Finite Group Databasebeta

← Group #13135717

Character table — Group #13135717

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122
size111122222222223333333344444466666666666666666666666688888812121212121212121212121212121212121218181818181818181818181818181818181818181818181824242424242424242424242424242424727272727272
order1244234688881212336612121212612242424243336666612121212121212122424242424242424246612126661212122424242424242424242424241616161616161616484848484848484848484848484848486666666612121212121212128824242424
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111-1-1-1-1-1-1111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321111111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i3211−1−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+i321111111−1−i32−1+i321−1−i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i3211111111−1−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+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i32
χ611111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321111111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i3211−1−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+i321111111−1−i32−1+i321−1−i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-1-1-1-1-1-1-1-11+i321+i321+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i321−i321−i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i32
χ711111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321111111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i3211−1−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+i32-1-1-1-1-1-11−1−i32−1+i321−1−i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i3211111111−1−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−i32-1-11+i321+i321−i321−i321+i321−i32-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i32
χ811111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321111111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i3211−1−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+i32-1-1-1-1-1-11−1−i32−1+i321−1−i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-1-1-1-1-1-1-1-11+i321+i321+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i321−i321−i321+i321−i32-1-11+i321+i321−i321−i321+i321−i32-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i32
χ911111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321111111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i3211−1+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−i321111111−1+i32−1−i321−1+i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i3211111111−1+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−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i32
χ1011111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321111111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i3211−1+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−i321111111−1+i32−1−i321−1+i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-1-1-1-1-1-1-1-11−i321−i321−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i321+i321+i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i32
χ1111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321111111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i3211−1+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−i32-1-1-1-1-1-11−1+i32−1−i321−1+i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i3211111111−1+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+i32-1-11−i321−i321+i321+i321−i321+i32-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i32
χ1211111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321111111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i3211−1+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−i32-1-1-1-1-1-11−1+i32−1−i321−1+i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-1-1-1-1-1-1-1-11−i321−i321−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i321+i321+i321−i321+i32-1-11−i321−i321+i321+i321−i321+i32-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i32
χ1311-1-1-111111-1-1-1-11111-1-1-1-1-1111-1-1111-1-1111-1-1-1-1-1-1111111-1-1-1-11-111-1-1-1-1-111111-1-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i11111111-1-1-1-1-1-1-1-1i−ii−ii−i
χ1411-1-1-111111-1-1-1-11111-1-1-1-1-1111-1-1111-1-1111-1-1-1-1-1-1111111-1-1-1-11-111-1-1-1-1-111111-1-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii11111111-1-1-1-1-1-1-1-1−ii−ii−ii
χ1511-1-1-111111-1-1-1-11111-1-1-1-1-1111-1-1111-1-1111-1-1-1-1-1-1111111-1-1-1-1-11-1-111-1-1-111111-1-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i-1-1-1-1-1-1-1-111111111−ii−ii−ii
χ1611-1-1-111111-1-1-1-11111-1-1-1-1-1111-1-1111-1-1111-1-1-1-1-1-1111111-1-1-1-1-11-1-111-1-1-111111-1-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii-1-1-1-1-1-1-1-111111111i−ii−ii−i
χ1711-1-1-111111-1-1-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32-1111-1-11−1−i32−1+i321+i321−i321−1−i32−1+i32-1-11+i321+i321−i321−i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i321-111-1-1-11+i321−i321−1−i32−1+i3211-1-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32iiii−i−i−i−iζ44ζ44ζ44ζ44−ζ44−ζ44−ζ44−ζ44ζ28ζ28ζ28ζ28−ζ28−ζ28−ζ28−ζ28−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321+i321−i32-1-11+i321+i321−i321−i32i−iζ44−ζ44ζ28−ζ28
χ1811-1-1-111111-1-1-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32-1111-1-11−1−i32−1+i321+i321−i321−1−i32−1+i32-1-11+i321+i321−i321−i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i321-111-1-1-11+i321−i321−1−i32−1+i3211-1-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−i−i−i−iiiii−ζ44−ζ44−ζ44−ζ44ζ44ζ44ζ44ζ44−ζ28−ζ28−ζ28−ζ28ζ28ζ28ζ28ζ28−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321+i321−i32-1-11+i321+i321−i321−i32−ii−ζ44ζ44−ζ28ζ28
χ1911-1-1-111111-1-1-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32-1111-1-11−1−i32−1+i321+i321−i321−1−i32−1+i32-1-11+i321+i321−i321−i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32-11-1-111-11+i321−i321−1−i32−1+i3211-1-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32iiii−i−i−i−iζ44ζ44ζ44ζ44−ζ44−ζ44−ζ44−ζ44ζ28ζ28ζ28ζ28−ζ28−ζ28−ζ28−ζ281+i321−i32-1-11+i321+i321−i321−i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−ii−ζ44ζ44−ζ28ζ28
χ2011-1-1-111111-1-1-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32-1111-1-11−1−i32−1+i321+i321−i321−1−i32−1+i32-1-11+i321+i321−i321−i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32-11-1-111-11+i321−i321−1−i32−1+i3211-1-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−i−i−i−iiiii−ζ44−ζ44−ζ44−ζ44ζ44ζ44ζ44ζ44−ζ28−ζ28−ζ28−ζ28ζ28ζ28ζ28ζ281+i321−i32-1-11+i321+i321−i321−i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32i−iζ44−ζ44ζ28−ζ28
χ2111-1-1-111111-1-1-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32-1111-1-11−1+i32−1−i321−i321+i321−1+i32−1−i32-1-11−i321−i321+i321+i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i321-111-1-1-11−i321+i321−1+i32−1−i3211-1-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32iiii−i−i−i−iζ28ζ28ζ28ζ28−ζ28−ζ28−ζ28−ζ28ζ44ζ44ζ44ζ44−ζ44−ζ44−ζ44−ζ44−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−i321+i32-1-11−i321−i321+i321+i32i−iζ28−ζ28ζ44−ζ44
χ2211-1-1-111111-1-1-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32-1111-1-11−1+i32−1−i321−i321+i321−1+i32−1−i32-1-11−i321−i321+i321+i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i321-111-1-1-11−i321+i321−1+i32−1−i3211-1-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−i−i−i−iiiii−ζ28−ζ28−ζ28−ζ28ζ28ζ28ζ28ζ28−ζ44−ζ44−ζ44−ζ44ζ44ζ44ζ44ζ44−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−i321+i32-1-11−i321−i321+i321+i32−ii−ζ28ζ28−ζ44ζ44
χ2311-1-1-111111-1-1-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32-1111-1-11−1+i32−1−i321−i321+i321−1+i32−1−i32-1-11−i321−i321+i321+i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32-11-1-111-11−i321+i321−1+i32−1−i3211-1-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32iiii−i−i−i−iζ28ζ28ζ28ζ28−ζ28−ζ28−ζ28−ζ28ζ44ζ44ζ44ζ44−ζ44−ζ44−ζ44−ζ441−i321+i32-1-11−i321−i321+i321+i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−ii−ζ28ζ28−ζ44ζ44
χ2411-1-1-111111-1-1-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32-1111-1-11−1+i32−1−i321−i321+i321−1+i32−1−i32-1-11−i321−i321+i321+i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32-11-1-111-11−i321+i321−1+i32−1−i3211-1-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−i−i−i−iiiii−ζ28−ζ28−ζ28−ζ28ζ28ζ28ζ28ζ28−ζ44−ζ44−ζ44−ζ44ζ44ζ44ζ44ζ441−i321+i32-1-11−i321−i321+i321+i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32i−iζ28−ζ28ζ44−ζ44
χ252222222222222222222222222222-1-1-122-1-1-1-1-1-1-1-1-12222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000022-1-1-1-1-1-122-1-1-1-1-1-1000000
χ262222222222222222222222222222-1-1-122-1-1-1-1-1-1-1-1-12222222222-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000-2-2111111-2-2111111000000
χ2722222222222222−1−i3−1+i3−1−i3−1+i3−1−i3−1−i3−1+i3−1+i3222222-11+i321−i32−1−i3−1+i3-11+i321−i32-1-11+i321+i321−i321−i32−1−i3−1+i3−1−i3−1−i3−1+i3−1+i3−1−i3−1−i3−1+i3−1+i3222222-11+i321−i32-11+i321−i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32000000000000000000000000−1−i3−1+i3-1-11+i321+i321−i321−i32−1−i3−1+i3-1-11+i321+i321−i321−i32000000
χ2822222222222222−1−i3−1+i3−1−i3−1+i3−1−i3−1−i3−1+i3−1+i3222222-11+i321−i32−1−i3−1+i3-11+i321−i32-1-11+i321+i321−i321−i32−1−i3−1+i3−1−i3−1−i3−1+i3−1+i3−1−i3−1−i3−1+i3−1+i3-2-2-2-2-2-2-11+i321−i32-11+i321−i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i320000000000000000000000001+i31−i311−1−i32−1−i32−1+i32−1+i321+i31−i311−1−i32−1−i32−1+i32−1+i32000000
χ2922222222222222−1+i3−1−i3−1+i3−1−i3−1+i3−1+i3−1−i3−1−i3222222-11−i321+i32−1+i3−1−i3-11−i321+i32-1-11−i321−i321+i321+i32−1+i3−1−i3−1+i3−1+i3−1−i3−1−i3−1+i3−1+i3−1−i3−1−i3222222-11−i321+i32-11−i321+i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32000000000000000000000000−1+i3−1−i3-1-11−i321−i321+i321+i32−1+i3−1−i3-1-11−i321−i321+i321+i32000000
χ3022222222222222−1+i3−1−i3−1+i3−1−i3−1+i3−1+i3−1−i3−1−i3222222-11−i321+i32−1+i3−1−i3-11−i321+i32-1-11−i321−i321+i321+i32−1+i3−1−i3−1+i3−1+i3−1−i3−1−i3−1+i3−1+i3−1−i3−1−i3-2-2-2-2-2-2-11−i321+i32-11−i321+i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i320000000000000000000000001−i31+i311−1+i32−1+i32−1−i32−1−i321−i31+i311−1+i32−1+i32−1−i32−1−i32000000
χ3122222222-2-2-2-2222222222222-2-2-2-22222222222222222-2-2-2-2-2-2-2-2000000222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000000000000000000
χ3222222222-2-2-2-2222222222222-2-2-2-2-1-1-122-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2000000-1-1-1-1-1-111111111111100000000000000000000000000−i3i3−i3i3−i3i300−i3i3−i3i3−i3i3000000
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χ5922-2-2-2222-2-222-2-22222-2-2-2-2-22-2-222-1-1-1-2-2-1-1-111111122-2-2-2-22222000000111-1-1-111-1-111-1-111-1-100000000000000000000000000−i3i3−i3i3−i3i300i3−i3i3−i3i3−i3000000
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Here ζ is a primitive root of unity of order 48 (ζ48 = 1); i = ζ12.