564-44-4004i−4i00-440000−4i4i0000000000000000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ00000000000000000000
χ574-44-400−4i4i004-40000−4i4i00000000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ00000000000000000000
χ584-44-400−4i4i004-40000−4i4i0000000000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ00000000000000000000
χ594-44-400−4i4i00-4400004i−4i00000000000000002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ300000000000000000000
χ604-44-400−4i4i00-4400004i−4i0000000000000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ300000000000000000000
χ618-8-888-800000000000000000000000000000000000000000000000000000000
χ628-8-88-8800000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.