Finite Group Databasebeta

← Group #72319389

Character table — Group #72319389

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112
size1111222222222222222244444444444444444444444444444888888888888888888888888888888888161616161616161616161616161616161616161616163232323232323232
order12224444444488888888222224488888888888888161616161616161622444444448888888888816161616161616161616161644444488888888161616161616161622448888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-1111111-1-111111-1-1-1-111111111111111-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111-1-1-1-1111111111111111111111111111-1-1-1-1-1-1111-1-1-1-1111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ611111111111111111111-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111111111-1-1-1-111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-111111111-1-1-1-11111
χ811111111111111111111-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111111111-1-1-1-1
χ9111111111111-1-1-1-1111111-1-111111-1-1-1-1-1-1-1-1-1-111111111111111-1-11-111111-1-11111-1-11111-1-1-1-1-1-1-1-111-1-1-1-11-1-1-1-1-1111111-1-1-1-11-11-111-1-1
χ10111111111111-1-1-1-1111111-1-111111-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-11-1-1-1111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111-11111-1-11111-1-1-1-1-11-11-1-111
χ11111111111111-1-1-1-1111111-1-111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-11-111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-111111-11-1-1-111
χ12111111111111-1-1-1-1111111-1-111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-11-1-1-1111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-11-1111111-1-1-1-11111-11-1111-1-1
χ13111111111111-1-1-1-11111-1-11111111-1-1-1-1-1-1-1-1-1-1111111111111-1-111-11111-1-1111111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-11-1-1-1-111-1-1-1-11111-11-11-1-111
χ14111111111111-1-1-1-11111-1-11111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-11-1-11-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-111111-1-1-1-1-1-111111-11-111-1-1
χ15111111111111-1-1-1-11111-1-11111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-111-11111-1-111-1-1-1-1-1-1-1-1-1-111111111111111-11-1-1-1-1-1-11111-1-1-1-1-11-1111-1-1
χ16111111111111-1-1-1-11111-1-11111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-11-1-11-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-1-111111111111-1-1-1-11-11-1-1-111
χ171111-1-11111-1-11111-1-1-1-11111-1-111111-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i111-11-1-1-1-1-11-1-1-1-1ii−i−i11ii−i−iiiii−i−i−i−i1-1ii−i−i1111-1-1i−iii−i−iii−i−i11-1-1i−ii−i
χ181111-1-11111-1-11111-1-1-1-11111-1-111111-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i-1-11-11-1-1-1111-1-1-1-1−i−iii11ii−i−iiiii−i−i−i−i-11−i−iii11-1-111−iiii−i−iii−i−i-1-111−ii−ii
χ191111-1-11111-1-11111-1-1-1-11111-1-111111-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii111-11-1-1-1-1-11-1-1-1-1−i−iii11−i−iii−i−i−i−iiiii1-1−i−iii1111-1-1−ii−i−iii−i−iii11-1-1−ii−ii
χ201111-1-11111-1-11111-1-1-1-11111-1-111111-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii-1-11-11-1-1-1111-1-1-1-1ii−i−i11−i−iii−i−i−i−iiiii-11ii−i−i11-1-111i−i−i−iii−i−iii-1-111i−ii−i
χ211111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i11-11-1111-1-111111ii−i−i11ii−i−iiiii−i−i−i−i1-1ii−i−i-1-111-1-1i−i−i−iii−i−iii-1-111−ii−ii
χ221111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i-1-1-11-11111111111−i−iii11ii−i−iiiii−i−i−i−i-11−i−iii-1-1-1-111−ii−i−iii−i−iii11-1-1i−ii−i
χ231111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii11-11-1111-1-111111−i−iii11−i−iii−i−i−i−iiiii1-1−i−iii-1-111-1-1−iiii−i−iii−i−i-1-111i−ii−i
χ241111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii-1-1-11-11111111111ii−i−i11−i−iii−i−i−i−iiiii-11ii−i−i-1-1-1-111i−iii−i−iii−i−i11-1-1−ii−ii
χ251111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111-1-111111111-1-1iiii−i−i−i−i111-1-11-11-1-11-1-111ii−i−i-1-1ii−i−i−i−i−i−iiiii1-1−i−iii1-1-1-111i−iii−i−i−i−iii1-1-11i−i−ii
χ261111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111-1-111111111-1-1iiii−i−i−i−i-1-11-1-11-11111-1-111−i−iii-1-1ii−i−i−i−i−i−iiiii-11ii−i−i1-111-1-1−iiii−i−i−i−iii-111-1−iii−i
χ271111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111-1-111111111-1-1−i−i−i−iiiii111-1-11-11-1-11-1-111−i−iii-1-1−i−iiiiiii−i−i−i−i1-1ii−i−i1-1-1-111−ii−i−iiiii−i−i1-1-11−iii−i
χ281111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111-1-111111111-1-1−i−i−i−iiiii-1-11-1-11-11111-1-111ii−i−i-1-1−i−iiiiiii−i−i−i−i-11−i−iii1-111-1-1i−i−i−iiiii−i−i-111-1i−i−ii
χ291111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111-1-111111111-1-1iiii−i−i−i−i11-111-11-1-1-1111-1-1ii−i−i-1-1ii−i−i−i−i−i−iiiii1-1−i−iii-11-1-111i−i−i−iiiii−i−i-111-1−iii−i
χ301111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111-1-111111111-1-1iiii−i−i−i−i-1-1-111-11-111111-1-1−i−iii-1-1ii−i−i−i−i−i−iiiii-11ii−i−i-1111-1-1−ii−i−iiiii−i−i1-1-11i−i−ii
χ311111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111-1-111111111-1-1−i−i−i−iiiii11-111-11-1-1-1111-1-1−i−iii-1-1−i−iiiiiii−i−i−i−i1-1ii−i−i-11-1-111−iiii−i−i−i−iii-111-1i−i−ii
χ321111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111-1-111111111-1-1−i−i−i−iiiii-1-1-111-11-111111-1-1ii−i−i-1-1−i−iiiiiii−i−i−i−i-11−i−iii-1111-1-1i−iii−i−i−i−iii1-1-11−iii−i
χ332222222222222222-2-2-2-22222222-2-2222222-2-2-2-2-2-2000000000022222200-2-2-2-2-20000-2-2000000000000000000-2-20000000000000000000000
χ342222222222222222-2-2-2-2-2-2-2-2222-2-2222222-2-2-2-2-2-20000000000-2-2-2-2-2-200-222220000-2-2000000000000000000220000000000000000000000
χ35222222222222-2-2-2-2-2-2-2-222-2-2222-2-2-2-2-2-2-2-22222-2-2000000000022-2-22-200-2-2-222000022000000000000000000-220000000000000000000000
χ36222222222222-2-2-2-2-2-2-2-2-2-222222-2-2-2-2-2-2-2-22222-2-20000000000-2-222-2200-222-2-20000220000000000000000002-20000000000000000000000
χ3722222222-2-222000022220000-2-2-2220000000000-2-2222222222200000022-20000222200-2-2-2-200000000-2-20000000000-2-20000000000000000
χ3822222222-2-222000022220000-2-2-2220000000000-2-222222222-2-2000000-2-2-20000-2-2-2-200-2-2-2-200000000220000000000220000000000000000
χ3922222222-2-222000022220000-2-2-2220000000000-2-2-2-2-2-2-2-2-2-22200000022-20000-2-2-2-200222200000000-2-20000000000220000000000000000
χ4022222222-2-222000022220000-2-2-2220000000000-2-2-2-2-2-2-2-2-2-2-2-2000000-2-2-20000222200222200000000220000000000-2-20000000000000000
χ41222222-2-222-2-2222200002222-22-200-2-222-2-2000000i2i2−i2−i2i2i2−i2−i200-2-2-2-2220000000000000i2−i2i2−i2i2i2−i2−i2i2i2−i2−i200000000000000i2−i2i2−i2i2−i2i2−i200000000
χ42222222-2-222-2-2222200002222-22-200-2-222-2-2000000−i2−i2i2i2−i2−i2i2i200-2-2-2-2220000000000000−i2i2−i2i2−i2−i2i2i2−i2−i2i2i200000000000000−i2i2−i2i2−i2i2−i2i200000000
χ43222222-2-222-2-222220000-2-2-2-2-22-200-2-222-2-2000000i2i2−i2−i2i2i2−i2−i2002222-2-20000000000000i2−i2i2−i2i2i2−i2−i2i2i2−i2−i200000000000000−i2i2−i2i2−i2i2−i2i200000000
χ44222222-2-222-2-222220000-2-2-2-2-22-200-2-222-2-2000000−i2−i2i2i2−i2−i2i2i2002222-2-20000000000000−i2i2−i2i2−i2−i2i2i2−i2−i2i2i200000000000000i2−i2i2−i2i2−i2i2−i200000000
χ45222222-2-222-2-2-2-2-2-2000022-2-2-22-20022-2-222000000i2i2−i2−i2i2i2−i2−i200-2-2222-20000000000000i2−i2i2−i2−i2−i2i2i2−i2−i2i2i200000000000000i2−i2i2−i2−i2i2−i2i200000000
χ46222222-2-222-2-2-2-2-2-2000022-2-2-22-20022-2-222000000−i2−i2i2i2−i2−i2i2i200-2-2222-20000000000000−i2i2−i2i2i2i2−i2−i2i2i2−i2−i200000000000000−i2i2−i2i2i2−i2i2−i200000000
χ47222222-2-222-2-2-2-2-2-20000-2-222-22-20022-2-222000000i2i2−i2−i2i2i2−i2−i20022-2-2-220000000000000i2−i2i2−i2−i2−i2i2i2−i2−i2i2i200000000000000−i2i2−i2i2i2−i2i2−i200000000
χ48222222-2-222-2-2-2-2-2-20000-2-222-22-20022-2-222000000−i2−i2i2i2−i2−i2i2i20022-2-2-220000000000000−i2i2−i2i2i2i2−i2−i2i2i2−i2−i200000000000000i2−i2i2−i2−i2i2−i2i200000000
χ492222-2-22222-2-2222222222222-2-22-2-222-2-2-2-222222200000000002-22-2-2-200-222220000-2-2000000000000000000-2-20000000000000000000000
χ502222-2-22222-2-222222222-2-2-2-2-2-22-2-222-2-2-2-22222220000000000-22-222200-2-2-2-2-20000-2-2000000000000000000220000000000000000000000
χ512222-2-22222-2-2-2-2-2-2222222-2-2-2-22-2-2-2-22222-2-2-2-22200000000002-2-22-2200-222-2-2000022000000000000000000-220000000000000000000000
χ522222-2-22222-2-2-2-2-2-22222-2-222-2-22-2-2-2-22222-2-2-2-2220000000000-222-22-200-2-2-2220000220000000000000000002-20000000000000000000000
χ532222-2-222-2-2-2-20000-2-2-2-2000022-2220000000000222i2i2i2i−2i−2i−2i−2i22000000-2-2-200002i2i−2i−2i00−2i−2i2i2i00000000-220000000000−2i2i0000000000000000
χ542222-2-222-2-2-2-20000-2-2-2-2000022-2220000000000222i2i2i2i−2i−2i−2i−2i-2-200000022-20000−2i−2i2i2i00−2i−2i2i2i000000002-200000000002i−2i0000000000000000
χ552222-2-222-2-2-2-20000-2-2-2-2000022-222000000000022−2i−2i−2i−2i2i2i2i2i22000000-2-2-20000−2i−2i2i2i002i2i−2i−2i00000000-2200000000002i−2i0000000000000000
χ562222-2-222-2-2-2-20000-2-2-2-2000022-222000000000022−2i−2i−2i−2i2i2i2i2i-2-200000022-200002i2i−2i−2i002i2i−2i−2i000000002-20000000000−2i2i0000000000000000
χ572222-2-2-2-222222222000022222-2-200-2-2-2-22200000022−2−2−2−22200-22-22-2-200000000000002−2−2222−2−2−2−222000000000000002−2−222−2−2200000000
χ582222-2-2-2-222222222000022222-2-200-2-2-2-222000000−2−22222−2−200-22-22-2-20000000000000−222−2−2−22222−2−200000000000000−222−2−222−200000000
χ592222-2-2-2-2222222220000-2-2-2-22-2-200-2-2-2-22200000022−2−2−2−222002-22-22200000000000002−2−2222−2−2−2−22200000000000000−222−2−222−200000000
χ602222-2-2-2-2222222220000-2-2-2-22-2-200-2-2-2-222000000−2−22222−2−2002-22-2220000000000000−222−2−2−22222−2−2000000000000002−2−222−2−2200000000
χ612222-2-2-2-22222-2-2-2-2000022-2-22-2-2002222-2-200000022−2−2−2−22200-222-2-2200000000000002−2−22−2−22222−2−2000000000000002−2−22−222−200000000
χ622222-2-2-2-22222-2-2-2-2000022-2-22-2-2002222-2-2000000−2−22222−2−200-222-2-220000000000000−222−222−2−2−2−22200000000000000−222−22−2−2200000000
χ632222-2-2-2-22222-2-2-2-20000-2-2222-2-2002222-2-200000022−2−2−2−222002-2-222-200000000000002−2−22−2−22222−2−200000000000000−222−22−2−2200000000
χ642222-2-2-2-22222-2-2-2-20000-2-2222-2-2002222-2-2000000−2−22222−2−2002-2-222-20000000000000−222−222−2−2−2−222000000000000002−2−22−222−200000000
χ6522-2-22i−2i2-2002i−2i22−2−22i2i−2i−2i00000002-22−2i2−i2i2−i2i2i2−i2−i2002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ32-20000002i−2i000002ζ−2ζ2ζ3−2ζ32−200001+i−1−i1+i−1−i1−i−1+i1−i−1+i001+i−1−i1−i−1+i002−2i2−i2000000000000000000
χ6622-2-22i−2i2-2002i−2i22−2−22i2i−2i−2i00000002-22−2i2−i2i2−i2i2i2−i2−i2002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3-22000000−2i2i00000−2ζ2ζ−2ζ32ζ32−200001+i−1−i1+i−1−i1−i−1+i1−i−1+i00−1−i1+i−1+i1−i00−22−i2i2000000000000000000
χ6722-2-22i−2i2-2002i−2i22−2−22i2i−2i−2i00000002-22−2i2−i2i2−i2i2i2−i2−i200−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ32-20000002i−2i00000−2ζ2ζ−2ζ32ζ32−20000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00−1−i1+i−1+i1−i002−2i2−i2000000000000000000
χ6822-2-22i−2i2-2002i−2i22−2−22i2i−2i−2i00000002-22−2i2−i2i2−i2i2i2−i2−i200−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3-22000000−2i2i000002ζ−2ζ2ζ3−2ζ32−20000−1−i1+i−1−i1+i−1+i1−i−1+i1−i001+i−1−i1−i−1+i00−22−i2i2000000000000000000
χ6922-2-22i−2i2-2002i−2i−2−2222i2i−2i−2i00000002-2−22−i2i2−i2i2−i2−i2i2i2002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ32-20000002i−2i000002ζ−2ζ2ζ3−2ζ3−220000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00−1−i1+i−1+i1−i00−22−i2i2000000000000000000
χ7022-2-22i−2i2-2002i−2i−2−2222i2i−2i−2i00000002-2−22−i2i2−i2i2−i2−i2i2i2002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3-22000000−2i2i00000−2ζ2ζ−2ζ32ζ3−220000−1−i1+i−1−i1+i−1+i1−i−1+i1−i001+i−1−i1−i−1+i002−2i2−i2000000000000000000
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Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.