Finite Group Databasebeta

← Group #106909

Character table — Group #106909

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size1111111122222222222222224444444444444444444444888888888888888888888888888888881616161616161616
order12222222444444444444444422222244444444888888884444444444448888888888888888888844448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111-1-1-1-111111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ61111111111111111111111111-1-1-1-111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ71111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ81111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-11111
χ91111111111-1-1-1-1-1-1-1-111-1-1-1-1-11111-11111-1-1-1-1iiii−i−i−i−i11-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−iiiii−i−i−i−i11-1-111-1-1
χ101111111111-1-1-1-1-1-1-1-111-1-1-1-1-11111-11111-1-1-1-1iiii−i−i−i−i11-1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−iiiii−i−i−i−i-1-111-1-111
χ111111111111-1-1-1-1-1-1-1-111-1-1-1-1-11111-11111-1-1-1-1−i−i−i−iiiii11-1-1iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−i−i−iiiii-1-111-1-111
χ121111111111-1-1-1-1-1-1-1-111-1-1-1-1-11111-11111-1-1-1-1−i−i−i−iiiii11-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−i−i−iiiii11-1-111-1-1
χ131111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111iiii−i−i−i−i-1-111iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−i−i−iiiii-1-11111-1-1
χ141111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111iiii−i−i−i−i-1-111−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−i−i−iiiii11-1-1-1-111
χ151111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111−i−i−i−iiiii-1-111iiii−i−i−i−i−i−i−i−iiiii−i−iiiiiii−i−i−i−i11-1-1-1-111
χ161111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111−i−i−i−iiiii-1-111−i−i−i−iiiiiiiii−i−i−i−i−i−iiiiiii−i−i−i−i-1-11111-1-1
χ171-1-1111-1-1111111-1-1-1-1-1-111-1-1-111-1-1111-1-111-1-1ii−i−iii−i−i1-11-111-1-111-1-111-1-111-1-1i−ii−iii−i−iii−i−ii−ii−ii−ii−i
χ181-1-1111-1-1111111-1-1-1-1-1-111-1-1-111-1-1111-1-111-1-1ii−i−iii−i−i1-11-1-1-111-1-111-1-111-1-111i−ii−iii−i−iii−i−i−ii−ii−ii−ii
χ191-1-1111-1-1111111-1-1-1-1-1-111-1-1-111-1-1111-1-111-1-1−i−iii−i−iii1-11-111-1-111-1-111-1-111-1-1−ii−ii−i−iii−i−iii−ii−ii−ii−ii
χ201-1-1111-1-1111111-1-1-1-1-1-111-1-1-111-1-1111-1-111-1-1−i−iii−i−iii1-11-1-1-111-1-111-1-111-1-111−ii−ii−i−iii−i−iiii−ii−ii−ii−i
χ211-1-1111-1-1111111-1-1-1-1-1-111-1-1-1-1-111111-1-1-1-111ii−i−iii−i−i-11-1111-1-111-1-1-1-111-1-111i−ii−i−i−iii−i−iii−ii−iii−ii−i
χ221-1-1111-1-1111111-1-1-1-1-1-111-1-1-1-1-111111-1-1-1-111ii−i−iii−i−i-11-11-1-111-1-11111-1-111-1-1i−ii−i−i−iii−i−iiii−ii−i−ii−ii
χ231-1-1111-1-1111111-1-1-1-1-1-111-1-1-1-1-111111-1-1-1-111−i−iii−i−iii-11-1111-1-111-1-1-1-111-1-111−ii−iiii−i−iii−i−ii−ii−i−ii−ii
χ241-1-1111-1-1111111-1-1-1-1-1-111-1-1-1-1-111111-1-1-1-111−i−iii−i−iii-11-11-1-111-1-11111-1-111-1-1−ii−iiii−i−iii−i−i−ii−iii−ii−i
χ251-1-1111-1-111-1-1-1-11111-1-1-1-111111-1-1-111-1-1-1-11111-1-1-1-1111-1-11ii−i−i−i−iiiii−i−i−i−iii1-1-1111-1-1-1-111−iii−i−iii−i
χ261-1-1111-1-111-1-1-1-11111-1-1-1-111111-1-1-111-1-1-1-11111-1-1-1-1111-1-11−i−iiiii−i−i−i−iiiii−i−i1-1-1111-1-1-1-111i−i−iii−i−ii
χ271-1-1111-1-111-1-1-1-11111-1-1-1-111111-1-1-111-1-1-1-111-1-11111-1-11-1-11ii−i−i−i−iiiii−i−i−i−iii-111-1-1-11111-1-1i−i−iii−i−ii
χ281-1-1111-1-111-1-1-1-11111-1-1-1-111111-1-1-111-1-1-1-111-1-11111-1-11-1-11−i−iiiii−i−i−i−iiiii−i−i-111-1-1-11111-1-1−iii−i−iii−i
χ291-1-1111-1-111-1-1-1-11111-1-1-1-1111-1-111-111-1-111-1-111-1-1-1-111-111-1ii−i−i−i−iii−i−iiiii−i−i1-1-11-1-11111-1-1i−i−ii−iii−i
χ301-1-1111-1-111-1-1-1-11111-1-1-1-1111-1-111-111-1-111-1-111-1-1-1-111-111-1−i−iiiii−i−iii−i−i−i−iii1-1-11-1-11111-1-1−iii−ii−i−ii
χ311-1-1111-1-111-1-1-1-11111-1-1-1-1111-1-111-111-1-111-1-1-1-11111-1-1-111-1ii−i−i−i−iii−i−iiiii−i−i-111-111-1-1-1-111−iii−ii−i−ii
χ321-1-1111-1-111-1-1-1-11111-1-1-1-1111-1-111-111-1-111-1-1-1-11111-1-1-111-1−i−iiiii−i−iii−i−i−i−iii-111-111-1-1-1-111i−i−ii−iii−i
χ332222222222222222-2-222-2-222-22222-2-2-2-2-2222200000000-2-2-2-2000000000000000000000000000000000000
χ342222222222222222-2-222-2-222-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000002222000000000000000000000000000000000000
χ352222222222-2-2-2-2-2-2222222-2-2222222-2-2-2-2-2-2-2-200000000-2-222000000000000000000000000000000000000
χ362222222222-2-2-2-2-2-2222222-2-22-2-2-2-22-2-2-2-222220000000022-2-2000000000000000000000000000000000000
χ3722222222-2-222-2-22222-2-222-2-2-20000-22-22-20000000000000000000000000000000000002i−2i2i−2i2i−2i2i−2i00000000
χ3822222222-2-222-2-22222-2-222-2-2-20000-22-22-2000000000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i00000000
χ3922222222-2-222-2-222-2-2-2-2-2-2-2-2200002-22-2200002i2i2i2i−2i−2i−2i−2i00000000000000000000−2i−2i2i2i0000000000000000
χ4022222222-2-222-2-222-2-2-2-2-2-2-2-2200002-22-220000−2i−2i−2i−2i2i2i2i2i000000000000000000002i2i−2i−2i0000000000000000
χ4122222222-2-2-2-222-2-222-2-22222-20000-2-22-2200002222222200000000000000000000-2-2-2-20000000000000000
χ4222222222-2-2-2-222-2-222-2-22222-20000-2-22-220000-2-2-2-2-2-2-2-20000000000000000000022220000000000000000
χ4322222222-2-2-2-222-2-2-2-2-2-2-2-2222000022-22-20000000000000000000000000000000000002-22-2-22-2200000000
χ4422222222-2-2-2-222-2-2-2-2-2-2-2-2222000022-22-2000000000000000000000000000000000000-22-222-22-200000000
χ4522-22-2-22-22-22i−2i2i−2i2i−2i002-2002i−2i02-22-2000002i−2i2i−2i0000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000000000000
χ4622-22-2-22-22-22i−2i2i−2i2i−2i002-2002i−2i02-22-2000002i−2i2i−2i000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000000000000
χ4722-22-2-22-22-22i−2i2i−2i2i−2i002-2002i−2i0-22-2200000−2i2i−2i2i0000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000000000000
χ4822-22-2-22-22-22i−2i2i−2i2i−2i002-2002i−2i0-22-2200000−2i2i−2i2i000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000000000000
χ4922-22-2-22-22-2−2i2i−2i2i−2i2i002-200−2i2i02-22-200000−2i2i−2i2i0000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000000000000
χ5022-22-2-22-22-2−2i2i−2i2i−2i2i002-200−2i2i02-22-200000−2i2i−2i2i000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000000000000
χ5122-22-2-22-22-2−2i2i−2i2i−2i2i002-200−2i2i0-22-22000002i−2i2i−2i0000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000000000000
χ5222-22-2-22-22-2−2i2i−2i2i−2i2i002-200−2i2i0-22-22000002i−2i2i−2i000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000000000000
χ532-222-2-2-222-22i−2i2i−2i−2i2i00-2200−2i2i02-2-22000002i−2i−2i2i0000000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i1+i−1−i−1−i1+i1−i−1+i−1+i1−i00000000000000000000
χ542-222-2-2-222-22i−2i2i−2i−2i2i00-2200−2i2i02-2-22000002i−2i−2i2i000000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i−1−i1+i1+i−1−i−1+i1−i1−i−1+i00000000000000000000
χ552-222-2-2-222-22i−2i2i−2i−2i2i00-2200−2i2i0-222-200000−2i2i2i−2i0000000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i−1−i1+i1+i−1−i−1+i1−i1−i−1+i00000000000000000000
χ562-222-2-2-222-22i−2i2i−2i−2i2i00-2200−2i2i0-222-200000−2i2i2i−2i000000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i1+i−1−i−1−i1+i1−i−1+i−1+i1−i00000000000000000000
χ572-222-2-2-222-2−2i2i−2i2i2i−2i00-22002i−2i02-2-2200000−2i2i2i−2i0000000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i1−i−1+i−1+i1−i1+i−1−i−1−i1+i00000000000000000000
χ582-222-2-2-222-2−2i2i−2i2i2i−2i00-22002i−2i02-2-2200000−2i2i2i−2i000000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i−1+i1−i1−i−1+i−1−i1+i1+i−1−i00000000000000000000
χ592-222-2-2-222-2−2i2i−2i2i2i−2i00-22002i−2i0-222-2000002i−2i−2i2i0000000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i−1+i1−i1−i−1+i−1−i1+i1+i−1−i00000000000000000000
χ602-222-2-2-222-2−2i2i−2i2i2i−2i00-22002i−2i0-222-2000002i−2i−2i2i000000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i1−i−1+i−1+i1−i1+i−1−i−1−i1+i00000000000000000000
χ612-2-2222-2-2222222-2-222-2-2-2-2-2-2222-2-2-2-2-22222-2-200000000-22-22000000000000000000000000000000000000
χ622-2-2222-2-2222222-2-222-2-2-2-2-2-22-2-222-2-2-222-2-222000000002-22-2000000000000000000000000000000000000
χ632-2-2222-2-222-2-2-2-222-2-2-2-22222-222-2-22-2-222-2-22200000000-222-2000000000000000000000000000000000000
χ642-2-2222-2-222-2-2-2-222-2-2-2-22222-2-2-2222-2-22222-2-2000000002-2-22000000000000000000000000000000000000
χ652-2-2222-2-2-2-222-2-2-2-22222-2-222-200002-222-2000022-2-2-2-22200000000000000000000-222-20000000000000000
χ662-2-2222-2-2-2-222-2-2-2-22222-2-222-200002-222-20000-2-22222-2-2000000000000000000002-2-220000000000000000
χ672-2-2222-2-2-2-222-2-2-2-2-2-222222220000-22-2-220000000000000000000000000000000000002-2-222-2-2200000000
χ682-2-2222-2-2-2-222-2-2-2-2-2-222222220000-22-2-22000000000000000000000000000000000000-222-2-222-200000000
χ692-2-2222-2-2-2-2-2-222222222-2-2-2-2-2000022-2-220000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000
χ702-2-2222-2-2-2-2-2-222222222-2-2-2-2-2000022-2-22000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000
χ712-2-2222-2-2-2-2-2-22222-2-22222-2-220000-2-222-200002i2i−2i−2i2i2i−2i−2i00000000000000000000−2i2i−2i2i0000000000000000
χ722-2-2222-2-2-2-2-2-22222-2-22222-2-220000-2-222-20000−2i−2i2i2i−2i−2i2i2i000000000000000000002i−2i2i−2i0000000000000000
χ7344-44-4-44-4-444i−4i−4i4i4i−4i00-4400−4i4i00000000000000000000000000000000000000000000000000000000000000
χ7444-44-4-44-4-44−4i4i4i−4i−4i4i00-44004i−4i00000000000000000000000000000000000000000000000000000000000000
χ7544-4-44-4-44000000004i−4i004i−4i00000000000000002+2i−2−2i2+2i−2−2i2−2i−2+2i2−2i−2+2i0000000000000000000000000000000000000000
χ7644-4-44-4-44000000004i−4i004i−4i0000000000000000−2−2i2+2i−2−2i2+2i−2+2i2−2i−2+2i2−2i0000000000000000000000000000000000000000
χ7744-4-44-4-4400000000−4i4i00−4i4i00000000000000002−2i−2+2i2−2i−2+2i2+2i−2−2i2+2i−2−2i0000000000000000000000000000000000000000
χ7844-4-44-4-4400000000−4i4i00−4i4i0000000000000000−2+2i2−2i−2+2i2−2i−2−2i2+2i−2−2i2+2i0000000000000000000000000000000000000000
χ794-444-4-4-44-444i−4i−4i4i−4i4i004-4004i−4i00000000000000000000000000000000000000000000000000000000000000
χ804-444-4-4-44-44−4i4i4i−4i4i−4i004-400−4i4i00000000000000000000000000000000000000000000000000000000000000
χ814-44-44-44-4000000004i−4i00−4i4i00000000000000002+2i−2−2i−2−2i2+2i−2+2i2−2i2−2i−2+2i0000000000000000000000000000000000000000
χ824-44-44-44-4000000004i−4i00−4i4i0000000000000000−2−2i2+2i2+2i−2−2i2−2i−2+2i−2+2i2−2i0000000000000000000000000000000000000000
χ834-44-44-44-400000000−4i4i004i−4i00000000000000002−2i−2+2i−2+2i2−2i−2−2i2+2i2+2i−2−2i0000000000000000000000000000000000000000
χ844-44-44-44-400000000−4i4i004i−4i0000000000000000−2+2i2−2i2−2i−2+2i2+2i−2−2i−2−2i2+2i0000000000000000000000000000000000000000
χ85888-8-88-8-8000000000000000000000000000000000000000000000000000000000000000000000000000000
χ868-8-8-8-8888000000000000000000000000000000000000000000000000000000000000000000000000000000

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