Finite Group Databasebeta

← Group #14512530

Character table — Group #14512530

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size111122444444444444444455556666888810101010101010101010161616161616161616161616161616162020202020202020242424243030303030303030303030304040404040404040404040404040404040404040
order12224433566666610101020202020222244441212121244444444441515303030303030606060606060606066666666202020204444444444441212121212121212121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111-1-1-1-111111111-1-1iiii−i−i−i−i1111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−i-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i
χ41111111111111111111111-1-1-1-111111111-1-1−i−i−i−iiiii1111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii
χ5111111−1−i32−1+i321−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32111111111111111−1−i32−1−i32−1+i32−1+i321111111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321111111111111111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32
χ6111111−1−i32−1+i321−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32111111111111111−1−i32−1−i32−1+i32−1+i3211-1-1-1-1-1-1-1-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i3211111111-1-1-1-1-1-1-1-1−1−i32−1−i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i321+i321+i321+i321+i321−i321−i321−i321−i32
χ7111111−1−i32−1+i321−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321111111-1-1-1-11111−1−i32−1−i32−1+i32−1+i32-1-1iiii−i−i−i−i−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321+i321+i321−i321−i321+i321+i321−i321−i321111-1-1-1-1iiii−i−i−i−i1+i321+i321−i321−i32−ζ7−ζ19−ζ31−ζ43−ζ7−ζ19−ζ31−ζ43−ζ7−ζ19−ζ31−ζ43−ζ7−ζ19−ζ31−ζ43−ζ11−ζ23−ζ47−ζ59−ζ11−ζ23−ζ47−ζ59−ζ11−ζ23−ζ47−ζ59−ζ11−ζ23−ζ47−ζ59ζ7+ζ19+ζ31+ζ43ζ7+ζ19+ζ31+ζ43ζ7+ζ19+ζ31+ζ43ζ7+ζ19+ζ31+ζ43ζ11+ζ23+ζ47+ζ59ζ11+ζ23+ζ47+ζ59ζ11+ζ23+ζ47+ζ59ζ11+ζ23+ζ47+ζ59
χ8111111−1−i32−1+i321−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321111111-1-1-1-11111−1−i32−1−i32−1+i32−1+i32-1-1−i−i−i−iiiii−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321+i321+i321−i321−i321+i321+i321−i321−i321111-1-1-1-1−i−i−i−iiiii1+i321+i321−i321−i32ζ7+ζ19+ζ31+ζ43ζ7+ζ19+ζ31+ζ43ζ7+ζ19+ζ31+ζ43ζ7+ζ19+ζ31+ζ43ζ11+ζ23+ζ47+ζ59ζ11+ζ23+ζ47+ζ59ζ11+ζ23+ζ47+ζ59ζ11+ζ23+ζ47+ζ59−ζ7−ζ19−ζ31−ζ43−ζ7−ζ19−ζ31−ζ43−ζ7−ζ19−ζ31−ζ43−ζ7−ζ19−ζ31−ζ43−ζ11−ζ23−ζ47−ζ59−ζ11−ζ23−ζ47−ζ59−ζ11−ζ23−ζ47−ζ59−ζ11−ζ23−ζ47−ζ59
χ9111111−1+i32−1−i321−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32111111111111111−1+i32−1+i32−1−i32−1−i321111111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321111111111111111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32
χ10111111−1+i32−1−i321−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32111111111111111−1+i32−1+i32−1−i32−1−i3211-1-1-1-1-1-1-1-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i3211111111-1-1-1-1-1-1-1-1−1+i32−1+i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i321−i321−i321−i321−i321+i321+i321+i321+i32
χ11111111−1+i32−1−i321−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321111111-1-1-1-11111−1+i32−1+i32−1−i32−1−i32-1-1iiii−i−i−i−i−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321−i321−i321+i321+i321−i321−i321+i321+i321111-1-1-1-1iiii−i−i−i−i1−i321−i321+i321+i32−ζ11−ζ23−ζ47−ζ59−ζ11−ζ23−ζ47−ζ59−ζ11−ζ23−ζ47−ζ59−ζ11−ζ23−ζ47−ζ59−ζ7−ζ19−ζ31−ζ43−ζ7−ζ19−ζ31−ζ43−ζ7−ζ19−ζ31−ζ43−ζ7−ζ19−ζ31−ζ43ζ11+ζ23+ζ47+ζ59ζ11+ζ23+ζ47+ζ59ζ11+ζ23+ζ47+ζ59ζ11+ζ23+ζ47+ζ59ζ7+ζ19+ζ31+ζ43ζ7+ζ19+ζ31+ζ43ζ7+ζ19+ζ31+ζ43ζ7+ζ19+ζ31+ζ43
χ12111111−1+i32−1−i321−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321111111-1-1-1-11111−1+i32−1+i32−1−i32−1−i32-1-1−i−i−i−iiiii−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321−i321−i321+i321+i321−i321−i321+i321+i321111-1-1-1-1−i−i−i−iiiii1−i321−i321+i321+i32ζ11+ζ23+ζ47+ζ59ζ11+ζ23+ζ47+ζ59ζ11+ζ23+ζ47+ζ59ζ11+ζ23+ζ47+ζ59ζ7+ζ19+ζ31+ζ43ζ7+ζ19+ζ31+ζ43ζ7+ζ19+ζ31+ζ43ζ7+ζ19+ζ31+ζ43−ζ11−ζ23−ζ47−ζ59−ζ11−ζ23−ζ47−ζ59−ζ11−ζ23−ζ47−ζ59−ζ11−ζ23−ζ47−ζ59−ζ7−ζ19−ζ31−ζ43−ζ7−ζ19−ζ31−ζ43−ζ7−ζ19−ζ31−ζ43−ζ7−ζ19−ζ31−ζ43
χ131111-1-1111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-1-1-1-1-11111111111-1-111-1-111-1-111-1-1-1-1-1-111-1-111-1-111-1-111-1-1
χ141111-1-1111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-111-1-111-1-1-1-1-1-111-1-111-1-111-1-111
χ151111-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111ii−i−i−i−iii11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111ii−i−i−i−iii1111ii−i−iii−i−i−i−iii−i−iii
χ161111-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111−i−iiiii−i−i11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111−i−iiiii−i−i1111−i−iii−i−iiiii−i−iii−i−i
χ171111-1-1−1−i32−1+i321−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32111-1-1-1-1111111-1-11+i321+i321−i321−i32-1-111-1-111-1-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i3211-1-111-1-111-1-111-1-11+i321+i321−i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32
χ181111-1-1−1−i32−1+i321−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32111-1-1-1-1111111-1-11+i321+i321−i321−i32-1-1-1-111-1-111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i3211-1-111-1-1-1-111-1-1111+i321+i321−i321−i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32
χ191111-1-1−1−i32−1+i321−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32111-1-1-1-1-1-1-1-111-1-11+i321+i321−i321−i3211ii−i−i−i−iii−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i321+i321+i321−i321−i321+i321+i321−i321−i3211-1-1-1-111ii−i−i−i−iii−1−i32−1−i32−1+i32−1+i32−ζ7−ζ19−ζ31−ζ43−ζ7−ζ19−ζ31−ζ43ζ7+ζ19+ζ31+ζ43ζ7+ζ19+ζ31+ζ43−ζ11−ζ23−ζ47−ζ59−ζ11−ζ23−ζ47−ζ59ζ11+ζ23+ζ47+ζ59ζ11+ζ23+ζ47+ζ59ζ7+ζ19+ζ31+ζ43ζ7+ζ19+ζ31+ζ43−ζ7−ζ19−ζ31−ζ43−ζ7−ζ19−ζ31−ζ43ζ11+ζ23+ζ47+ζ59ζ11+ζ23+ζ47+ζ59−ζ11−ζ23−ζ47−ζ59−ζ11−ζ23−ζ47−ζ59
χ201111-1-1−1−i32−1+i321−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32111-1-1-1-1-1-1-1-111-1-11+i321+i321−i321−i3211−i−iiiii−i−i−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i321+i321+i321−i321−i321+i321+i321−i321−i3211-1-1-1-111−i−iiiii−i−i−1−i32−1−i32−1+i32−1+i32ζ7+ζ19+ζ31+ζ43ζ7+ζ19+ζ31+ζ43−ζ7−ζ19−ζ31−ζ43−ζ7−ζ19−ζ31−ζ43ζ11+ζ23+ζ47+ζ59ζ11+ζ23+ζ47+ζ59−ζ11−ζ23−ζ47−ζ59−ζ11−ζ23−ζ47−ζ59−ζ7−ζ19−ζ31−ζ43−ζ7−ζ19−ζ31−ζ43ζ7+ζ19+ζ31+ζ43ζ7+ζ19+ζ31+ζ43−ζ11−ζ23−ζ47−ζ59−ζ11−ζ23−ζ47−ζ59ζ11+ζ23+ζ47+ζ59ζ11+ζ23+ζ47+ζ59
χ211111-1-1−1+i32−1−i321−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32111-1-1-1-1111111-1-11−i321−i321+i321+i32-1-111-1-111-1-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i3211-1-111-1-111-1-111-1-11−i321−i321+i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32
χ221111-1-1−1+i32−1−i321−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32111-1-1-1-1111111-1-11−i321−i321+i321+i32-1-1-1-111-1-111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i3211-1-111-1-1-1-111-1-1111−i321−i321+i321+i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32
χ231111-1-1−1+i32−1−i321−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32111-1-1-1-1-1-1-1-111-1-11−i321−i321+i321+i3211ii−i−i−i−iii−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i321−i321−i321+i321+i321−i321−i321+i321+i3211-1-1-1-111ii−i−i−i−iii−1+i32−1+i32−1−i32−1−i32−ζ11−ζ23−ζ47−ζ59−ζ11−ζ23−ζ47−ζ59ζ11+ζ23+ζ47+ζ59ζ11+ζ23+ζ47+ζ59−ζ7−ζ19−ζ31−ζ43−ζ7−ζ19−ζ31−ζ43ζ7+ζ19+ζ31+ζ43ζ7+ζ19+ζ31+ζ43ζ11+ζ23+ζ47+ζ59ζ11+ζ23+ζ47+ζ59−ζ11−ζ23−ζ47−ζ59−ζ11−ζ23−ζ47−ζ59ζ7+ζ19+ζ31+ζ43ζ7+ζ19+ζ31+ζ43−ζ7−ζ19−ζ31−ζ43−ζ7−ζ19−ζ31−ζ43
χ241111-1-1−1+i32−1−i321−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32111-1-1-1-1-1-1-1-111-1-11−i321−i321+i321+i3211−i−iiiii−i−i−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i321−i321−i321+i321+i321−i321−i321+i321+i3211-1-1-1-111−i−iiiii−i−i−1+i32−1+i32−1−i32−1−i32ζ11+ζ23+ζ47+ζ59ζ11+ζ23+ζ47+ζ59−ζ11−ζ23−ζ47−ζ59−ζ11−ζ23−ζ47−ζ59ζ7+ζ19+ζ31+ζ43ζ7+ζ19+ζ31+ζ43−ζ7−ζ19−ζ31−ζ43−ζ7−ζ19−ζ31−ζ43−ζ11−ζ23−ζ47−ζ59−ζ11−ζ23−ζ47−ζ59ζ11+ζ23+ζ47+ζ59ζ11+ζ23+ζ47+ζ59−ζ7−ζ19−ζ31−ζ43−ζ7−ζ19−ζ31−ζ43ζ7+ζ19+ζ31+ζ43ζ7+ζ19+ζ31+ζ43
χ251-11-1i−i1111-11-1-1-1-11-1ii−i−i1-11-11-1i−ii−ii−ii−i1-1i−i1-1i−i111-11-1-1-1ii−i−iii−i−i1-11-11-11-11-1i−i1-1i−i1-1i−i1-1i−ii−ii−i1-1i−i1-1i−i1-1i−i1-1i−i
χ261-11-1i−i1111-11-1-1-1-11-1ii−i−i1-11-11-1i−ii−ii−ii−i-11−ii-11−ii111-11-1-1-1ii−i−iii−i−i1-11-11-11-11-1i−i1-1i−i-11−ii-11−iii−ii−i-11−ii-11−ii-11−ii-11−ii
χ271-11-1i−i1111-11-1-1-1-11-1ii−i−i-11-111-1i−ii−ii−i−iii−i-11−ii1-1111-11-1-1-1ii−i−iii−i−i-11-11-11-111-1i−i-11−iii−i-11−ii1-1−ii−iii−i-11i−i-11−ii1-1−ii1-1
χ281-11-1i−i1111-11-1-1-1-11-1ii−i−i-11-111-1i−ii−ii−i−ii−ii1-1i−i-11111-11-1-1-1ii−i−iii−i−i-11-11-11-111-1i−i-11−ii−ii1-1i−i-11−ii−ii−ii1-1−ii1-1i−i-11i−i-11
χ291-11-1i−i−1−i32−1+i321−1−i321+i32−1+i321−i321+i321−i32-11-1ii−i−i1-11-11-1i−i−ζ7−ζ19−ζ31−ζ43ζ7+ζ19+ζ31+ζ43−ζ11−ζ23−ζ47−ζ59ζ11+ζ23+ζ47+ζ59i−i1-1i−i1-1i−i−1−i32−1+i32−1−i321+i32−1+i321−i321+i321−i32−ζ7−ζ19−ζ31−ζ43−ζ7−ζ19−ζ31−ζ43ζ7+ζ19+ζ31+ζ43ζ7+ζ19+ζ31+ζ43−ζ11−ζ23−ζ47−ζ59−ζ11−ζ23−ζ47−ζ59ζ11+ζ23+ζ47+ζ59ζ11+ζ23+ζ47+ζ59−1−i321+i32−1+i321−i32−1−i321+i32−1+i321−i321-1i−i1-1i−i1-1i−i1-1i−i−ζ7−ζ19−ζ31−ζ43ζ7+ζ19+ζ31+ζ43−ζ11−ζ23−ζ47−ζ59ζ11+ζ23+ζ47+ζ59−1−i321+i32−ζ7−ζ19−ζ31−ζ43ζ7+ζ19+ζ31+ζ43−1+i321−i32−ζ11−ζ23−ζ47−ζ59ζ11+ζ23+ζ47+ζ59−1−i321+i32−ζ7−ζ19−ζ31−ζ43ζ7+ζ19+ζ31+ζ43−1+i321−i32−ζ11−ζ23−ζ47−ζ59ζ11+ζ23+ζ47+ζ59
χ301-11-1i−i−1−i32−1+i321−1−i321+i32−1+i321−i321+i321−i32-11-1ii−i−i1-11-11-1i−i−ζ7−ζ19−ζ31−ζ43ζ7+ζ19+ζ31+ζ43−ζ11−ζ23−ζ47−ζ59ζ11+ζ23+ζ47+ζ59i−i-11−ii-11−ii−1−i32−1+i32−1−i321+i32−1+i321−i321+i321−i32−ζ7−ζ19−ζ31−ζ43−ζ7−ζ19−ζ31−ζ43ζ7+ζ19+ζ31+ζ43ζ7+ζ19+ζ31+ζ43−ζ11−ζ23−ζ47−ζ59−ζ11−ζ23−ζ47−ζ59ζ11+ζ23+ζ47+ζ59ζ11+ζ23+ζ47+ζ59−1−i321+i32−1+i321−i32−1−i321+i32−1+i321−i321-1i−i1-1i−i-11−ii-11−ii−ζ7−ζ19−ζ31−ζ43ζ7+ζ19+ζ31+ζ43−ζ11−ζ23−ζ47−ζ59ζ11+ζ23+ζ47+ζ591+i32−1−i32ζ7+ζ19+ζ31+ζ43−ζ7−ζ19−ζ31−ζ431−i32−1+i32ζ11+ζ23+ζ47+ζ59−ζ11−ζ23−ζ47−ζ591+i32−1−i32ζ7+ζ19+ζ31+ζ43−ζ7−ζ19−ζ31−ζ431−i32−1+i32ζ11+ζ23+ζ47+ζ59−ζ11−ζ23−ζ47−ζ59
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Here ζ is a primitive root of unity of order 60 (ζ60 = 1); i = ζ15.