Finite Group Databasebeta

← Group #494649

Character table — Group #494649

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size112222222224444444444444444444444444441616161616161616112222222224444444444444444444444444441616161616161616
order1222244448822448888888161616161616161616161616161616162244888822222444488224488888881616161616161616161616161616161622448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ41111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ511111111111-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111111-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ611111111111-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ711111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ811111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1
χ9111-1-1-111-1-1-11-11-111-111-1-1iiii−i−i−i−iiiii−i−i−i−i1-1i−i1-1i−i111-1-1-111-1-1-11-11-111-111-1-1iiii−i−i−i−iiiii−i−i−i−i1-1i−i1-1i−i
χ10111-1-1-111-1-1-11-11-111-111-1-1iiii−i−i−i−iiiii−i−i−i−i-11−ii-11−ii111-1-1-111-1-1-11-11-111-111-1-1iiii−i−i−i−iiiii−i−i−i−i-11−ii-11−ii
χ11111-1-1-111-1-1-11-11-111-111-1-1−i−i−i−iiiii−i−i−i−iiiii1-1−ii1-1−ii111-1-1-111-1-1-11-11-111-111-1-1−i−i−i−iiiii−i−i−i−iiiii1-1−ii1-1−ii
χ12111-1-1-111-1-1-11-11-111-111-1-1−i−i−i−iiiii−i−i−i−iiiii-11i−i-11i−i111-1-1-111-1-1-11-11-111-111-1-1−i−i−i−iiiii−i−i−i−iiiii-11i−i-11i−i
χ13111-1-1-111-1-1-1-11-1111-1-1-111iiii−i−i−i−i−i−i−i−iiiii1-1i−i-11−ii111-1-1-111-1-1-1-11-1111-1-1-111iiii−i−i−i−i−i−i−i−iiiii1-1i−i-11−ii
χ14111-1-1-111-1-1-1-11-1111-1-1-111iiii−i−i−i−i−i−i−i−iiiii-11−ii1-1i−i111-1-1-111-1-1-1-11-1111-1-1-111iiii−i−i−i−i−i−i−i−iiiii-11−ii1-1i−i
χ15111-1-1-111-1-1-1-11-1111-1-1-111−i−i−i−iiiiiiiii−i−i−i−i1-1−ii-11i−i111-1-1-111-1-1-1-11-1111-1-1-111−i−i−i−iiiiiiiii−i−i−i−i1-1−ii-11i−i
χ16111-1-1-111-1-1-1-11-1111-1-1-111−i−i−i−iiiiiiiii−i−i−i−i-11i−i1-1−ii111-1-1-111-1-1-1-11-1111-1-1-111−i−i−i−iiiiiiiii−i−i−i−i-11i−i1-1−ii
χ17222222222-2-22222-2-2-2-2-2-2-2000000000000000000000000222222222-2-22222-2-2-2-2-2-2-2000000000000000000000000
χ18222222222-2-2-2-2-2-2-2-2-22222000000000000000000000000222222222-2-2-2-2-2-2-2-2-22222000000000000000000000000
χ1922222-2-2-2-20000000002i−2i2i−2i22−2−222−2−2i2i2−i2−i2i2i2−i2−i20000000022222-2-2-2-20000000002i−2i2i−2i22−2−222−2−2i2i2−i2−i2i2i2−i2−i200000000
χ2022222-2-2-2-20000000002i−2i2i−2i−2−222−2−222−i2−i2i2i2−i2−i2i2i20000000022222-2-2-2-20000000002i−2i2i−2i−2−222−2−222−i2−i2i2i2−i2−i2i2i200000000
χ2122222-2-2-2-2000000000−2i2i−2i2i22−2−222−2−2−i2−i2i2i2−i2−i2i2i20000000022222-2-2-2-2000000000−2i2i−2i2i22−2−222−2−2−i2−i2i2i2−i2−i2i2i200000000
χ2222222-2-2-2-2000000000−2i2i−2i2i−2−222−2−222i2i2−i2−i2i2i2−i2−i20000000022222-2-2-2-2000000000−2i2i−2i2i−2−222−2−222i2i2−i2−i2i2i2−i2−i200000000
χ23222-2-22-2-220000000002i−2i−2i2ii2i2−i2−i2−i2−i2i2i2−2−22222−2−200000000222-2-22-2-220000000002i−2i−2i2ii2i2−i2−i2−i2−i2i2i2−2−22222−2−200000000
χ24222-2-22-2-220000000002i−2i−2i2i−i2−i2i2i2i2i2−i2−i222−2−2−2−22200000000222-2-22-2-220000000002i−2i−2i2i−i2−i2i2i2i2i2−i2−i222−2−2−2−22200000000
χ25222-2-22-2-22000000000−2i2i2i−2ii2i2−i2−i2−i2−i2i2i222−2−2−2−22200000000222-2-22-2-22000000000−2i2i2i−2ii2i2−i2−i2−i2−i2i2i222−2−2−2−22200000000
χ26222-2-22-2-22000000000−2i2i2i−2i−i2−i2i2i2i2i2−i2−i2−2−22222−2−200000000222-2-22-2-22000000000−2i2i2i−2i−i2−i2i2i2i2i2−i2−i2−2−22222−2−200000000
χ27222-2-2-222-2222-22-2-2-22-2-222000000000000000000000000222-2-2-222-2222-22-2-2-22-2-222000000000000000000000000
χ28222-2-2-222-222-22-22-2-2222-2-2000000000000000000000000222-2-2-222-222-22-22-2-2222-2-2000000000000000000000000
χ2922-22-222-2-20022-2-20000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000000022-22-222-2-20022-2-20000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i200000000
χ3022-22-222-2-20022-2-20000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000000022-22-222-2-20022-2-20000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i200000000
χ3122-22-222-2-200-2-2220000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i20000000022-22-222-2-200-2-2220000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i200000000
χ3222-22-222-2-200-2-2220000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i20000000022-22-222-2-200-2-2220000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i200000000
χ3322-22-2-2-2222200002-2-20000000000002-2-222-2-220000000022-22-2-2-2222200002-2-20000000000002-2-222-2-2200000000
χ3422-22-2-2-2222200002-2-2000000000000-222-2-222-20000000022-22-2-2-2222200002-2-2000000000000-222-2-222-200000000
χ3522-22-2-2-222-2-20000-22200002i−2i−2i2i2i−2i−2i2i000000000000000022-22-2-2-222-2-20000-22200002i−2i−2i2i2i−2i−2i2i0000000000000000
χ3622-22-2-2-222-2-20000-2220000−2i2i2i−2i−2i2i2i−2i000000000000000022-22-2-2-222-2-20000-2220000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ3722-2-222-22-2220000-22-200002-2-22-222-2000000000000000022-2-222-22-2220000-22-200002-2-22-222-20000000000000000
χ3822-2-222-22-2220000-22-20000-222-22-2-22000000000000000022-2-222-22-2220000-22-20000-222-22-2-220000000000000000
χ3922-2-222-22-2-2-200002-220000000000002i−2i−2i2i−2i2i2i−2i0000000022-2-222-22-2-2-200002-220000000000002i−2i−2i2i−2i2i2i−2i00000000
χ4022-2-222-22-2-2-200002-22000000000000−2i2i2i−2i2i−2i−2i2i0000000022-2-222-22-2-2-200002-22000000000000−2i2i2i−2i2i−2i−2i2i00000000
χ4122-2-22-22-22002-2-2200000002−22−2−22−222−22−2−22−220000000022-2-22-22-22002-2-2200000002−22−2−22−222−22−2−22−2200000000
χ4222-2-22-22-22002-2-220000000−22−222−22−2−22−222−22−20000000022-2-22-22-22002-2-220000000−22−222−22−2−22−222−22−200000000
χ4322-2-22-22-2200-222-200000002−22−2−22−22−22−222−22−20000000022-2-22-22-2200-222-200000002−22−2−22−22−22−222−22−200000000
χ4422-2-22-22-2200-222-20000000−22−222−22−22−22−2−22−220000000022-2-22-22-2200-222-20000000−22−222−22−22−22−2−22−2200000000
χ458-8000000042−42000000000000000000000000000000000008-8000000042−4200000000000000000000000000000000000
χ468-80000000−4242000000000000000000000000000000000008-80000000−424200000000000000000000000000000000000
χ471111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ4811111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ491111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-111-1-111
χ501111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-111-1-1
χ5111111111111-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ5211111111111-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-11111-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ5311111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ5411111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-111
χ55111-1-1-111-1-1-11-11-111-111-1-1iiii−i−i−i−iiiii−i−i−i−i1-1i−i1-1i−i-1-1-1111-1-1111-11-11-1-11-1-111−i−i−i−iiiii−i−i−i−iiiii-11−ii-11−ii
χ56111-1-1-111-1-1-11-11-111-111-1-1iiii−i−i−i−iiiii−i−i−i−i-11−ii-11−ii-1-1-1111-1-1111-11-11-1-11-1-111−i−i−i−iiiii−i−i−i−iiiii1-1i−i1-1i−i
χ57111-1-1-111-1-1-11-11-111-111-1-1−i−i−i−iiiii−i−i−i−iiiii1-1−ii1-1−ii-1-1-1111-1-1111-11-11-1-11-1-111iiii−i−i−i−iiiii−i−i−i−i-11i−i-11i−i
χ58111-1-1-111-1-1-11-11-111-111-1-1−i−i−i−iiiii−i−i−i−iiiii-11i−i-11i−i-1-1-1111-1-1111-11-11-1-11-1-111iiii−i−i−i−iiiii−i−i−i−i1-1−ii1-1−ii
χ59111-1-1-111-1-1-1-11-1111-1-1-111iiii−i−i−i−i−i−i−i−iiiii1-1i−i-11−ii-1-1-1111-1-11111-11-1-1-1111-1-1−i−i−i−iiiiiiiii−i−i−i−i-11−ii1-1i−i
χ60111-1-1-111-1-1-1-11-1111-1-1-111iiii−i−i−i−i−i−i−i−iiiii-11−ii1-1i−i-1-1-1111-1-11111-11-1-1-1111-1-1−i−i−i−iiiiiiiii−i−i−i−i1-1i−i-11−ii
χ61111-1-1-111-1-1-1-11-1111-1-1-111−i−i−i−iiiiiiiii−i−i−i−i1-1−ii-11i−i-1-1-1111-1-11111-11-1-1-1111-1-1iiii−i−i−i−i−i−i−i−iiiii-11i−i1-1−ii
χ62111-1-1-111-1-1-1-11-1111-1-1-111−i−i−i−iiiiiiiii−i−i−i−i-11i−i1-1−ii-1-1-1111-1-11111-11-1-1-1111-1-1iiii−i−i−i−i−i−i−i−iiiii1-1−ii-11i−i
χ63222222222-2-22222-2-2-2-2-2-2-2000000000000000000000000-2-2-2-2-2-2-2-2-222-2-2-2-22222222000000000000000000000000
χ64222222222-2-2-2-2-2-2-2-2-22222000000000000000000000000-2-2-2-2-2-2-2-2-2222222222-2-2-2-2000000000000000000000000
χ6522222-2-2-2-20000000002i−2i2i−2i22−2−222−2−2i2i2−i2−i2i2i2−i2−i200000000-2-2-2-2-22222000000000−2i2i−2i2i−2−222−2−222−i2−i2i2i2−i2−i2i2i200000000
χ6622222-2-2-2-20000000002i−2i2i−2i−2−222−2−222−i2−i2i2i2−i2−i2i2i200000000-2-2-2-2-22222000000000−2i2i−2i2i22−2−222−2−2i2i2−i2−i2i2i2−i2−i200000000
χ6722222-2-2-2-2000000000−2i2i−2i2i22−2−222−2−2−i2−i2i2i2−i2−i2i2i200000000-2-2-2-2-222220000000002i−2i2i−2i−2−222−2−222i2i2−i2−i2i2i2−i2−i200000000
χ6822222-2-2-2-2000000000−2i2i−2i2i−2−222−2−222i2i2−i2−i2i2i2−i2−i200000000-2-2-2-2-222220000000002i−2i2i−2i22−2−222−2−2−i2−i2i2i2−i2−i2i2i200000000
χ69222-2-22-2-220000000002i−2i−2i2ii2i2−i2−i2−i2−i2i2i2−2−22222−2−200000000-2-2-222-222-2000000000−2i2i2i−2i−i2−i2i2i2i2i2−i2−i222−2−2−2−22200000000
χ70222-2-22-2-220000000002i−2i−2i2i−i2−i2i2i2i2i2−i2−i222−2−2−2−22200000000-2-2-222-222-2000000000−2i2i2i−2ii2i2−i2−i2−i2−i2i2i2−2−22222−2−200000000
χ71222-2-22-2-22000000000−2i2i2i−2ii2i2−i2−i2−i2−i2i2i222−2−2−2−22200000000-2-2-222-222-20000000002i−2i−2i2i−i2−i2i2i2i2i2−i2−i2−2−22222−2−200000000
χ72222-2-22-2-22000000000−2i2i2i−2i−i2−i2i2i2i2i2−i2−i2−2−22222−2−200000000-2-2-222-222-20000000002i−2i−2i2ii2i2−i2−i2−i2−i2i2i222−2−2−2−22200000000
χ73222-2-2-222-2222-22-2-2-22-2-222000000000000000000000000-2-2-2222-2-22-2-2-22-2222-222-2-2000000000000000000000000
χ74222-2-2-222-222-22-22-2-2222-2-2000000000000000000000000-2-2-2222-2-22-2-22-22-222-2-2-222000000000000000000000000
χ7522-22-222-2-20022-2-20000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i200000000-2-22-22-2-22200-2-2220000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i200000000
χ7622-22-222-2-20022-2-20000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i200000000-2-22-22-2-22200-2-2220000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i200000000
χ7722-22-222-2-200-2-2220000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i200000000-2-22-22-2-2220022-2-20000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i200000000
χ7822-22-222-2-200-2-2220000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i200000000-2-22-22-2-2220022-2-20000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i200000000
χ7922-22-2-2-2222200002-2-20000000000002-2-222-2-2200000000-2-22-2222-2-2-2-20000-222000000000000-222-2-222-200000000
χ8022-22-2-2-2222200002-2-2000000000000-222-2-222-200000000-2-22-2222-2-2-2-20000-2220000000000002-2-222-2-2200000000
χ8122-22-2-2-222-2-20000-22200002i−2i−2i2i2i−2i−2i2i0000000000000000-2-22-2222-2-22200002-2-20000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ8222-22-2-2-222-2-20000-2220000−2i2i2i−2i−2i2i2i−2i0000000000000000-2-22-2222-2-22200002-2-200002i−2i−2i2i2i−2i−2i2i0000000000000000
χ8322-2-222-22-2220000-22-200002-2-22-222-20000000000000000-2-222-2-22-22-2-200002-220000-222-22-2-220000000000000000
χ8422-2-222-22-2220000-22-20000-222-22-2-220000000000000000-2-222-2-22-22-2-200002-2200002-2-22-222-20000000000000000
χ8522-2-222-22-2-2-200002-220000000000002i−2i−2i2i−2i2i2i−2i00000000-2-222-2-22-22220000-22-2000000000000−2i2i2i−2i2i−2i−2i2i00000000
χ8622-2-222-22-2-2-200002-22000000000000−2i2i2i−2i2i−2i−2i2i00000000-2-222-2-22-22220000-22-20000000000002i−2i−2i2i−2i2i2i−2i00000000
χ8722-2-22-22-22002-2-2200000002−22−2−22−222−22−2−22−2200000000-2-222-22-22-200-222-20000000−22−222−22−2−22−222−22−200000000
χ8822-2-22-22-22002-2-220000000−22−222−22−2−22−222−22−200000000-2-222-22-22-200-222-200000002−22−2−22−222−22−2−22−2200000000
χ8922-2-22-22-2200-222-200000002−22−2−22−22−22−222−22−200000000-2-222-22-22-2002-2-220000000−22−222−22−22−22−2−22−2200000000
χ9022-2-22-22-2200-222-20000000−22−222−22−22−22−2−22−2200000000-2-222-22-22-2002-2-2200000002−22−2−22−22−22−222−22−200000000
χ918-8000000042−4200000000000000000000000000000000000-880000000−424200000000000000000000000000000000000
χ928-80000000−424200000000000000000000000000000000000-88000000042−4200000000000000000000000000000000000

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