Finite Group Databasebeta

← Group #368792

Character table — Group #368792

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size1111111122222222222222224444444444444444444444888888888888888888888888888888881616161616161616
order12222222222222222222222222222222224444444444442244444444444444444444444444444424444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
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
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1
χ91111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-1iiii−i−i−i−i1-11111-1-1-1-11-1ii−i−iiiii−i−i−i−iii−i−iii−i−i1-1-11ii−i−i
χ101111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-1iiii−i−i−i−i1-1-1-1-1-111111-1ii−i−i−i−i−i−iiiiiii−i−iii−i−i-111-1−i−iii
χ111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-1−i−i−i−iiiii1-11111-1-1-1-11-1−i−iii−i−i−i−iiiii−i−iii−i−iii1-1-11−i−iii
χ121111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-1−i−i−i−iiiii1-1-1-1-1-111111-1−i−iiiiiii−i−i−i−i−i−iii−i−iii-111-1ii−i−i
χ131111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-111iiii−i−i−i−i-111111-1-1-1-1-11−i−iiiiiii−i−i−i−iii−i−i−i−iii-111-1−i−iii
χ141111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-111iiii−i−i−i−i-11-1-1-1-11111-11−i−iii−i−i−i−iiiiiii−i−i−i−iii1-1-11ii−i−i
χ151111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-111−i−i−i−iiiii-111111-1-1-1-1-11ii−i−i−i−i−i−iiiii−i−iiiii−i−i-111-1ii−i−i
χ161111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-111−i−i−i−iiiii-11-1-1-1-11111-11ii−i−iiiii−i−i−i−i−i−iiiii−i−i1-1-11−i−iii
χ17111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1111111-1-11-11-1
χ18111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-11111111111-1-111-1-111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-111-11-11
χ19111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-111-1-1111111-1-1-1-111-1-1-11-11
χ20111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1111111-1-111-1-11111-1-1-1-1-1-1111-11-1
χ21111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-111-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-11-11
χ22111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-111111111-1-111-1-111-1-1-1-1-1-1-1-111-1-11-11-1
χ23111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-1-1-111-1-11111111111-1-1111-11-1
χ24111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-111-1-11111111111-1-1-11-11
χ25111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111iiii−i−i−i−i1-111-1-1-1-111-11−i−iiiii−i−i−i−iii−i−iiiii−i−i1-11-1i−i−ii
χ26111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111iiii−i−i−i−i1-1-1-11111-1-1-11−i−iii−i−iiiii−i−i−i−iiiii−i−i-11-11−iii−i
χ27111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111−i−i−i−iiiii1-111-1-1-1-111-11ii−i−i−i−iiiii−i−iii−i−i−i−iii1-11-1−iii−i
χ28111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111−i−i−i−iiiii1-1-1-11111-1-1-11ii−i−iii−i−i−i−iiiii−i−i−i−iii-11-11i−i−ii
χ29111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1iiii−i−i−i−i-1111-1-1-1-1111-1ii−i−iii−i−i−i−iii−i−iii−i−iii-11-11−iii−i
χ30111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1iiii−i−i−i−i-11-1-11111-1-11-1ii−i−i−i−iiiii−i−i−i−iii−i−iii1-11-1i−i−ii
χ31111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1−i−i−i−iiiii-1111-1-1-1-1111-1−i−iii−i−iiiii−i−iii−i−iii−i−i-11-11i−i−ii
χ32111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1−i−i−i−iiiii-11-1-11111-1-11-1−i−iiiii−i−i−i−iiiii−i−iii−i−i1-11-1−iii−i
χ3322222222-2-2-2-2222222-22-2-2-22-2-222-2-22222222200000000-2-200000000-2-20000000000000000000000000000
χ3422222222-2-2-2-2222222-22-2-2-22-2-222-2-2-2-2-2-2-2-2-2-2000000002200000000220000000000000000000000000000
χ3522222222-2-2-2-22222-2-22-2222-2-2-2-2-22222-2-222-2-200000000-2200000000-220000000000000000000000000000
χ3622222222-2-2-2-22222-2-22-2222-2-2-2-2-222-2-222-2-222000000002-2000000002-20000000000000000000000000000
χ3722222222-2-2-2-2-2-2-2-222-22-2-2-2222-2-2222222-2-2-2-200000000-2-200000000220000000000000000000000000000
χ3822222222-2-2-2-2-2-2-2-222-22-2-2-2222-2-222-2-2-2-22222000000002200000000-2-20000000000000000000000000000
χ3922222222-2-2-2-2-2-2-2-2-2-22-2222-22222-2-222-2-2-2-22200000000-22000000002-20000000000000000000000000000
χ4022222222-2-2-2-2-2-2-2-2-2-22-2222-22222-2-2-2-22222-2-2000000002-200000000-220000000000000000000000000000
χ412222-2-2-2-222-2-200002-22-22-2-220000000000000022-2-222-2-200002i−2i002i−2i000000002i−2i002i−2i0000000000000000
χ422222-2-2-2-222-2-200002-22-22-2-220000000000000022-2-222-2-20000−2i2i00−2i2i00000000−2i2i00−2i2i0000000000000000
χ432222-2-2-2-222-2-200002-22-22-2-2200000000000000-2-222-2-22200002i−2i002i−2i00000000−2i2i00−2i2i0000000000000000
χ442222-2-2-2-222-2-200002-22-22-2-2200000000000000-2-222-2-2220000−2i2i00−2i2i000000002i−2i002i−2i0000000000000000
χ452222-2-2-2-222-2-20000-22-22-222-2000000000000002i2i−2i−2i−2i−2i2i2i00002i−2i00−2i2i00000000-22002-20000000000000000
χ462222-2-2-2-222-2-20000-22-22-222-2000000000000002i2i−2i−2i−2i−2i2i2i0000−2i2i002i−2i000000002-200-220000000000000000
χ472222-2-2-2-222-2-20000-22-22-222-200000000000000−2i−2i2i2i2i2i−2i−2i00002i−2i00−2i2i000000002-200-220000000000000000
χ482222-2-2-2-222-2-20000-22-22-222-200000000000000−2i−2i2i2i2i2i−2i−2i0000−2i2i002i−2i00000000-22002-20000000000000000
χ492-2-222-2-222-22-222-2-2222-2-2-22-22-22-22-2000000002i−2i2i−2i2i−2i2i−2i0000000000000000000000002i−2i2i−2i000000000000
χ502-2-222-2-222-22-222-2-2222-2-2-22-22-22-22-200000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000−2i2i−2i2i000000000000
χ512-2-222-2-222-22-222-2-2-2-2-2222-222-2-22-22000000002-22-2-22-220000000000000000000000002-2-22000000000000
χ522-2-222-2-222-22-222-2-2-2-2-2222-222-2-22-2200000000-22-222-22-2000000000000000000000000-222-2000000000000
χ532-2-222-2-222-22-2-2-222222-2-2-22-2-22-22-22000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000−2i2i−2i2i000000000000
χ542-2-222-2-222-22-2-2-222222-2-2-22-2-22-22-2200000000−2i2i−2i2i−2i2i−2i2i0000000000000000000000002i−2i2i−2i000000000000
χ552-2-222-2-222-22-2-2-222-2-2-2222-22-222-22-2000000002-22-2-22-22000000000000000000000000-222-2000000000000
χ562-2-222-2-222-22-2-2-222-2-2-2222-22-222-22-200000000-22-222-22-20000000000000000000000002-2-22000000000000
χ572-2-222-2-22-22-2222-2-222-2-222-2-2-222-2-2200000000000000000000000000002i−2i2i−2i0000000000002i−2i2i−2i00000000
χ582-2-222-2-22-22-2222-2-222-2-222-2-2-222-2-220000000000000000000000000000−2i2i−2i2i000000000000−2i2i−2i2i00000000
χ592-2-222-2-22-22-2222-2-2-2-222-2-222-22-222-200000000000000000000000000002-2-220000000000002-2-2200000000
χ602-2-222-2-22-22-2222-2-2-2-222-2-222-22-222-20000000000000000000000000000-222-2000000000000-222-200000000
χ612-2-222-2-22-22-22-2-22222-2-222-2-22-2-222-200000000000000000000000000002i−2i2i−2i000000000000−2i2i−2i2i00000000
χ622-2-222-2-22-22-22-2-22222-2-222-2-22-2-222-20000000000000000000000000000−2i2i−2i2i0000000000002i−2i2i−2i00000000
χ632-2-222-2-22-22-22-2-222-2-222-2-2222-22-2-2200000000000000000000000000002-2-22000000000000-222-200000000
χ642-2-222-2-22-22-22-2-222-2-222-2-2222-22-2-220000000000000000000000000000-222-20000000000002-2-2200000000
χ652-2-22-222-22-2-2200002-222-22-2-2000000000000002i−2i−2i2i2i−2i−2i2i002-2002-2000000002i−2i002i−2i000000000000000000
χ662-2-22-222-22-2-2200002-222-22-2-2000000000000002i−2i−2i2i2i−2i−2i2i00-2200-2200000000−2i2i00−2i2i000000000000000000
χ672-2-22-222-22-2-2200002-222-22-2-200000000000000−2i2i2i−2i−2i2i2i−2i002-2002-200000000−2i2i00−2i2i000000000000000000
χ682-2-22-222-22-2-2200002-222-22-2-200000000000000−2i2i2i−2i−2i2i2i−2i00-2200-22000000002i−2i002i−2i000000000000000000
χ692-2-22-222-22-2-220000-22-2-22-222000000000000002-2-22-222-2002-200-22000000002-200-22000000000000000000
χ702-2-22-222-22-2-220000-22-2-22-222000000000000002-2-22-222-200-22002-200000000-22002-2000000000000000000
χ712-2-22-222-22-2-220000-22-2-22-22200000000000000-222-22-2-22002-200-2200000000-22002-2000000000000000000
χ722-2-22-222-22-2-220000-22-2-22-22200000000000000-222-22-2-2200-22002-2000000002-200-22000000000000000000
χ734444-4-4-4-4-4-44400004-4-4-4-444400000000000000000000000000000000000000000000000000000000000000
χ744444-4-4-4-4-4-4440000-44444-4-4-400000000000000000000000000000000000000000000000000000000000000
χ7544-4-4-44-4400004-44-400000000000000004-4004-4000000000000000000000000000000000000000000000000
χ7644-4-4-44-4400004-44-40000000000000000-4400-44000000000000000000000000000000000000000000000000
χ7744-4-4-44-440000-44-4400000000000000004-400-44000000000000000000000000000000000000000000000000
χ7844-4-4-44-440000-44-440000000000000000-44004-4000000000000000000000000000000000000000000000000
χ794-44-4-4-44400004-4-44000000000000004-4004-400000000000000000000000000000000000000000000000000
χ804-44-4-4-44400004-4-4400000000000000-4400-4400000000000000000000000000000000000000000000000000
χ814-44-4-4-4440000-444-4000000000000004-400-4400000000000000000000000000000000000000000000000000
χ824-44-4-4-4440000-444-400000000000000-44004-400000000000000000000000000000000000000000000000000
χ834-4-44-444-4-444-400004-4-444-44-400000000000000000000000000000000000000000000000000000000000000
χ844-4-44-444-4-444-40000-444-4-44-4400000000000000000000000000000000000000000000000000000000000000
χ8588-8-88-88-8000000000000000000000000000000000000000000000000000000000000000000000000000000
χ868-88-888-8-8000000000000000000000000000000000000000000000000000000000000000000000000000000

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