Finite Group Databasebeta

← Group #72222650

Character table — Group #72222650

Order 2304.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156
size11112222222222222222224444444444444444444444444444448888888888888888888899991212121212121212121212121212121216161616161616161616161616161616181818181818181818182424242424242424242424242424242424242424242424243636484848484848484872727272
order1222334444446666668888366688121212121212121212121212121212122424242424242424224412121212242424242424242424242424222216161616161616161616161616161616666666661212121212121212444444888888888888484848484848484848484848484848488824242424242424242244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111
χ3111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1
χ51111111111111111111111111111111111111111111111111111-1-1-1-1111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ71111111111111111111111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ81111111111111111111111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-11111
χ9111111-1-111-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i11111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i11ii−i−iii−i−i11-1-1
χ10111111-1-111-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii11111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii11−i−iii−i−iii11-1-1
χ11111111-1-111-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii11111111-1-1-1-1-1-1-1-1-1-111111111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii-1-1ii−i−i−i−iii-1-111
χ12111111-1-111-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i11111111-1-1-1-1-1-1-1-1-1-111111111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-1−i−iiiii−i−i-1-111
χ13111111-1-111-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1−i−iii−i−iiiiiii−i−i−i−iiiii−i−i−i−i11−i−iii−i−iii-1-111
χ14111111-1-111-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1ii−i−iii−i−i−i−i−i−iiiii−i−i−i−iiiii11ii−i−iii−i−i-1-111
χ15111111-1-111-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii-1-1-1-1-1-1-1-111111111-1-111111111−i−iiiii−i−iiiii−i−i−i−i−i−i−i−iiiii-1-1−i−iiiii−i−i11-1-1
χ16111111-1-111-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-1-1-1-1-111111111-1-111111111ii−i−i−i−iii−i−i−i−iiiiiiiii−i−i−i−i-1-1ii−i−i−i−iii11-1-1
χ1711-1-111i−i1-1i−i11-1-1-1-1ii−i−i11-1-11-1ii−i−iii−i−i11-1-1ii−i−iiiii−i−i−i−i1-1i−ii−i1-111-1-111-1-1ii−i−i11-1-1ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ311-1-111-1-1ii−i−iii−i−i1-1i−ii−iii−i−iζ−ζζ3−ζ3ζ−ζζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ31-1ζ−ζζ3−ζ3ζ−ζζ3−ζ31-1i−i
χ1811-1-111i−i1-1i−i11-1-1-1-1ii−i−i11-1-11-1ii−i−iii−i−i11-1-1ii−i−iiiii−i−i−i−i1-1i−ii−i1-111-1-111-1-1ii−i−i11-1-1−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ311-1-111-1-1ii−i−iii−i−i1-1i−ii−iii−i−i−ζζ−ζ3ζ3−ζζ−ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ31-1−ζζ−ζ3ζ3−ζζ−ζ3ζ31-1i−i
χ1911-1-111i−i1-1i−i11-1-1-1-1ii−i−i11-1-11-1ii−i−iii−i−i11-1-1ii−i−iiiii−i−i−i−i1-1i−ii−i1-111-1-111-1-1ii−i−i-1-111ζζ−ζ−ζζ3ζ3−ζ3−ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ311-1-111-1-1ii−i−iii−i−i-11−ii−ii−i−iiiζ−ζζ3−ζ3−ζζ−ζ3ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3-11ζ−ζζ3−ζ3−ζζ−ζ3ζ3-11−ii
χ2011-1-111i−i1-1i−i11-1-1-1-1ii−i−i11-1-11-1ii−i−iii−i−i11-1-1ii−i−iiiii−i−i−i−i1-1i−ii−i1-111-1-111-1-1ii−i−i-1-111−ζ−ζζζ−ζ3−ζ3ζ3ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ311-1-111-1-1ii−i−iii−i−i-11−ii−ii−i−iii−ζζ−ζ3ζ3ζ−ζζ3−ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3-11−ζζ−ζ3ζ3ζ−ζζ3−ζ3-11−ii
χ2111-1-111i−i1-1i−i11-1-1-1-1ii−i−i11-1-11-1ii−i−iii−i−i11-1-1ii−i−iiiii−i−i−i−i-11−iii−i1-111-1-111-1-1ii−i−i11-1-1ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3-1-111-1-111−i−iii−i−iii1-1i−ii−iii−i−i−ζζ−ζ3ζ3−ζζ−ζ3ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ31-1−ζζ−ζ3ζ3−ζζ−ζ3ζ3-11−ii
χ2211-1-111i−i1-1i−i11-1-1-1-1ii−i−i11-1-11-1ii−i−iii−i−i11-1-1ii−i−iiiii−i−i−i−i-11−iii−i1-111-1-111-1-1ii−i−i11-1-1−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3-1-111-1-111−i−iii−i−iii1-1i−ii−iii−i−iζ−ζζ3−ζ3ζ−ζζ3−ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ31-1ζ−ζζ3−ζ3ζ−ζζ3−ζ3-11−ii
χ2311-1-111i−i1-1i−i11-1-1-1-1ii−i−i11-1-11-1ii−i−iii−i−i11-1-1ii−i−iiiii−i−i−i−i-11−iii−i1-111-1-111-1-1ii−i−i-1-111ζζ−ζ−ζζ3ζ3−ζ3−ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3-1-111-1-111−i−iii−i−iii-11−ii−ii−i−iii−ζζ−ζ3ζ3ζ−ζζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3-11−ζζ−ζ3ζ3ζ−ζζ3−ζ31-1i−i
χ2411-1-111i−i1-1i−i11-1-1-1-1ii−i−i11-1-11-1ii−i−iii−i−i11-1-1ii−i−iiiii−i−i−i−i-11−iii−i1-111-1-111-1-1ii−i−i-1-111−ζ−ζζζ−ζ3−ζ3ζ3ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3-1-111-1-111−i−iii−i−iii-11−ii−ii−i−iiiζ−ζζ3−ζ3−ζζ−ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3-11ζ−ζζ3−ζ3−ζζ−ζ3ζ31-1i−i
χ2511-1-111−ii1-1−ii11-1-1-1-1−i−iii11-1-11-1−i−iii−i−iii11-1-1−i−iii−i−i−i−iiiii1-1−ii−ii1-111-1-111-1-1−i−iii11-1-1ζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ11-1-111-1-1−i−iii−i−iii1-1−ii−ii−i−iiiζ3−ζ3ζ−ζζ3−ζ3ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ1-1ζ3−ζ3ζ−ζζ3−ζ3ζ−ζ1-1−ii
χ2611-1-111−ii1-1−ii11-1-1-1-1−i−iii11-1-11-1−i−iii−i−iii11-1-1−i−iii−i−i−i−iiiii1-1−ii−ii1-111-1-111-1-1−i−iii11-1-1−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ11-1-111-1-1−i−iii−i−iii1-1−ii−ii−i−iii−ζ3ζ3−ζζ−ζ3ζ3−ζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ1-1−ζ3ζ3−ζζ−ζ3ζ3−ζζ1-1−ii
χ2711-1-111−ii1-1−ii11-1-1-1-1−i−iii11-1-11-1−i−iii−i−iii11-1-1−i−iii−i−i−i−iiiii1-1−ii−ii1-111-1-111-1-1−i−iii-1-111ζ3ζ3−ζ3−ζ3ζζ−ζ−ζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ11-1-111-1-1−i−iii−i−iii-11i−ii−iii−i−iζ3−ζ3ζ−ζ−ζ3ζ3−ζζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ-11ζ3−ζ3ζ−ζ−ζ3ζ3−ζζ-11i−i
χ2811-1-111−ii1-1−ii11-1-1-1-1−i−iii11-1-11-1−i−iii−i−iii11-1-1−i−iii−i−i−i−iiiii1-1−ii−ii1-111-1-111-1-1−i−iii-1-111−ζ3−ζ3ζ3ζ3−ζ−ζζζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ11-1-111-1-1−i−iii−i−iii-11i−ii−iii−i−i−ζ3ζ3−ζζζ3−ζ3ζ−ζ−ζ3−ζ3ζ3ζ3−ζ−ζζζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ-11−ζ3ζ3−ζζζ3−ζ3ζ−ζ-11i−i
χ2911-1-111−ii1-1−ii11-1-1-1-1−i−iii11-1-11-1−i−iii−i−iii11-1-1−i−iii−i−i−i−iiiii-11i−i−ii1-111-1-111-1-1−i−iii11-1-1ζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ-1-111-1-111ii−i−iii−i−i1-1−ii−ii−i−iii−ζ3ζ3−ζζ−ζ3ζ3−ζζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ1-1−ζ3ζ3−ζζ−ζ3ζ3−ζζ-11i−i
χ3011-1-111−ii1-1−ii11-1-1-1-1−i−iii11-1-11-1−i−iii−i−iii11-1-1−i−iii−i−i−i−iiiii-11i−i−ii1-111-1-111-1-1−i−iii11-1-1−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ-1-111-1-111ii−i−iii−i−i1-1−ii−ii−i−iiiζ3−ζ3ζ−ζζ3−ζ3ζ−ζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ1-1ζ3−ζ3ζ−ζζ3−ζ3ζ−ζ-11i−i
χ3111-1-111−ii1-1−ii11-1-1-1-1−i−iii11-1-11-1−i−iii−i−iii11-1-1−i−iii−i−i−i−iiiii-11i−i−ii1-111-1-111-1-1−i−iii-1-111ζ3ζ3−ζ3−ζ3ζζ−ζ−ζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ-1-111-1-111ii−i−iii−i−i-11i−ii−iii−i−i−ζ3ζ3−ζζζ3−ζ3ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ-11−ζ3ζ3−ζζζ3−ζ3ζ−ζ1-1−ii
χ3211-1-111−ii1-1−ii11-1-1-1-1−i−iii11-1-11-1−i−iii−i−iii11-1-1−i−iii−i−i−i−iiiii-11i−i−ii1-111-1-111-1-1−i−iii-1-111−ζ3−ζ3ζ3ζ3−ζ−ζζζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ-1-111-1-111ii−i−iii−i−i-11i−ii−iii−i−iζ3−ζ3ζ−ζ−ζ3ζ3−ζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ-11ζ3−ζ3ζ−ζ−ζ3ζ3−ζζ1-1−ii
χ33222222222222222222-2-2-2-22222-2-22222222222222222-2-2-2-2-2-2-2-200002222-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000222222-2-2-2-2000000000000000000000000-2-2000000000000
χ34222222222222222222-2-2-2-22222-2-22222222222222222-2-2-2-2-2-2-2-200002222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000-2-2-2-2-2-2222200000000000000000000000022000000000000
χ3522222222-2-2-2-2222222000022220022222222-2-2-2-2-2-2-2-2000000000000-2-2-2-20000000000002222i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000000000000000-2-2-2-222000000000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i200000000000000
χ3622222222-2-2-2-2222222000022220022222222-2-2-2-2-2-2-2-2000000000000-2-2-2-20000000000002222−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000000000000000-2-2-2-222000000000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i200000000000000
χ3722222222-2-2-2-2222222000022220022222222-2-2-2-2-2-2-2-2000000000000-2-2-2-2000000000000-2-2-2-2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i200000000000000002222-2-2000000000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i200000000000000
χ3822222222-2-2-2-2222222000022220022222222-2-2-2-2-2-2-2-2000000000000-2-2-2-2000000000000-2-2-2-2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i200000000000000002222-2-2000000000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i200000000000000
χ39222222-2-222-2-222222222222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-2222222220000-2-222-2-2-2-2-2-2-2-2222222220000000000000000000000000000000022-2-2-2-22222000000000000000000000000-2-2000000000000
χ40222222-2-222-2-222222222222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-2222222220000-2-222-2-2-2-2-2-2-2-22222-2-2-2-200000000000000000000000000000000-2-22222-2-2-2-200000000000000000000000022000000000000
χ41222222-2-2-2-2222222220000222200-2-2-2-2-2-2-2-2-2-2-2-2222200000000000022-2-200000000000022222−22−2−22−222−22−2−22−220000000000000000-2-222-2-20000000000002−22−2−22−222−22−2−22−2200000000000000
χ42222222-2-2-2-2222222220000222200-2-2-2-2-2-2-2-2-2-2-2-2222200000000000022-2-20000000000002222−22−222−22−2−22−222−22−20000000000000000-2-222-2-2000000000000−22−222−22−2−22−222−22−200000000000000
χ43222222-2-2-2-2222222220000222200-2-2-2-2-2-2-2-2-2-2-2-2222200000000000022-2-2000000000000-2-2-2-22−22−2−22−22−22−222−22−2000000000000000022-2-2220000000000002−22−2−22−22−22−222−22−200000000000000
χ44222222-2-2-2-2222222220000222200-2-2-2-2-2-2-2-2-2-2-2-2222200000000000022-2-2000000000000-2-2-2-2−22−222−22−22−22−2−22−22000000000000000022-2-222000000000000−22−222−22−22−22−2−22−2200000000000000
χ4522222-12222222-12-12-12222-1-1-1-1222-12-1-1-1-1-12-12-12-12-122-1-122-1-12222-1-1-1-12-12-1-1-1-1-1-1-1-1-1000000000000222222222-12-1-1-1-1-12-12-1-1-1-1-100000000000000222200000000-1-1-1-1-1-1-1-1000000-1-1-1-10000
χ4622222-12222222-12-12-12222-1-1-1-1222-12-1-1-1-1-12-12-12-12-122-1-122-1-12222-1-1-1-12-12-1-1-1-1-1-1-1-1-1000000000000-2-2-2-2-2-2-2-22-12-1-1-1-1-12-12-1-1-1-1-100000000000000-2-2-2-2000000001111111100000011110000
χ4722222-12222222-12-12-12222-1-1-1-1222-12-1-1-1-1-12-12-12-12-122-1-122-1-1-2-2-2-2-1-1-1-12-12-1-1-1-1-1-1-1-1-100000000000022222222-21-211111-21-21111100000000000000-2-2-2-200000000-1-1-1-1-1-1-1-100000011110000
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χ4922222-1-2-222-2-22-12-12-1-2-2-2-2-1-1-1-122-21-2111112-12-1-21-21-2-211-2-21122-2-211-1-12-12-1-1-1-1-111110000000000002i2i2i2i−2i−2i−2i−2i2-12-1-1-1-1-1-21-211111000000000000002i2i−2i−2i00000000−i−i−i−iiiii000000−i−iii0000
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Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.