Finite Group Databasebeta

← Group #13145715

Character table — Group #13145715

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162
size111122222222222222222222222222222244444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444181818181818181818181818181818181818181818181818727272727272727272727272
order1222333446666666668888121212122424242424242424333336666666666666661212121212121212121212121212121212121212121212122424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424241616161616161616484848484848484848484848484848482244666612121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ51-11-1111-11-1-1-1-1-1111-111-1-1-1-1111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i1-1i−i11-1-1ii−i−i
χ61-11-1111-11-1-1-1-1-1111-111-1-1-1-1111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i-11−ii-1-111−i−iii
χ71-11-1111-11-1-1-1-1-1111-111-1-1-1-1111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiii1-1−ii11-1-1−i−iii
χ81-11-1111-11-1-1-1-1-1111-111-1-1-1-1111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiii-11i−i-1-111ii−i−i
χ9222222222222222222-2-2-2-22222-2-2-2-2-2-2-2-222222222222222222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000
χ102222222-2-22222222220000-2-2-2-20000000022222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000000000000000000022−2−222−2−22222−2−2−2−22222−2−2−2−2000000000000
χ112222222-2-22222222220000-2-2-2-20000000022222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000−2−222−2−222−2−2−2−22222−2−2−2−22222000000000000
χ12222222-122222-1-122-1222222222222222222-1-1-1-122-1-1-1-1-1-1-1-12-1-1-1-12-122-1-1-1-1-1-1-1-12-122-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000002200-1-1-1-10000
χ13222222-122222-1-122-1222222222222222222-1-1-1-122-1-1-1-1-1-1-1-12-1-1-1-12-122-1-1-1-1-1-1-1-12-122-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000-2-20011110000
χ14222222-122222-1-122-12-2-2-2-22222-2-2-2-2-2-2-2-22-1-1-1-122-1-1-1-1-1-1-1-12-1-1-1-12-122-1-1-1-1-1-1-1-12-122-1-1-1-1-1-1-1-1-2-2-2-2-2-2111111111111111111-2-2-2-2-2-21111111111111111110000000000000000000000000000−i3i3−i3i30000
χ15222222-122222-1-122-12-2-2-2-22222-2-2-2-2-2-2-2-22-1-1-1-122-1-1-1-1-1-1-1-12-1-1-1-12-122-1-1-1-1-1-1-1-12-122-1-1-1-1-1-1-1-1-2-2-2-2-2-2111111111111111111-2-2-2-2-2-21111111111111111110000000000000000000000000000i3−i3i3−i30000
χ1622222-122222-1222-12-12222222222222222-12-1-1-1-1-122-1-1-1-1-1-1-12-1-1-1-12-1-122-1-1-1-1-1-1-12-1-122-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000000220000-1-1-1-1
χ1722222-122222-1222-12-12222222222222222-12-1-1-1-1-122-1-1-1-1-1-1-12-1-1-1-12-1-122-1-1-1-1-1-1-12-1-122-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000000-2-200001111
χ1822222-122222-1222-12-1-2-2-2-22222-2-2-2-2-2-2-2-2-12-1-1-1-1-122-1-1-1-1-1-1-12-1-1-1-12-1-122-1-1-1-1-1-1-12-1-122-1-1-1-1-1-1111111-2-2-2-2-2-2111111111111111111-2-2-2-2-2-211111111111100000000000000000000000000000000−i3i3−i3i3
χ1922222-122222-1222-12-1-2-2-2-22222-2-2-2-2-2-2-2-2-12-1-1-1-1-122-1-1-1-1-1-1-12-1-1-1-12-1-122-1-1-1-1-1-1-12-1-122-1-1-1-1-1-1111111-2-2-2-2-2-2111111111111111111-2-2-2-2-2-211111111111100000000000000000000000000000000i3−i3i3−i3
χ202222-12222-1-1222-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-12-1-1-1-1-1-122-1-1-1-1-1-12-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ212222-12222-1-1222-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-12-1-1-1-1-1-122-1-1-1-1-1-12-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111111111111111000000000000
χ222222-12222-1-1222-1222-2-2-2-2-1-1-1-111111111-1-12-1-1-1-1-1-122-1-1-1-1-1-12-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-1-2-21111-2-21111-2-2-2-211111111-2-21111-2-21111-2-2-2-2111111110000000033−3−333−3−333−3−333−3−3000000000000
χ232222-12222-1-1222-1222-2-2-2-2-1-1-1-111111111-1-12-1-1-1-1-1-122-1-1-1-1-1-12-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-1-2-21111-2-21111-2-2-2-211111111-2-21111-2-21111-2-2-2-21111111100000000−3−333−3−333−3−333−3−333000000000000
χ242222-122-2-2-1-1222-12220000111133−3−333−3−3-1-12-1-1-1-1-1-122-1-1-1-1-1-12-1-1-2-21111-2-21111-2-21111-2-211110033−3−30033−3−300003333−3−3−3−30033−3−30033−3−300003333−3−3−3−322−2−222−2−2ζ10−ζ14ζ10−ζ14ζ26−ζ46ζ26−ζ46−ζ10+ζ14−ζ10+ζ14−ζ26+ζ46−ζ26+ζ46ζ10−ζ14ζ10−ζ14ζ26−ζ46ζ26−ζ46−ζ10+ζ14−ζ10+ζ14−ζ26+ζ46−ζ26+ζ46000000000000
χ252222-122-2-2-1-1222-12220000111133−3−333−3−3-1-12-1-1-1-1-1-122-1-1-1-1-1-12-1-1-2-21111-2-21111-2-21111-2-211110033−3−30033−3−300003333−3−3−3−30033−3−30033−3−300003333−3−3−3−3−2−222−2−222−ζ10+ζ14−ζ10+ζ14−ζ26+ζ46−ζ26+ζ46ζ10−ζ14ζ10−ζ14ζ26−ζ46ζ26−ζ46−ζ10+ζ14−ζ10+ζ14−ζ26+ζ46−ζ26+ζ46ζ10−ζ14ζ10−ζ14ζ26−ζ46ζ26−ζ46000000000000
χ262222-122-2-2-1-1222-122200001111−3−333−3−333-1-12-1-1-1-1-1-122-1-1-1-1-1-12-1-1-2-21111-2-21111-2-21111-2-2111100−3−33300−3−3330000−3−3−3−3333300−3−33300−3−3330000−3−3−3−3333322−2−222−2−2ζ26−ζ46ζ26−ζ46ζ10−ζ14ζ10−ζ14−ζ26+ζ46−ζ26+ζ46−ζ10+ζ14−ζ10+ζ14ζ26−ζ46ζ26−ζ46ζ10−ζ14ζ10−ζ14−ζ26+ζ46−ζ26+ζ46−ζ10+ζ14−ζ10+ζ14000000000000
χ272222-122-2-2-1-1222-122200001111−3−333−3−333-1-12-1-1-1-1-1-122-1-1-1-1-1-12-1-1-2-21111-2-21111-2-21111-2-2111100−3−33300−3−3330000−3−3−3−3333300−3−33300−3−3330000−3−3−3−33333−2−222−2−222−ζ26+ζ46−ζ26+ζ46−ζ10+ζ14−ζ10+ζ14ζ26−ζ46ζ26−ζ46ζ10−ζ14ζ10−ζ14−ζ26+ζ46−ζ26+ζ46−ζ10+ζ14−ζ10+ζ14ζ26−ζ46ζ26−ζ46ζ10−ζ14ζ10−ζ14000000000000
χ2822-2-2222002-222-2-2-2-2-22−22−200002−22−22−22−2222222-22-22-222-2-2-2-2-2-2-20000000000000000000000002−22−22−22−22−22−222−2−222−2−222−2−22−22−22−22−22−22−222−2−222−2−222−2−2−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43000000000000
χ2922-2-2222002-222-2-2-2-2-22−22−200002−22−22−22−2222222-22-22-222-2-2-2-2-2-2-20000000000000000000000002−22−22−22−22−22−222−2−222−2−222−2−22−22−22−22−22−22−222−2−222−2−222−2−2ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43000000000000
χ3022-2-2222002-222-2-2-2-2-2−22−220000−22−22−22−22222222-22-22-222-2-2-2-2-2-2-2000000000000000000000000−22−22−22−22−22−22−2−222−2−222−2−222−22−22−22−22−22−22−2−222−2−222−2−222ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47000000000000
χ3122-2-2222002-222-2-2-2-2-2−22−220000−22−22−22−22222222-22-22-222-2-2-2-2-2-2-2000000000000000000000000−22−22−22−22−22−22−2−222−2−222−2−222−22−22−22−22−22−22−2−222−2−222−2−222−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47000000000000
χ3222-2-2-12200-1122-21-2-2-22−22−23−33−3ζ10−ζ14−ζ10+ζ14ζ26−ζ46−ζ26+ζ46ζ10−ζ14−ζ10+ζ14ζ26−ζ46−ζ26+ζ46-1-12-1-1-11-112-2-1-11111-211003−33−30033−3−3003−33−30033−3−32−2ζ10−ζ14−ζ10+ζ14ζ26−ζ46−ζ26+ζ462−2ζ10−ζ14−ζ10+ζ14ζ26−ζ46−ζ26+ζ4622−2−2ζ10−ζ14ζ10−ζ14−ζ10+ζ14−ζ10+ζ14ζ26−ζ46ζ26−ζ46−ζ26+ζ46−ζ26+ζ462−2ζ10−ζ14−ζ10+ζ14ζ26−ζ46−ζ26+ζ462−2ζ10−ζ14−ζ10+ζ14ζ26−ζ46−ζ26+ζ4622−2−2ζ10−ζ14ζ10−ζ14−ζ10+ζ14−ζ10+ζ14ζ26−ζ46ζ26−ζ46−ζ26+ζ46−ζ26+ζ46−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ25+ζ47−ζ25−ζ47ζ31+ζ41−ζ31−ζ41−ζ11−ζ13ζ11+ζ13−ζ29−ζ43ζ29+ζ43ζ25+ζ47−ζ25−ζ47ζ31+ζ41−ζ31−ζ41−ζ11−ζ13ζ11+ζ13−ζ29−ζ43ζ29+ζ43000000000000
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χ1614-4-44-2-2-2002-222-2222-2−222222−22−232323−23−2ζ10+2ζ142ζ10−2ζ14−2ζ26+2ζ462ζ26−2ζ462ζ10−2ζ14−2ζ10+2ζ142ζ26−2ζ46−2ζ26+2ζ46111−1−3i32−1+3i32-11-11-111+3i321−3i32−1−3i32−1+3i32-1-1-11+3i321−3i32003−33−3−3i3i−ζ28−2ζ442ζ28+ζ44ζ28+2ζ44−2ζ28−ζ4400−33−333i−3iζ28+2ζ44−2ζ28−ζ44−ζ28−2ζ442ζ28+ζ442−2ζ10−ζ14−ζ10+ζ14ζ26−ζ46−ζ26+ζ462−2ζ10−ζ14−ζ10+ζ14ζ26−ζ46−ζ26+ζ46−ζ10−2ζ14−ζ26−2ζ462ζ10+ζ14+2ζ26+ζ46ζ10+2ζ14+ζ26+2ζ46−2ζ10−ζ14−2ζ26−ζ46ζ10+2ζ14−2ζ10−ζ14−ζ10−2ζ142ζ10+ζ14ζ26+2ζ46−2ζ26−ζ46−ζ26−2ζ462ζ26+ζ46−22−ζ10+ζ14ζ10−ζ14−ζ26+ζ46ζ26−ζ46−22−ζ10+ζ14ζ10−ζ14−ζ26+ζ46ζ26−ζ46ζ10+2ζ14+ζ26+2ζ46−2ζ10−ζ14−2ζ26−ζ46−ζ10−2ζ14−ζ26−2ζ462ζ10+ζ14+2ζ26+ζ46−ζ10−2ζ142ζ10+ζ14ζ10+2ζ14−2ζ10−ζ14−ζ26−2ζ462ζ26+ζ46ζ26+2ζ46−2ζ26−ζ46000000000000000000000000000000000000
χ1624-4-44-2-2-2002-222-2222-2−222222−22−232323−23−2ζ10+2ζ142ζ10−2ζ14−2ζ26+2ζ462ζ26−2ζ462ζ10−2ζ14−2ζ10+2ζ142ζ26−2ζ46−2ζ26+2ζ46111−1+3i32−1−3i32-11-11-111−3i321+3i32−1+3i32−1−3i32-1-1-11−3i321+3i32003−33−33i−3i2ζ28+ζ44−ζ28−2ζ44−2ζ28−ζ44ζ28+2ζ4400−33−33−3i3i−2ζ28−ζ44ζ28+2ζ442ζ28+ζ44−ζ28−2ζ442−2ζ10−ζ14−ζ10+ζ14ζ26−ζ46−ζ26+ζ462−2ζ10−ζ14−ζ10+ζ14ζ26−ζ46−ζ26+ζ462ζ10+ζ14+2ζ26+ζ46−ζ10−2ζ14−ζ26−2ζ46−2ζ10−ζ14−2ζ26−ζ46ζ10+2ζ14+ζ26+2ζ46−2ζ10−ζ14ζ10+2ζ142ζ10+ζ14−ζ10−2ζ14−2ζ26−ζ46ζ26+2ζ462ζ26+ζ46−ζ26−2ζ46−22−ζ10+ζ14ζ10−ζ14−ζ26+ζ46ζ26−ζ46−22−ζ10+ζ14ζ10−ζ14−ζ26+ζ46ζ26−ζ46−2ζ10−ζ14−2ζ26−ζ46ζ10+2ζ14+ζ26+2ζ462ζ10+ζ14+2ζ26+ζ46−ζ10−2ζ14−ζ26−2ζ462ζ10+ζ14−ζ10−2ζ14−2ζ10−ζ14ζ10+2ζ142ζ26+ζ46−ζ26−2ζ46−2ζ26−ζ46ζ26+2ζ46000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 48 (ζ48 = 1); i = ζ12.