Finite Group Databasebeta

← Group #13025137

Character table — Group #13025137

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size11112222224444444444444444444444444444888888888888888888888888101010101010101010101010202020202020202020208080808080808080
order124424888844588101010161616161616161620202020404040404040404020202020404040408080808080808080808080808080808088881616161616161616244488161616161616161616161616
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii
χ5111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-1
χ6111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-111
χ7111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111ii−i−i−i−iii
χ8111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111−i−iiiii−i−i
χ91111111111-1-11-1-11111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-11-11-11-11-1
χ101111111111-1-11-1-11111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-1-11-11-11-11
χ111111111111-1-11-1-11111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111i−ii−i−ii−ii
χ121111111111-1-11-1-11111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111−ii−iii−ii−i
χ131111111111-1-11-1-1111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-111111-1-111-1-11
χ141111111111-1-11-1-1111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-11111-111-1-111-1
χ151111111111-1-11-1-1111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-111-1-1-1-1i−i−ii−iii−i
χ161111111111-1-11-1-1111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-111-1-1-1-1−iii−ii−i−ii
χ17222222-2-2-2-2222-2-2222000000002222-2-2-2-2-2-2-2-22222-2-2-2-20000000000000000222200000000-2-2-2-222000000000000
χ18222222-2-2-2-2222-2-2222000000002222-2-2-2-2-2-2-2-22222-2-2-2-20000000000000000-2-2-2-2000000002222-2-2000000000000
χ19222222-2-2-2-2-2-2222222000000002222-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000022220000000022-2-2-2-2000000000000
χ20222222-2-2-2-2-2-2222222000000002222-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000-2-2-2-200000000-2-22222000000000000
χ212222-2-200002i−2i2002-2-222−2−2i2i2−i2−i222-2-2000000002i2i−2i−2i00002222−2−2−2−2i2i2i2i2−i2−i2−i2−i222-2-22222−2−2−2−200002i−2ii2i2−i2−i200000000
χ222222-2-200002i−2i2002-2-222−2−2i2i2−i2−i222-2-2000000002i2i−2i−2i00002222−2−2−2−2i2i2i2i2−i2−i2−i2−i2-2-222−2−2−2−222220000−2i2i−i2−i2i2i200000000
χ232222-2-200002i−2i2002-2-2−2−222−i2−i2i2i222-2-2000000002i2i−2i−2i0000−2−2−2−22222−i2−i2−i2−i2i2i2i2i222-2-2−2−2−2−2222200002i−2i−i2−i2i2i200000000
χ242222-2-200002i−2i2002-2-2−2−222−i2−i2i2i222-2-2000000002i2i−2i−2i0000−2−2−2−22222−i2−i2−i2−i2i2i2i2i2-2-2222222−2−2−2−20000−2i2ii2i2−i2−i200000000
χ252222-2-20000−2i2i2002-2-222−2−2−i2−i2i2i222-2-200000000−2i−2i2i2i00002222−2−2−2−2−i2−i2−i2−i2i2i2i2i222-2-22222−2−2−2−20000−2i2i−i2−i2i2i200000000
χ262222-2-20000−2i2i2002-2-222−2−2−i2−i2i2i222-2-200000000−2i−2i2i2i00002222−2−2−2−2−i2−i2−i2−i2i2i2i2i2-2-222−2−2−2−2222200002i−2ii2i2−i2−i200000000
χ272222-2-20000−2i2i2002-2-2−2−222i2i2−i2−i222-2-200000000−2i−2i2i2i0000−2−2−2−22222i2i2i2i2−i2−i2−i2−i222-2-2−2−2−2−222220000−2i2ii2i2−i2−i200000000
χ282222-2-20000−2i2i2002-2-2−2−222i2i2−i2−i222-2-200000000−2i−2i2i2i0000−2−2−2−22222i2i2i2i2−i2−i2−i2−i2-2-2222222−2−2−2−200002i−2i−i2−i2i2i200000000
χ2922-2-22-200000022i−2i222i2−i2i2−i22−22−2-2-2-2-20000000000002i2i−2i−2ii2i2−i2−i2i2i2−i2−i222−2−222−2−22i−2i2i−2i22−2−222−2−22-20000i2−i2i2−i200000000
χ3022-2-22-200000022i−2i222i2−i2i2−i22−22−2-2-2-2-20000000000002i2i−2i−2ii2i2−i2−i2i2i2−i2−i222−2−222−2−2−2i2i−2i2i−2−222−2−222-220000−i2i2−i2i200000000
χ3122-2-22-200000022i−2i222−i2i2−i2i2−22−22-2-2-2-20000000000002i2i−2i−2i−i2−i2i2i2−i2−i2i2i2−2−222−2−2222i−2i2i−2i−2−222−2−2222-20000−i2i2−i2i200000000
χ3222-2-22-200000022i−2i222−i2i2−i2i2−22−22-2-2-2-20000000000002i2i−2i−2i−i2−i2i2i2−i2−i2i2i2−2−222−2−222−2i2i−2i2i22−2−222−2−2-220000i2−i2i2−i200000000
χ3322-2-22-20000002−2i2i222i2−i2i2−i2−22−22-2-2-2-2000000000000−2i−2i2i2ii2i2−i2−i2i2i2−i2−i2−2−222−2−2222i−2i2i−2i22−2−222−2−2-220000−i2i2−i2i200000000
χ3422-2-22-20000002−2i2i222i2−i2i2−i2−22−22-2-2-2-2000000000000−2i−2i2i2ii2i2−i2−i2i2i2−i2−i2−2−222−2−222−2i2i−2i2i−2−222−2−2222-20000i2−i2i2−i200000000
χ3522-2-22-20000002−2i2i222−i2i2−i2i22−22−2-2-2-2-2000000000000−2i−2i2i2i−i2−i2i2i2−i2−i2i2i222−2−222−2−22i−2i2i−2i−2−222−2−222-220000i2−i2i2−i200000000
χ3622-2-22-20000002−2i2i222−i2i2−i2i22−22−2-2-2-2-2000000000000−2i−2i2i2i−i2−i2i2i2−i2−i2i2i222−2−222−2−2−2i2i−2i2i22−2−222−2−22-20000−i2i2−i2i200000000
χ3722-2-2-2222-2-2002002-2-200002i−2i−2i2i-2-2222222-2-2-2-200000000000000002i2i−2i−2i−2i−2i2i2i2i−2i−2i2i00000000002i−2i00-222-200000000
χ3822-2-2-2222-2-2002002-2-200002i−2i−2i2i-2-2222222-2-2-2-200000000000000002i2i−2i−2i−2i−2i2i2i−2i2i2i−2i0000000000−2i2i002-2-2200000000
χ3922-2-2-2222-2-2002002-2-20000−2i2i2i−2i-2-2222222-2-2-2-20000000000000000−2i−2i2i2i2i2i−2i−2i2i−2i−2i2i00000000002i−2i002-2-2200000000
χ4022-2-2-2222-2-2002002-2-20000−2i2i2i−2i-2-2222222-2-2-2-20000000000000000−2i−2i2i2i2i2i−2i−2i−2i2i2i−2i0000000000−2i2i00-222-200000000
χ4122-2-2-22-2-222002002-2-22i−2i−2i2i0000-2-222-2-2-2-22222000000002i2i−2i−2i−2i−2i2i2i000000002i−2i−2i2i22-2-2-2-22200−2i2i00000000000000
χ4222-2-2-22-2-222002002-2-22i−2i−2i2i0000-2-222-2-2-2-22222000000002i2i−2i−2i−2i−2i2i2i00000000−2i2i2i−2i-2-22222-2-2002i−2i00000000000000
χ4322-2-2-22-2-222002002-2-2−2i2i2i−2i0000-2-222-2-2-2-2222200000000−2i−2i2i2i2i2i−2i−2i000000002i−2i−2i2i-2-22222-2-200−2i2i00000000000000
χ4422-2-2-22-2-222002002-2-2−2i2i2i−2i0000-2-222-2-2-2-2222200000000−2i−2i2i2i2i2i−2i−2i00000000−2i2i2i−2i22-2-2-2-222002i−2i00000000000000
χ45444444444444-144-1-1-144444444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000000000
χ46444444444444-144-1-1-1-4-4-4-4-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111000000000000000000000000000000
χ474444444444-4-4-1-4-4-1-1-14444-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111000000000000000000000000000000
χ484444444444-4-4-1-4-4-1-1-1-4-4-4-44444-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1000000000000000000000000000000
χ49444444-4-4-4-444-1-4-4-1-1-100000000-1-1-1-111111111-1-1-1-11111i5−i5i5−i5i5−i5i5−i5i5−i5i5−i5i5−i5i5−i5000000000000000000000000000000
χ50444444-4-4-4-444-1-4-4-1-1-100000000-1-1-1-111111111-1-1-1-11111−i5i5−i5i5−i5i5−i5i5−i5i5−i5i5−i5i5−i5i5000000000000000000000000000000
χ51444444-4-4-4-4-4-4-144-1-1-100000000-1-1-1-1111111111111-1-1-1-1i5−i5i5−i5i5−i5i5−i5−i5i5−i5i5−i5i5−i5i5000000000000000000000000000000
χ52444444-4-4-4-4-4-4-144-1-1-100000000-1-1-1-1111111111111-1-1-1-1−i5i5−i5i5−i5i5−i5i5i5−i5i5−i5i5−i5i5−i5000000000000000000000000000000
χ534444-4-400004i−4i-100-1112222−22−222i22i2−2i2−2i2-1-111i5i5−i5−i5i5i5−i5−i5−i−iii5−55−5−ζ14+ζ42−ζ46+ζ58ζ26−ζ62+ζ74−ζ78−ζ14+ζ42−ζ46+ζ58ζ26−ζ62+ζ74−ζ78ζ14−ζ42+ζ46−ζ58−ζ26+ζ62−ζ74+ζ78ζ14−ζ42+ζ46−ζ58−ζ26+ζ62−ζ74+ζ78ζ26+ζ62+ζ74+ζ78ζ14+ζ42+ζ46+ζ58ζ26+ζ62+ζ74+ζ78ζ14+ζ42+ζ46+ζ58−ζ26−ζ62−ζ74−ζ78−ζ14−ζ42−ζ46−ζ58−ζ26−ζ62−ζ74−ζ78−ζ14−ζ42−ζ46−ζ58000000000000000000000000000000
χ544444-4-400004i−4i-100-1112222−22−222i22i2−2i2−2i2-1-111−i5−i5i5i5−i5−i5i5i5−i−iii−55−55ζ26−ζ62+ζ74−ζ78−ζ14+ζ42−ζ46+ζ58ζ26−ζ62+ζ74−ζ78−ζ14+ζ42−ζ46+ζ58−ζ26+ζ62−ζ74+ζ78ζ14−ζ42+ζ46−ζ58−ζ26+ζ62−ζ74+ζ78ζ14−ζ42+ζ46−ζ58ζ14+ζ42+ζ46+ζ58ζ26+ζ62+ζ74+ζ78ζ14+ζ42+ζ46+ζ58ζ26+ζ62+ζ74+ζ78−ζ14−ζ42−ζ46−ζ58−ζ26−ζ62−ζ74−ζ78−ζ14−ζ42−ζ46−ζ58−ζ26−ζ62−ζ74−ζ78000000000000000000000000000000
χ554444-4-400004i−4i-100-111−22−222222−2i2−2i22i22i2-1-111i5i5−i5−i5i5i5−i5−i5−i−iii5−55−5ζ14−ζ42+ζ46−ζ58−ζ26+ζ62−ζ74+ζ78ζ14−ζ42+ζ46−ζ58−ζ26+ζ62−ζ74+ζ78−ζ14+ζ42−ζ46+ζ58ζ26−ζ62+ζ74−ζ78−ζ14+ζ42−ζ46+ζ58ζ26−ζ62+ζ74−ζ78−ζ26−ζ62−ζ74−ζ78−ζ14−ζ42−ζ46−ζ58−ζ26−ζ62−ζ74−ζ78−ζ14−ζ42−ζ46−ζ58ζ26+ζ62+ζ74+ζ78ζ14+ζ42+ζ46+ζ58ζ26+ζ62+ζ74+ζ78ζ14+ζ42+ζ46+ζ58000000000000000000000000000000
χ564444-4-400004i−4i-100-111−22−222222−2i2−2i22i22i2-1-111−i5−i5i5i5−i5−i5i5i5−i−iii−55−55−ζ26+ζ62−ζ74+ζ78ζ14−ζ42+ζ46−ζ58−ζ26+ζ62−ζ74+ζ78ζ14−ζ42+ζ46−ζ58ζ26−ζ62+ζ74−ζ78−ζ14+ζ42−ζ46+ζ58ζ26−ζ62+ζ74−ζ78−ζ14+ζ42−ζ46+ζ58−ζ14−ζ42−ζ46−ζ58−ζ26−ζ62−ζ74−ζ78−ζ14−ζ42−ζ46−ζ58−ζ26−ζ62−ζ74−ζ78ζ14+ζ42+ζ46+ζ58ζ26+ζ62+ζ74+ζ78ζ14+ζ42+ζ46+ζ58ζ26+ζ62+ζ74+ζ78000000000000000000000000000000
χ574444-4-40000−4i4i-100-1112222−22−22−2i2−2i22i22i2-1-111i5i5−i5−i5i5i5−i5−i5ii−i−i−55−55−ζ14+ζ42−ζ46+ζ58ζ26−ζ62+ζ74−ζ78−ζ14+ζ42−ζ46+ζ58ζ26−ζ62+ζ74−ζ78ζ14−ζ42+ζ46−ζ58−ζ26+ζ62−ζ74+ζ78ζ14−ζ42+ζ46−ζ58−ζ26+ζ62−ζ74+ζ78−ζ26−ζ62−ζ74−ζ78−ζ14−ζ42−ζ46−ζ58−ζ26−ζ62−ζ74−ζ78−ζ14−ζ42−ζ46−ζ58ζ26+ζ62+ζ74+ζ78ζ14+ζ42+ζ46+ζ58ζ26+ζ62+ζ74+ζ78ζ14+ζ42+ζ46+ζ58000000000000000000000000000000
χ584444-4-40000−4i4i-100-1112222−22−22−2i2−2i22i22i2-1-111−i5−i5i5i5−i5−i5i5i5ii−i−i5−55−5ζ26−ζ62+ζ74−ζ78−ζ14+ζ42−ζ46+ζ58ζ26−ζ62+ζ74−ζ78−ζ14+ζ42−ζ46+ζ58−ζ26+ζ62−ζ74+ζ78ζ14−ζ42+ζ46−ζ58−ζ26+ζ62−ζ74+ζ78ζ14−ζ42+ζ46−ζ58−ζ14−ζ42−ζ46−ζ58−ζ26−ζ62−ζ74−ζ78−ζ14−ζ42−ζ46−ζ58−ζ26−ζ62−ζ74−ζ78ζ14+ζ42+ζ46+ζ58ζ26+ζ62+ζ74+ζ78ζ14+ζ42+ζ46+ζ58ζ26+ζ62+ζ74+ζ78000000000000000000000000000000
χ594444-4-40000−4i4i-100-111−22−2222222i22i2−2i2−2i2-1-111i5i5−i5−i5i5i5−i5−i5ii−i−i−55−55ζ14−ζ42+ζ46−ζ58−ζ26+ζ62−ζ74+ζ78ζ14−ζ42+ζ46−ζ58−ζ26+ζ62−ζ74+ζ78−ζ14+ζ42−ζ46+ζ58ζ26−ζ62+ζ74−ζ78−ζ14+ζ42−ζ46+ζ58ζ26−ζ62+ζ74−ζ78ζ26+ζ62+ζ74+ζ78ζ14+ζ42+ζ46+ζ58ζ26+ζ62+ζ74+ζ78ζ14+ζ42+ζ46+ζ58−ζ26−ζ62−ζ74−ζ78−ζ14−ζ42−ζ46−ζ58−ζ26−ζ62−ζ74−ζ78−ζ14−ζ42−ζ46−ζ58000000000000000000000000000000
χ604444-4-40000−4i4i-100-111−22−2222222i22i2−2i2−2i2-1-111−i5−i5i5i5−i5−i5i5i5ii−i−i5−55−5−ζ26+ζ62−ζ74+ζ78ζ14−ζ42+ζ46−ζ58−ζ26+ζ62−ζ74+ζ78ζ14−ζ42+ζ46−ζ58ζ26−ζ62+ζ74−ζ78−ζ14+ζ42−ζ46+ζ58ζ26−ζ62+ζ74−ζ78−ζ14+ζ42−ζ46+ζ58ζ14+ζ42+ζ46+ζ58ζ26+ζ62+ζ74+ζ78ζ14+ζ42+ζ46+ζ58ζ26+ζ62+ζ74+ζ78−ζ14−ζ42−ζ46−ζ58−ζ26−ζ62−ζ74−ζ78−ζ14−ζ42−ζ46−ζ58−ζ26−ζ62−ζ74−ζ78000000000000000000000000000000
χ6144-4-44-4000000-14i−4i-1-1-12i2−2i22i2−2i222−2222−221111i5i5−i5−i5−i5−i5i5i55−55−5−i−iiiζ14+ζ42+ζ46+ζ58ζ26+ζ62+ζ74+ζ78−ζ14−ζ42−ζ46−ζ58−ζ26−ζ62−ζ74−ζ78ζ14+ζ42+ζ46+ζ58ζ26+ζ62+ζ74+ζ78−ζ14−ζ42−ζ46−ζ58−ζ26−ζ62−ζ74−ζ78−ζ14+ζ42−ζ46+ζ58ζ26−ζ62+ζ74−ζ78ζ14−ζ42+ζ46−ζ58−ζ26+ζ62−ζ74+ζ78−ζ14+ζ42−ζ46+ζ58ζ26−ζ62+ζ74−ζ78ζ14−ζ42+ζ46−ζ58−ζ26+ζ62−ζ74+ζ78000000000000000000000000000000
χ6244-4-44-4000000-14i−4i-1-1-12i2−2i22i2−2i222−2222−221111−i5−i5i5i5i5i5−i5−i5−55−55−i−iiiζ26+ζ62+ζ74+ζ78ζ14+ζ42+ζ46+ζ58−ζ26−ζ62−ζ74−ζ78−ζ14−ζ42−ζ46−ζ58ζ26+ζ62+ζ74+ζ78ζ14+ζ42+ζ46+ζ58−ζ26−ζ62−ζ74−ζ78−ζ14−ζ42−ζ46−ζ58ζ26−ζ62+ζ74−ζ78−ζ14+ζ42−ζ46+ζ58−ζ26+ζ62−ζ74+ζ78ζ14−ζ42+ζ46−ζ58ζ26−ζ62+ζ74−ζ78−ζ14+ζ42−ζ46+ζ58−ζ26+ζ62−ζ74+ζ78ζ14−ζ42+ζ46−ζ58000000000000000000000000000000
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Here ζ is a primitive root of unity of order 80 (ζ80 = 1); i = ζ20.