Finite Group Databasebeta

← Group #271087

Character table — Group #271087

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444488888888888888888888888888161616161616161616163232
order12222222444444442222224444444444444444448888888888888888244444888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ311111111111111111111111111111111-1-11111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111-1-1-1-11-1-1-1-111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1111-1-111-1-11-1
χ611111111111111111111-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1111-1-1-1-111-11
χ711111111111111111111-1-1-1-11-1-1-1-1111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-11-1-1-111-1-111-11
χ811111111111111111111-1-1-1-11-1-1-1-1111-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111-1-1-11111-1-11-1
χ91111111111111111-1-1-1-11111111111-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111
χ101111111111111111-1-1-1-11111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1
χ111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1
χ121111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-111
χ131111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1111111-1-11111-1-1-1-1-1-1-1-11111-11-1-111-1-1111-1
χ141111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1111111-1-1-1-1-1-111111111-1-1-1-1-11-1-11111-1-1-11
χ151111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-11111111111-1-1-1-1-1-1-1-111111-111-1-111-1-1-11
χ161111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1111111-1-1-1-111111111-1-1-1-11-111-1-1-1-1111-1
χ1722222222222-2-2-2-2200002222-2-2-2-2-2-200220000-2-200000000000000002-20000000000
χ1822222222222-2-2-2-2200002222-2-2-2-2-2-200-2-20000220000000000000000-220000000000
χ1922222222222-2-2-2-220000-2-2-2-2-22222-200220000220000000000000000-2-20000000000
χ2022222222222-2-2-2-220000-2-2-2-2-22222-200-2-20000-2-20000000000000000220000000000
χ2122222222-2-2-22222-2222222-2-2-2-2-222-2-2-200-2-222000000000000000000000000000000
χ2222222222-2-2-22222-22222-2-222-222-2-2-2-2-20022-2-2000000000000000000000000000000
χ2322222222-2-2-22222-2-2-2-2-222-2-2-2-2-222-2220022-2-2000000000000000000000000000000
χ2422222222-2-2-22222-2-2-2-2-2-2-222-222-2-2-22200-2-222000000000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-2000022-2-2222-2-2200000000000000000000000000002-22-2000000
χ2622222222-2-2-2-2-2-2-2-2000022-2-2222-2-220000000000000000000000000000-22-22000000
χ2722222222-2-2-2-2-2-2-2-20000-2-2222-2-222200000000000000000000000000002-2-22000000
χ2822222222-2-2-2-2-2-2-2-20000-2-2222-2-22220000000000000000000000000000-222-2000000
χ2922-22-2-2-220002-22-2022-2-2002i−2i02i−2i00000002i−2i0000i2i2−i2−i222−2−2i2i2−i2−i222−2−2000000000000
χ3022-22-2-2-220002-22-2022-2-2002i−2i02i−2i00000002i−2i0000−i2−i2i2i2−2−222−i2−i2i2i2−2−222000000000000
χ3122-22-2-2-220002-22-2022-2-200−2i2i0−2i2i0000000−2i2i0000i2i2−i2−i2−2−222i2i2−i2−i2−2−222000000000000
χ3222-22-2-2-220002-22-2022-2-200−2i2i0−2i2i0000000−2i2i0000−i2−i2i2i222−2−2−i2−i2i2i222−2−2000000000000
χ3322-22-2-2-220002-22-20-2-222002i−2i02i−2i0000000−2i2i0000i2i2−i2−i222−2−2−i2−i2i2i2−2−222000000000000
χ3422-22-2-2-220002-22-20-2-222002i−2i02i−2i0000000−2i2i0000−i2−i2i2i2−2−222i2i2−i2−i222−2−2000000000000
χ3522-22-2-2-220002-22-20-2-22200−2i2i0−2i2i00000002i−2i0000i2i2−i2−i2−2−222−i2−i2i2i222−2−2000000000000
χ3622-22-2-2-220002-22-20-2-22200−2i2i0−2i2i00000002i−2i0000−i2−i2i2i222−2−2i2i2−i2−i2−2−222000000000000
χ372-22-2-22-2200022-2-202-22-22-2000002-200000002-200i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000000000
χ382-22-2-22-2200022-2-202-22-22-2000002-200000002-200−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000000000
χ392-22-2-22-2200022-2-202-22-2-2200000-220000000-2200i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2000000000000
χ402-22-2-22-2200022-2-202-22-2-2200000-220000000-2200−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2000000000000
χ412-22-2-22-2200022-2-20-22-222-2000002-20000000-2200i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2000000000000
χ422-22-2-22-2200022-2-20-22-222-2000002-20000000-2200−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2000000000000
χ432-22-2-22-2200022-2-20-22-22-2200000-2200000002-200i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2000000000000
χ442-22-2-22-2200022-2-20-22-22-2200000-2200000002-200−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2000000000000
χ452-2-2-22-22222-22-2-22-22-2-22000020000-22-20000000000002i−2i−2i2i00002i−2i−2i2i000000000000
χ462-2-2-22-22222-22-2-22-22-2-22000020000-22-2000000000000−2i2i2i−2i0000−2i2i2i−2i000000000000
χ472-2-2-22-22222-22-2-22-2-222-2000020000-2-220000000000002i−2i−2i2i0000−2i2i2i−2i000000000000
χ482-2-2-22-22222-22-2-22-2-222-2000020000-2-22000000000000−2i2i2i−2i00002i−2i−2i2i000000000000
χ492-2-2-22-222-2-222-2-2222-2-220000-200002-22000000002-2-2200002-2-220000000000000000
χ502-2-2-22-222-2-222-2-2222-2-220000-200002-2200000000-222-20000-222-20000000000000000
χ512-2-2-22-222-2-222-2-222-222-20000-2000022-2000000002-2-220000-222-20000000000000000
χ522-2-2-22-222-2-222-2-222-222-20000-2000022-200000000-222-200002-2-220000000000000000
χ5344-44-4-4-44000-44-4400000004i−4i0−4i4i00000000000000000000000000000000000000000
χ5444-44-4-4-44000-44-440000000−4i4i04i−4i00000000000000000000000000000000000000000
χ5544-4-444-4-44-440000-400000000000000004-40000000000000000000000000000000000
χ5644-4-444-4-44-440000-40000000000000000-440000000000000000000000000000000000
χ5744-4-444-4-4-44-40000400000000000000000000004i−4i0000000000000000000000000000
χ5844-4-444-4-4-44-4000040000000000000000000000−4i4i0000000000000000000000000000
χ594-4444-4-4-44-4-4000040000000000000000000000000000000000000000000000002i2−2i200
χ604-4444-4-4-44-4-400004000000000000000000000000000000000000000000000000−2i22i200
χ614-4444-4-4-4-4440000-4000000000000000000000000000000000000000000000022−220000
χ624-4444-4-4-4-4440000-40000000000000000000000000000000000000000000000−22220000
χ634-44-4-44-44000-4-444000004-400000-44000000000000000000000000000000000000000
χ644-44-4-44-44000-4-44400000-44000004-4000000000000000000000000000000000000000
χ654-4-4-44-44444-4-444-4-400000000-40000400000000000000000000000000000000000000
χ664-4-4-44-444-4-44-444-440000000040000-400000000000000000000000000000000000000
χ67888-8-8-88-8000000000000000000000000000000000000000000000000000000000000
χ688-8-88-888-8000000000000000000000000000000000000000000000000000000000000

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