Finite Group Databasebeta

← Group #197739

Character table — Group #197739

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size1111111122222222222222224444444444444444444444888888888888888888888888888888881616161616161616
order12222222444444444444444422222244444444888888884444888888888888888888888888888822444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ511111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111
χ811111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-11111-1-1
χ91111111111-1-1-1-11-1-1-1-111111-1-1111111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ101111111111-1-1-1-11-1-1-1-111111-1-1111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ111111111111-1-1-1-11-1-1-1-111111-1-1111111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-111-1-111
χ121111111111-1-1-1-11-1-1-1-111111-1-1111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-111-1-111-1-1
χ131111111111-1-1-1-11-1-1-1-111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ141111111111-1-1-1-11-1-1-1-111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ151111111111-1-1-1-11-1-1-1-111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-111-1-1
χ161111111111-1-1-1-11-1-1-1-111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-111
χ171-1-111-1-111111-1-1111-1-1-1-1-1-111-111-1-11-11-111-1-1ii−i−iii−i−i1-11-1ii−i−iii−i−ii−ii−iii−i−iii−i−i11-1-111-1-11-1i−ii−i1-1
χ181-1-111-1-111111-1-1111-1-1-1-1-1-111-111-1-11-11-111-1-1ii−i−iii−i−i1-11-1−i−iii−i−iiii−ii−iii−i−iii−i−i-1-111-1-111-11−ii−ii-11
χ191-1-111-1-111111-1-1111-1-1-1-1-1-111-111-1-11-11-111-1-1−i−iii−i−iii1-11-1ii−i−iii−i−i−ii−ii−i−iii−i−iii-1-111-1-111-11i−ii−i-11
χ201-1-111-1-111111-1-1111-1-1-1-1-1-111-111-1-11-11-111-1-1−i−iii−i−iii1-11-1−i−iii−i−iii−ii−ii−i−iii−i−iii11-1-111-1-11-1−ii−ii1-1
χ211-1-111-1-111111-1-1111-1-1-1-1-1-111-1-1-1111-11-1-1-111ii−i−iii−i−i-11-11ii−i−iii−i−ii−ii−i−i−iii−i−iii11-1-111-1-1-11−ii−ii-11
χ221-1-111-1-111111-1-1111-1-1-1-1-1-111-1-1-1111-11-1-1-111ii−i−iii−i−i-11-11−i−iii−i−iiii−ii−i−i−iii−i−iii-1-111-1-1111-1i−ii−i1-1
χ231-1-111-1-111111-1-1111-1-1-1-1-1-111-1-1-1111-11-1-1-111−i−iii−i−iii-11-11ii−i−iii−i−i−ii−iiii−i−iii−i−i-1-111-1-1111-1−ii−ii1-1
χ241-1-111-1-111111-1-1111-1-1-1-1-1-111-1-1-1111-11-1-1-111−i−iii−i−iii-11-11−i−iii−i−iii−ii−iiii−i−iii−i−i11-1-111-1-1-11i−ii−i-11
χ251-1-111-1-1111-1-1111-1-111-1-1-1-11-1111-1-11-1-1111-1-1ii−i−i−i−iii-11-11ii−i−i−i−iiii−i−iiii−i−i−i−iii11-1-1-1-1111-1i−i−ii-11
χ261-1-111-1-1111-1-1111-1-111-1-1-1-11-1111-1-11-1-1111-1-1ii−i−i−i−iii-11-11−i−iiiii−i−ii−i−iiii−i−i−i−iii-1-11111-1-1-11−iii−i1-1
χ271-1-111-1-1111-1-1111-1-111-1-1-1-11-1111-1-11-1-1111-1-1−i−iiiii−i−i-11-11ii−i−i−i−iii−iii−i−i−iiiii−i−i-1-11111-1-1-11i−i−ii1-1
χ281-1-111-1-1111-1-1111-1-111-1-1-1-11-1111-1-11-1-1111-1-1−i−iiiii−i−i-11-11−i−iiiii−i−i−iii−i−i−iiiii−i−i11-1-1-1-1111-1−iii−i-11
χ291-1-111-1-1111-1-1111-1-111-1-1-1-11-11-1-1111-1-11-1-111ii−i−i−i−iii1-11-1ii−i−i−i−iiii−i−ii−i−iiiii−i−i11-1-1-1-111-11−iii−i1-1
χ301-1-111-1-1111-1-1111-1-111-1-1-1-11-11-1-1111-1-11-1-111ii−i−i−i−iii1-11-1−i−iiiii−i−ii−i−ii−i−iiiii−i−i-1-11111-1-11-1i−i−ii-11
χ311-1-111-1-1111-1-1111-1-111-1-1-1-11-11-1-1111-1-11-1-111−i−iiiii−i−i1-11-1ii−i−i−i−iii−iii−iii−i−i−i−iii-1-11111-1-11-1−iii−i-11
χ321-1-111-1-1111-1-1111-1-111-1-1-1-11-11-1-1111-1-11-1-111−i−iiiii−i−i1-11-1−i−iiiii−i−i−iii−iii−i−i−i−iii11-1-1-1-111-11i−i−ii1-1
χ3322222222222222-22222-2-222-2-2-20000-2-2-2-2000022222222000000000000-2-2-2-2000000000000000000000000
χ3422222222222222-22222-2-222-2-2-20000-2-2-2-20000-2-2-2-2-2-2-2-20000000000002222000000000000000000000000
χ352222222222-2-2-2-2-2-2-2-2-2-2-222-2220000-2-22200002222-2-2-2-2000000000000-2-222000000000000000000000000
χ362222222222-2-2-2-2-2-2-2-2-2-2-222-2220000-2-2220000-2-2-2-2222200000000000022-2-2000000000000000000000000
χ3722222222-2-222222-2-2-2-222-2-22-2-22222-2-222-2-2-2-20000000022-2-2000000000000000000000000000000000000
χ3822222222-2-222222-2-2-2-222-2-22-2-2-2-2-2-2-2-222222200000000-2-222000000000000000000000000000000000000
χ3922222222-2-22222-2-2-2-2-2-2-2-2-2-222000022-2-200000000000000000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ4022222222-2-22222-2-2-2-2-2-2-2-2-2-222000022-2-20000000000000000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000
χ4122222222-2-2-2-2-2-22222222-2-22222222-2-2-2-2-2-2-2-200000000-2-222000000000000000000000000000000000000
χ4222222222-2-2-2-2-2-22222222-2-2222-2-2-2-2-2-2-2-222220000000022-2-2000000000000000000000000000000000000
χ4322222222-2-2-2-2-2-2-22222-2-2-2-2-2-2-20000222200000000000000000000000000002i−2i2i−2i−2i2i−2i2i0000000000000000
χ4422222222-2-2-2-2-2-2-22222-2-2-2-2-2-2-2000022220000000000000000000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000
χ4522-22-22-2-22-22i−2i2i−2i02i−2i2i−2i002-20000000000000002-22-22i−2i2i−2i00002−22−2i2−i2i2−i20000000000002−22−2i2−i2i2−i200000000
χ4622-22-22-2-22-22i−2i2i−2i02i−2i2i−2i002-20000000000000002-22-22i−2i2i−2i0000−22−22−i2i2−i2i2000000000000−22−22−i2i2−i2i200000000
χ4722-22-22-2-22-22i−2i2i−2i02i−2i2i−2i002-2000000000000000-22-22−2i2i−2i2i00002−22−2i2−i2i2−i2000000000000−22−22−i2i2−i2i200000000
χ4822-22-22-2-22-22i−2i2i−2i02i−2i2i−2i002-2000000000000000-22-22−2i2i−2i2i0000−22−22−i2i2−i2i20000000000002−22−2i2−i2i2−i200000000
χ4922-22-22-2-22-2−2i2i−2i2i0−2i2i−2i2i002-20000000000000002-22-2−2i2i−2i2i00002−22−2−i2i2−i2i20000000000002−22−2−i2i2−i2i200000000
χ5022-22-22-2-22-2−2i2i−2i2i0−2i2i−2i2i002-20000000000000002-22-2−2i2i−2i2i0000−22−22i2−i2i2−i2000000000000−22−22i2−i2i2−i200000000
χ5122-22-22-2-22-2−2i2i−2i2i0−2i2i−2i2i002-2000000000000000-22-222i−2i2i−2i00002−22−2−i2i2−i2i2000000000000−22−22i2−i2i2−i200000000
χ5222-22-22-2-22-2−2i2i−2i2i0−2i2i−2i2i002-2000000000000000-22-222i−2i2i−2i0000−22−22i2−i2i2−i20000000000002−22−2−i2i2−i2i200000000
χ532-222-2-22-22-22i−2i−2i2i02i−2i−2i2i00-220000000000000002i−2i−2i2i-222-20000i2−i2−i2i2−222−20000000000002−2−22i2−i2−i2i200000000
χ542-222-2-22-22-22i−2i−2i2i02i−2i−2i2i00-220000000000000002i−2i−2i2i-222-20000−i2i2i2−i22−2−22000000000000−222−2−i2i2i2−i200000000
χ552-222-2-22-22-22i−2i−2i2i02i−2i−2i2i00-22000000000000000−2i2i2i−2i2-2-220000i2−i2−i2i2−222−2000000000000−222−2−i2i2i2−i200000000
χ562-222-2-22-22-22i−2i−2i2i02i−2i−2i2i00-22000000000000000−2i2i2i−2i2-2-220000−i2i2i2−i22−2−220000000000002−2−22i2−i2−i2i200000000
χ572-222-2-22-22-2−2i2i2i−2i0−2i2i2i−2i00-220000000000000002i−2i−2i2i2-2-220000i2−i2−i2i22−2−220000000000002−2−22−i2i2i2−i200000000
χ582-222-2-22-22-2−2i2i2i−2i0−2i2i2i−2i00-220000000000000002i−2i−2i2i2-2-220000−i2i2i2−i2−222−2000000000000−222−2i2−i2−i2i200000000
χ592-222-2-22-22-2−2i2i2i−2i0−2i2i2i−2i00-22000000000000000−2i2i2i−2i-222-20000i2−i2−i2i22−2−22000000000000−222−2i2−i2−i2i200000000
χ602-222-2-22-22-2−2i2i2i−2i0−2i2i2i−2i00-22000000000000000−2i2i2i−2i-222-20000−i2i2i2−i2−222−20000000000002−2−22−i2i2i2−i200000000
χ612-2-222-2-222222-2-2-222-2-222-2-2-2-220000-22-2200002i2i−2i−2i2i2i−2i−2i000000000000−2i2i−2i2i000000000000000000000000
χ622-2-222-2-222222-2-2-222-2-222-2-2-2-220000-22-220000−2i−2i2i2i−2i−2i2i2i0000000000002i−2i2i−2i000000000000000000000000
χ632-2-222-2-2222-2-222-2-2-22222-2-2-22-20000-222-200002i2i−2i−2i−2i−2i2i2i000000000000−2i2i2i−2i000000000000000000000000
χ642-2-222-2-2222-2-222-2-2-22222-2-2-22-20000-222-20000−2i−2i2i2i2i2i−2i−2i0000000000002i−2i−2i2i000000000000000000000000
χ652-2-222-2-22-2-222-2-22-2-222-2-2222-2222-2-2-222-2-2-222000000002-2-22000000000000000000000000000000000000
χ662-2-222-2-22-2-222-2-22-2-222-2-2222-22-2-222-222-222-2-200000000-222-2000000000000000000000000000000000000
χ672-2-222-2-22-2-222-2-2-2-2-2222222-22-200002-2-2200000000000000000000000000002-2-222-2-220000000000000000
χ682-2-222-2-22-2-222-2-2-2-2-2222222-22-200002-2-220000000000000000000000000000-222-2-222-20000000000000000
χ692-2-222-2-22-2-2-2-222222-2-2-2-22222-222-2-2-22-22-2-22200000000-222-2000000000000000000000000000000000000
χ702-2-222-2-22-2-2-2-222222-2-2-2-22222-2-2-222-22-2222-2-2000000002-2-22000000000000000000000000000000000000
χ712-2-222-2-22-2-2-2-222-222-2-22222-2-2200002-22-200000000000000000000000000002-2-22-222-20000000000000000
χ722-2-222-2-22-2-2-2-222-222-2-22222-2-2200002-22-20000000000000000000000000000-222-22-2-220000000000000000
χ7344-44-44-4-4-444i−4i4i−4i0−4i4i−4i4i00-44000000000000000000000000000000000000000000000000000000000000000
χ7444-44-44-4-4-44−4i4i−4i4i04i−4i4i−4i00-44000000000000000000000000000000000000000000000000000000000000000
χ7544-4-4-4-444000000400004-400-400000000004i−4i4i−4i000000000000000000000000000000000000000000000000
χ7644-4-4-4-444000000400004-400-40000000000−4i4i−4i4i000000000000000000000000000000000000000000000000
χ7744-4-4-4-444000000-40000-44004004-44-400000000000000000000000000000000000000000000000000000000
χ7844-4-4-4-444000000-40000-4400400-44-4400000000000000000000000000000000000000000000000000000000
χ794-444-4-44-4-444i−4i−4i4i0−4i4i4i−4i004-4000000000000000000000000000000000000000000000000000000000000000
χ804-444-4-44-4-44−4i4i4i−4i04i−4i−4i4i004-4000000000000000000000000000000000000000000000000000000000000000
χ814-44-4-44-4400000040000-4400-400000000004i−4i−4i4i000000000000000000000000000000000000000000000000
χ824-44-4-44-4400000040000-4400-40000000000−4i4i4i−4i000000000000000000000000000000000000000000000000
χ834-44-4-44-44000000-400004-4004004-4-4400000000000000000000000000000000000000000000000000000000
χ844-44-4-44-44000000-400004-400400-444-400000000000000000000000000000000000000000000000000000000
χ85888-88-8-8-8000000000000000000000000000000000000000000000000000000000000000000000000000000
χ868-8-8-8888-8000000000000000000000000000000000000000000000000000000000000000000000000000000

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