Finite Group Databasebeta

← Group #368798

Character table — Group #368798

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size1111111122222222222222224444444444444444444444888888888888888888888888888888881616161616161616
order12222222222222224444444422224444444444888888882444444444448888888888888888888844448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111-1-1-1-1-1-11111-1-111111111-1-1-111111111-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111
χ711111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ811111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1
χ91111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1iiii−i−i−i−i11-11111-1-1-1-1-1ii−i−iiiii−i−i−i−iii−i−iii−i−i1-11-1ii−i−i
χ101111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1iiii−i−i−i−i11-1-1-1-1-11111-1ii−i−i−i−i−i−iiiiiii−i−iii−i−i-11-11−i−iii
χ111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1−i−i−i−iiiii11-11111-1-1-1-1-1−i−iii−i−i−i−iiiii−i−iii−i−iii1-11-1−i−iii
χ121111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1−i−i−i−iiiii11-1-1-1-1-11111-1−i−iiiiiii−i−i−i−i−i−iii−i−iii-11-11ii−i−i
χ131111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111iiii−i−i−i−i-1-111111-1-1-1-11−i−iiiiiii−i−i−i−iii−i−i−i−iii-11-11−i−iii
χ141111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111iiii−i−i−i−i-1-11-1-1-1-111111−i−iii−i−i−i−iiiiiii−i−i−i−iii1-11-1ii−i−i
χ151111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111−i−i−i−iiiii-1-111111-1-1-1-11ii−i−i−i−i−i−iiiii−i−iiiii−i−i-11-11ii−i−i
χ161111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111−i−i−i−iiiii-1-11-1-1-1-111111ii−i−iiiii−i−i−i−i−i−iiiii−i−i1-11-1−i−iii
χ17111111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-111111111111-1-111-1-111-1-11-1-1-1-111-1-111-1-1-1-1-1-1111111-1-11-11-1
χ18111111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-111111111111-1-1-1-111-1-1111-1-1-1-1-1-111-1-111-1-1-1-11111-1-111-11-11
χ19111111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-111-1-111-1-111111-1-111-1-1111111-1-1-1-111-1-1-11-11
χ20111111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-111-1-1111111111-1-111-1-11111-1-1-1-1-1-1111-11-1
χ21111111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111111111-11111-1-111-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-11-11
χ22111111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111111111-111-1-111-1-111-11111-1-111-1-111-1-1-1-1-1-1-1-111-1-11-11-1
χ23111111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-111-1-11111111111-1-1111-11-1
χ24111111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-1-111-1-111-1-11111111111-1-1-11-11
χ25111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1iiii−i−i−i−i1-1111-1-1-1-111-1−i−iiiii−i−i−i−iii−i−iiiii−i−i1-1-11i−i−ii
χ26111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1iiii−i−i−i−i1-11-1-11111-1-1-1−i−iii−i−iiiii−i−i−i−iiiii−i−i-111-1−iii−i
χ27111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1−i−i−i−iiiii1-1111-1-1-1-111-1ii−i−i−i−iiiii−i−iii−i−i−i−iii1-1-11−iii−i
χ28111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1−i−i−i−iiiii1-11-1-11111-1-1-1ii−i−iii−i−i−i−iiiii−i−i−i−iii-111-1i−i−ii
χ29111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111iiii−i−i−i−i-11-111-1-1-1-1111ii−i−iii−i−i−i−iii−i−iii−i−iii-111-1−iii−i
χ30111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111iiii−i−i−i−i-11-1-1-11111-1-11ii−i−i−i−iiiii−i−i−i−iii−i−iii1-1-11i−i−ii
χ31111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111−i−i−i−iiiii-11-111-1-1-1-1111−i−iii−i−iiiii−i−iii−i−iii−i−i-111-1i−i−ii
χ32111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111−i−i−i−iiiii-11-1-1-11111-1-11−i−iiiii−i−i−i−iiiii−i−iii−i−i1-1-11−iii−i
χ3322222222-2-2-2-2222222-22-2-2-22-2-222222222-2-22200000000-2-2-200000000-20000000000000000000000000000
χ3422222222-2-2-2-2222222-22-2-2-22-2-2-2-2-2-2-2-222-2-2-2-2000000002220000000020000000000000000000000000000
χ3522222222-2-2-2-22222-2-22-2222-2-2-22222-2-2-2-222-2-200000000-2-220000000020000000000000000000000000000
χ3622222222-2-2-2-22222-2-22-2222-2-2-2-2-2-2-222-2-222220000000022-200000000-20000000000000000000000000000
χ3722222222-2-2-2-2-2-2-2-222-22-2-2-222222-2-2-2-2-2-2222200000000-22200000000-20000000000000000000000000000
χ3822222222-2-2-2-2-2-2-2-222-22-2-2-2222-2-22222-2-222-2-2000000002-2-20000000020000000000000000000000000000
χ3922222222-2-2-2-2-2-2-2-2-2-22-2222-22222-2-22222-2-2-2-200000000-22-20000000020000000000000000000000000000
χ4022222222-2-2-2-2-2-2-2-2-2-22-2222-222-2-222-2-222-2-222000000002-2200000000-20000000000000000000000000000
χ41222-2-2-2-2222-2-200002-22-22-2-220000000000000022-2-222-2-20002i−2i002i−2i00000002i−2i002i−2i000000000000000000
χ42222-2-2-2-2222-2-200002-22-22-2-220000000000000022-2-222-2-2000−2i2i00−2i2i0000000−2i2i00−2i2i000000000000000000
χ43222-2-2-2-2222-2-200002-22-22-2-2200000000000000-2-222-2-2220002i−2i002i−2i0000000−2i2i00−2i2i000000000000000000
χ44222-2-2-2-2222-2-200002-22-22-2-2200000000000000-2-222-2-222000−2i2i00−2i2i00000002i−2i002i−2i000000000000000000
χ45222-2-2-2-2222-2-20000-22-22-222-2000000000000002i2i−2i−2i−2i−2i2i2i0002i−2i00−2i2i0000000-22002-2000000000000000000
χ46222-2-2-2-2222-2-20000-22-22-222-2000000000000002i2i−2i−2i−2i−2i2i2i000−2i2i002i−2i00000002-200-22000000000000000000
χ47222-2-2-2-2222-2-20000-22-22-222-200000000000000−2i−2i2i2i2i2i−2i−2i0002i−2i00−2i2i00000002-200-22000000000000000000
χ48222-2-2-2-2222-2-20000-22-22-222-200000000000000−2i−2i2i2i2i2i−2i−2i000−2i2i002i−2i0000000-22002-2000000000000000000
χ492-2-22-2-2222-22-200002-222-22-2-2000000000000002i−2i2i−2i2i−2i2i−2i000002-2002-200000002i−2i002i−2i0000000000000000
χ502-2-22-2-2222-22-200002-222-22-2-2000000000000002i−2i2i−2i2i−2i2i−2i00000-2200-220000000−2i2i00−2i2i0000000000000000
χ512-2-22-2-2222-22-200002-222-22-2-200000000000000−2i2i−2i2i−2i2i−2i2i000002-2002-20000000−2i2i00−2i2i0000000000000000
χ522-2-22-2-2222-22-200002-222-22-2-200000000000000−2i2i−2i2i−2i2i−2i2i00000-2200-2200000002i−2i002i−2i0000000000000000
χ532-2-22-2-2222-22-20000-22-2-22-222000000000000002-22-2-22-22000002-200-2200000002-200-220000000000000000
χ542-2-22-2-2222-22-20000-22-2-22-222000000000000002-22-2-22-2200000-22002-20000000-22002-20000000000000000
χ552-2-22-2-2222-22-20000-22-2-22-22200000000000000-22-222-22-2000002-200-220000000-22002-20000000000000000
χ562-2-22-2-2222-22-20000-22-2-22-22200000000000000-22-222-22-200000-22002-200000002-200-220000000000000000
χ572-2-2-222-222-2-2222-2-2222-2-2-22-22-20000002-22-2002i−2i−2i2i2i−2i−2i2i0000000000000000000000002i−2i2i−2i000000000000
χ582-2-2-222-222-2-2222-2-2222-2-2-22-22-20000002-22-200−2i2i2i−2i−2i2i2i−2i000000000000000000000000−2i2i−2i2i000000000000
χ592-2-2-222-222-2-2222-2-2-2-2-2222-222-2000000-22-22002-2-22-222-20000000000000000000000002-2-22000000000000
χ602-2-2-222-222-2-2222-2-2-2-2-2222-222-2000000-22-2200-222-22-2-22000000000000000000000000-222-2000000000000
χ612-2-2-222-222-2-22-2-222222-2-2-22-2-22000000-22-22002i−2i−2i2i2i−2i−2i2i000000000000000000000000−2i2i−2i2i000000000000
χ622-2-2-222-222-2-22-2-222222-2-2-22-2-22000000-22-2200−2i2i2i−2i−2i2i2i−2i0000000000000000000000002i−2i2i−2i000000000000
χ632-2-2-222-222-2-22-2-222-2-2-2222-22-220000002-22-2002-2-22-222-2000000000000000000000000-222-2000000000000
χ642-2-2-222-222-2-22-2-222-2-2-2222-22-220000002-22-200-222-22-2-220000000000000000000000002-2-22000000000000
χ652-2-2-222-22-222-222-2-222-2-222-2-2-220000002-2-2200000000000000000000002i−2i2i−2i0000000000002i−2i2i−2i00000000
χ662-2-2-222-22-222-222-2-222-2-222-2-2-220000002-2-220000000000000000000000−2i2i−2i2i000000000000−2i2i−2i2i00000000
χ672-2-2-222-22-222-222-2-2-2-222-2-222-22000000-222-200000000000000000000002-2-220000000000002-2-2200000000
χ682-2-2-222-22-222-222-2-2-2-222-2-222-22000000-222-20000000000000000000000-222-2000000000000-222-200000000
χ692-2-2-222-22-222-2-2-22222-2-222-2-22-2000000-222-200000000000000000000002i−2i2i−2i000000000000−2i2i−2i2i00000000
χ702-2-2-222-22-222-2-2-22222-2-222-2-22-2000000-222-20000000000000000000000−2i2i−2i2i0000000000002i−2i2i−2i00000000
χ712-2-2-222-22-222-2-2-222-2-222-2-2222-20000002-2-2200000000000000000000002-2-22000000000000-222-200000000
χ722-2-2-222-22-222-2-2-222-2-222-2-2222-20000002-2-220000000000000000000000-222-20000000000002-2-2200000000
χ73444-4-4-4-44-4-44400004-4-4-4-444400000000000000000000000000000000000000000000000000000000000000
χ74444-4-4-4-44-4-4440000-44444-4-4-400000000000000000000000000000000000000000000000000000000000000
χ7544-444-4-4-400004-44-400000000004-44-400000000000000000000000000000000000000000000000000000000
χ7644-444-4-4-400004-44-40000000000-44-4400000000000000000000000000000000000000000000000000000000
χ7744-444-4-4-40000-44-4400000000004-4-4400000000000000000000000000000000000000000000000000000000
χ7844-444-4-4-40000-44-440000000000-444-400000000000000000000000000000000000000000000000000000000
χ794-44-44-44-400004-4-44000000000000004i−4i00004i−4i000000000000000000000000000000000000000000000000
χ804-44-44-44-400004-4-4400000000000000−4i4i0000−4i4i000000000000000000000000000000000000000000000000
χ814-44-44-44-40000-444-4000000000000004i−4i0000−4i4i000000000000000000000000000000000000000000000000
χ824-44-44-44-40000-444-400000000000000−4i4i00004i−4i000000000000000000000000000000000000000000000000
χ834-4-44-4-444-44-4400004-4-444-44-400000000000000000000000000000000000000000000000000000000000000
χ844-4-44-4-444-44-440000-444-4-44-4400000000000000000000000000000000000000000000000000000000000000
χ8588-8-8-888-8000000000000000000000000000000000000000000000000000000000000000000000000000000
χ868-888-88-8-8000000000000000000000000000000000000000000000000000000000000000000000000000000

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