Finite Group Databasebeta

← Group #72225255

Character table — Group #72225255

Order 4096.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160
size11112222222222444444444444444444888888888888888888888888888888888888888888881616161616161616161616161616161616161616161616161616161616161616161616163232323232323232323232323232323232323232323232323232323232323232128128128128128128128128128128128128128128128128
order122244444444442488888888888888884444888888888888888816161616161616161616161616161616161616161616161616161616323232323232323232323232323232323232323232323232323232323232323288888888161616161616161632323232323232323232323232323232224488881616161616161616
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-11111-1-1-1-1
χ611111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-1-1-11111
χ711111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-11-111-1-1-1-1-1-11111
χ811111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-11-11-1-1111111-1-1-1-1
χ911111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1ii−i−iii−i−i
χ1011111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111−i−iii−i−iii
χ1111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1−i−iii−i−iii
χ1211111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111ii−i−iii−i−i
χ1311111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii1-11-1-1-111ii−i−i−i−iii
χ1411111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii-11-1111-1-1−i−iiiii−i−i
χ1511111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111−i−i−i−iiiii−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−i−i−i1-11-1-1-111−i−iiiii−i−i
χ1611111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111−i−i−i−iiiii−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−i−i−i-11-1111-1-1ii−i−i−i−iii
χ171111111111-1-1-1-1-1-1111111111111-1-1-1-1ii−i−i-1-1-1-1ii−i−iii−i−iii−i−i1111-1-1-1-11111-1-1-1-1iiii−i−i−i−iii−i−i11111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζζζ−ζ−ζ−ζ−ζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ311-1-1i−ii−iζ−ζζ3−ζ3ζ−ζζ3−ζ3
χ181111111111-1-1-1-1-1-1111111111111-1-1-1-1ii−i−i-1-1-1-1ii−i−iii−i−iii−i−i1111-1-1-1-11111-1-1-1-1iiii−i−i−i−iii−i−i11111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζζζ−ζ−ζ−ζ−ζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3-1-111−ii−ii−ζζ−ζ3ζ3−ζζ−ζ3ζ3
χ191111111111-1-1-1-1-1-1111111111111-1-1-1-1ii−i−i-1-1-1-1ii−i−iii−i−iii−i−i1111-1-1-1-11111-1-1-1-1iiii−i−i−i−iii−i−i11111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζ−ζ−ζζζζζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ311-1-1i−ii−i−ζζ−ζ3ζ3−ζζ−ζ3ζ3
χ201111111111-1-1-1-1-1-1111111111111-1-1-1-1ii−i−i-1-1-1-1ii−i−iii−i−iii−i−i1111-1-1-1-11111-1-1-1-1iiii−i−i−i−iii−i−i11111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζ−ζ−ζζζζζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3-1-111−ii−iiζ−ζζ3−ζ3ζ−ζζ3−ζ3
χ211111111111-1-1-1-1-1-1111111111111-1-1-1-1ii−i−i-1-1-1-1ii−i−iii−i−iii−i−i1111-1-1-1-11111-1-1-1-1iiii−i−i−i−iii−i−i-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiiiζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3−ζ−ζ−ζ−ζζζζζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ31-1-11i−i−iiζ−ζζ3−ζ3−ζζ−ζ3ζ3
χ221111111111-1-1-1-1-1-1111111111111-1-1-1-1ii−i−i-1-1-1-1ii−i−iii−i−iii−i−i1111-1-1-1-11111-1-1-1-1iiii−i−i−i−iii−i−i-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiiiζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3−ζ−ζ−ζ−ζζζζζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3-111-1−iii−i−ζζ−ζ3ζ3ζ−ζζ3−ζ3
χ231111111111-1-1-1-1-1-1111111111111-1-1-1-1ii−i−i-1-1-1-1ii−i−iii−i−iii−i−i1111-1-1-1-11111-1-1-1-1iiii−i−i−i−iii−i−i-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiii−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3ζζζζ−ζ−ζ−ζ−ζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ31-1-11i−i−ii−ζζ−ζ3ζ3ζ−ζζ3−ζ3
χ241111111111-1-1-1-1-1-1111111111111-1-1-1-1ii−i−i-1-1-1-1ii−i−iii−i−iii−i−i1111-1-1-1-11111-1-1-1-1iiii−i−i−i−iii−i−i-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiii−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3ζζζζ−ζ−ζ−ζ−ζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3-111-1−iii−iζ−ζζ3−ζ3−ζζ−ζ3ζ3
χ251111111111-1-1-1-1-1-1111111111111-1-1-1-1−i−iii-1-1-1-1−i−iii−i−iii−i−iii1111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−iii11111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiiζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζζζζ−ζ−ζ−ζ−ζ11-1-1−ii−iiζ3−ζ3ζ−ζζ3−ζ3ζ−ζ
χ261111111111-1-1-1-1-1-1111111111111-1-1-1-1−i−iii-1-1-1-1−i−iii−i−iii−i−iii1111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−iii11111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiiζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζζζζ−ζ−ζ−ζ−ζ-1-111i−ii−i−ζ3ζ3−ζζ−ζ3ζ3−ζζ
χ271111111111-1-1-1-1-1-1111111111111-1-1-1-1−i−iii-1-1-1-1−i−iii−i−iii−i−iii1111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−iii11111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ−ζ−ζ−ζζζζζ11-1-1−ii−ii−ζ3ζ3−ζζ−ζ3ζ3−ζζ
χ281111111111-1-1-1-1-1-1111111111111-1-1-1-1−i−iii-1-1-1-1−i−iii−i−iii−i−iii1111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−iii11111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ−ζ−ζ−ζζζζζ-1-111i−ii−iζ3−ζ3ζ−ζζ3−ζ3ζ−ζ
χ291111111111-1-1-1-1-1-1111111111111-1-1-1-1−i−iii-1-1-1-1−i−iii−i−iii−i−iii1111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−iii-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−iζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ−ζ−ζ−ζζζζζ1-1-11−iii−iζ3−ζ3ζ−ζ−ζ3ζ3−ζζ
χ301111111111-1-1-1-1-1-1111111111111-1-1-1-1−i−iii-1-1-1-1−i−iii−i−iii−i−iii1111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−iii-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−iζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ−ζ−ζ−ζζζζζ-111-1i−i−ii−ζ3ζ3−ζζζ3−ζ3ζ−ζ
χ311111111111-1-1-1-1-1-1111111111111-1-1-1-1−i−iii-1-1-1-1−i−iii−i−iii−i−iii1111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−iii-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζζζζ−ζ−ζ−ζ−ζ1-1-11−iii−i−ζ3ζ3−ζζζ3−ζ3ζ−ζ
χ321111111111-1-1-1-1-1-1111111111111-1-1-1-1−i−iii-1-1-1-1−i−iii−i−iii−i−iii1111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−iii-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζζζζ−ζ−ζ−ζ−ζ-111-1i−i−iiζ3−ζ3ζ−ζ−ζ3ζ3−ζζ
χ332222222222222222222222222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000022222222-2-2-2-2-2-2-2-200000000000000000000000000000000
χ342222222222222222222222222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000-2-2-2-2-2-2-2-22222222200000000000000000000000000000000
χ3522222222222222222222222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222222222000000000000000000000000000000002i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i00000000000000000000000000000000
χ3622222222222222222222222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222222200000000000000000000000000000000−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i00000000000000000000000000000000
χ372222222222222222-2-2-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-22222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000000000000000000000002i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i0000000000000000
χ382222222222222222-2-2-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-22222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000000000000000000000000000000000000−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i0000000000000000
χ392222222222222222-2-2-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-22222222222222222-2-2-2-22222-2-2-2-22222-2-2-2-22222-2-2-2-22222-2-2-2-2000000000000000000000000000000000000000000000000
χ402222222222222222-2-2-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-22222222222222222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-22222-2-2-2-22222000000000000000000000000000000000000000000000000
χ412222222222222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-22222-2-2-2-2222222222222-2-2-2-2-2-2-2-222222222-2-2-2-200000000000000000000000000000000000000000000000022-2-222-2-2-2-222-2-2220000000000000000
χ422222222222222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-22222-2-2-2-2222222222222-2-2-2-2-2-2-2-222222222-2-2-2-2000000000000000000000000000000000000000000000000-2-222-2-22222-2-222-2-20000000000000000
χ432222222222222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-222222222-2-2-2-22222-2-2-2-2-2-2-2-22222-2-2-2-22222000000000000000000000000000000000000000000000000
χ442222222222222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-222222222-2-2-2-22222-2-2-2-2000000000000000000000000000000000000000000000000
χ452222222222-2-2-2-2-2-2222222222222-2-2-2-22i2i−2i−2i-2-2-2-22i2i−2i−2i2i2i−2i−2i2i2i−2i−2i-2-2-2-22222-2-2-2-22222−2i−2i−2i−2i2i2i2i2i−2i−2i2i2i000000000000000000000000000000002ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ3−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ300000000000000000000000000000000
χ462222222222-2-2-2-2-2-2222222222222-2-2-2-22i2i−2i−2i-2-2-2-22i2i−2i−2i2i2i−2i−2i2i2i−2i−2i-2-2-2-22222-2-2-2-22222−2i−2i−2i−2i2i2i2i2i−2i−2i2i2i00000000000000000000000000000000−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ32ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ300000000000000000000000000000000
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χ482222222222-2-2-2-2-2-2222222222222-2-2-2-2−2i−2i2i2i-2-2-2-2−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i-2-2-2-22222-2-2-2-222222i2i2i2i−2i−2i−2i−2i2i2i−2i−2i00000000000000000000000000000000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ2ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ00000000000000000000000000000000
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Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.