Finite Group Databasebeta

← Group #72227260

Character table — Group #72227260

Order 4096.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162C163C164C165C166C167C168C169C170C171C172C173C174C175C176C177C178C179C180C181C182C183C184
size1122222222222444444444444444444444444888888888888888888888888888888888888888888888888888881616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161632323232323232323232323232323232323232323232323264646464646464646464646464646464128128128128128128128128
order122224444888844888888888888881616161616161616444448888888816161616161616161616161616161616161616161616161632323232323232323232323232323232224488888888161616161616161616163232323232323232323232323232323232323232323232324488161616163232323232323232323232323232323232323232323232323232323232323232888816161616
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ711111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ811111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ91111111111111111111111111111111111111-1-11-1-1-1-11111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i
χ101111111111111111111111111111111111111-1-11-1-1-1-11111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii
χ111111111111111111111111111111111111111-1-11-1-1-1-11111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii
χ121111111111111111111111111111111111111-1-11-1-1-1-11111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i
χ131111111111111111111111111111111111111-1-11-1-1-1-11111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii
χ141111111111111111111111111111111111111-1-11-1-1-1-11111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i
χ151111111111111111111111111111111111111-1-11-1-1-1-11111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i
χ161111111111111111111111111111111111111-1-11-1-1-1-11111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii
χ17111-1-11-11-1111111111111111-1-11-1-111-1-111-1-1i−i-1i−ii−i-1-1-1-1i−i11-1-111-1-1ii−i−i11-1-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i1-11-111-1-1ii−i−i1111-1-1-1-1i−i11-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−ii−ii−iii−i−i1111-1-1-1-1iiii−i−i−i−iζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζ−ζζ3−ζ3ζ−ζζ3−ζ3
χ18111-1-11-11-1111111111111111-1-11-1-111-1-111-1-1i−i-1i−ii−i-1-1-1-1i−i11-1-111-1-1ii−i−i11-1-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i1-11-111-1-1ii−i−i1111-1-1-1-1i−i11-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−ii−ii−iii−i−i1111-1-1-1-1iiii−i−i−i−i−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζζ−ζ3ζ3−ζζ−ζ3ζ3
χ19111-1-11-11-1111111111111111-1-11-1-111-1-111-1-1i−i-1i−ii−i-1-1-1-1i−i11-1-111-1-1ii−i−i11-1-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i-11-11-1-111ii−i−i-1-1-1-11111i−i11-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i−ii−ii−i−iii-1-1-1-11111−i−i−i−iiiiiζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3−ζζ−ζ3ζ3−ζζ−ζ3ζ3
χ20111-1-11-11-1111111111111111-1-11-1-111-1-111-1-1i−i-1i−ii−i-1-1-1-1i−i11-1-111-1-1ii−i−i11-1-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i-11-11-1-111ii−i−i-1-1-1-11111i−i11-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i−ii−ii−i−iii-1-1-1-11111−i−i−i−iiiii−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3ζ−ζζ3−ζ3ζ−ζζ3−ζ3
χ21111-1-11-11-1111111111111111-1-11-1-111-1-111-1-1i−i-1i−ii−i-1-1-1-1i−i11-1-111-1-1ii−i−i11-1-1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii1-11-111-1-1ii−i−i1111-1-1-1-1i−i-1-111−i−iii-1-1-1-11111−i−i−i−iiiiii−ii−iii−i−i-1-1-1-11111−i−i−i−iiiiiζζ−ζ−ζζ3ζ3−ζ3−ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3ζ−ζζ3−ζ3−ζζ−ζ3ζ3
χ22111-1-11-11-1111111111111111-1-11-1-111-1-111-1-1i−i-1i−ii−i-1-1-1-1i−i11-1-111-1-1ii−i−i11-1-1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii1-11-111-1-1ii−i−i1111-1-1-1-1i−i-1-111−i−iii-1-1-1-11111−i−i−i−iiiiii−ii−iii−i−i-1-1-1-11111−i−i−i−iiiii−ζ−ζζζ−ζ3−ζ3ζ3ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3−ζζ−ζ3ζ3ζ−ζζ3−ζ3
χ23111-1-11-11-1111111111111111-1-11-1-111-1-111-1-1i−i-1i−ii−i-1-1-1-1i−i11-1-111-1-1ii−i−i11-1-1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii-11-11-1-111ii−i−i-1-1-1-11111i−i-1-111−i−iii-1-1-1-11111−i−i−i−iiiii−ii−ii−i−iii1111-1-1-1-1iiii−i−i−i−iζζ−ζ−ζζ3ζ3−ζ3−ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζζ−ζ3ζ3ζ−ζζ3−ζ3
χ24111-1-11-11-1111111111111111-1-11-1-111-1-111-1-1i−i-1i−ii−i-1-1-1-1i−i11-1-111-1-1ii−i−i11-1-1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii-11-11-1-111ii−i−i-1-1-1-11111i−i-1-111−i−iii-1-1-1-11111−i−i−i−iiiii−ii−ii−i−iii1111-1-1-1-1iiii−i−i−i−i−ζ−ζζζ−ζ3−ζ3ζ3ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζ−ζζ3−ζ3−ζζ−ζ3ζ3
χ25111-1-11-11-1111111111111111-1-11-1-111-1-111-1-1−ii-1−ii−ii-1-1-1-1−ii11-1-111-1-1−i−iii11-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii1-11-111-1-1−i−iii1111-1-1-1-1−ii11-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii−ii−ii−i−iii1111-1-1-1-1−i−i−i−iiiiiζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3−ζ3ζ−ζζ3−ζ3ζ−ζ
χ26111-1-11-11-1111111111111111-1-11-1-111-1-111-1-1−ii-1−ii−ii-1-1-1-1−ii11-1-111-1-1−i−iii11-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii1-11-111-1-1−i−iii1111-1-1-1-1−ii11-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii−ii−ii−i−iii1111-1-1-1-1−i−i−i−iiiii−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3ζ3−ζζ−ζ3ζ3−ζζ
χ27111-1-11-11-1111111111111111-1-11-1-111-1-111-1-1−ii-1−ii−ii-1-1-1-1−ii11-1-111-1-1−i−iii11-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii-11-11-1-111−i−iii-1-1-1-11111−ii11-1-1−i−iii1111-1-1-1-1−i−i−i−iiiiii−ii−iii−i−i-1-1-1-11111iiii−i−i−i−iζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ−ζ3ζ3−ζζ−ζ3ζ3−ζζ
χ28111-1-11-11-1111111111111111-1-11-1-111-1-111-1-1−ii-1−ii−ii-1-1-1-1−ii11-1-111-1-1−i−iii11-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii-11-11-1-111−i−iii-1-1-1-11111−ii11-1-1−i−iii1111-1-1-1-1−i−i−i−iiiiii−ii−iii−i−i-1-1-1-11111iiii−i−i−i−i−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζζ3−ζ3ζ−ζζ3−ζ3ζ−ζ
χ29111-1-11-11-1111111111111111-1-11-1-111-1-111-1-1−ii-1−ii−ii-1-1-1-1−ii11-1-111-1-1−i−iii11-1-1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i1-11-111-1-1−i−iii1111-1-1-1-1−ii-1-111ii−i−i-1-1-1-11111iiii−i−i−i−i−ii−ii−i−iii-1-1-1-11111iiii−i−i−i−iζ3ζ3−ζ3−ζ3ζζ−ζ−ζ−ζ3−ζ3ζ3ζ3−ζ−ζζζζ3−ζ3ζ−ζ−ζ3ζ3−ζζ
χ30111-1-11-11-1111111111111111-1-11-1-111-1-111-1-1−ii-1−ii−ii-1-1-1-1−ii11-1-111-1-1−i−iii11-1-1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i1-11-111-1-1−i−iii1111-1-1-1-1−ii-1-111ii−i−i-1-1-1-11111iiii−i−i−i−i−ii−ii−i−iii-1-1-1-11111iiii−i−i−i−i−ζ3−ζ3ζ3ζ3−ζ−ζζζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ−ζ3ζ3−ζζζ3−ζ3ζ−ζ
χ31111-1-11-11-1111111111111111-1-11-1-111-1-111-1-1−ii-1−ii−ii-1-1-1-1−ii11-1-111-1-1−i−iii11-1-1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i-11-11-1-111−i−iii-1-1-1-11111−ii-1-111ii−i−i-1-1-1-11111iiii−i−i−i−ii−ii−iii−i−i1111-1-1-1-1−i−i−i−iiiiiζ3ζ3−ζ3−ζ3ζζ−ζ−ζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3ζ3−ζζζ3−ζ3ζ−ζ
χ32111-1-11-11-1111111111111111-1-11-1-111-1-111-1-1−ii-1−ii−ii-1-1-1-1−ii11-1-111-1-1−i−iii11-1-1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i-11-11-1-111−i−iii-1-1-1-11111−ii-1-111ii−i−i-1-1-1-11111iiii−i−i−i−ii−ii−iii−i−i1111-1-1-1-1−i−i−i−iiiii−ζ3−ζ3ζ3ζ3−ζ−ζζζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3−ζ3ζ−ζ−ζ3ζ3−ζζ
χ3322222222222222222222222222222-2-2-2-2-2-2-2-22222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000222200000000-2-2000000000000000000000000000000002i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ3422222222222222222222222222222-2-2-2-2-2-2-2-22222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000222200000000-2-200000000000000000000000000000000−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ3522222222222222222222222222222-2-2-2-2-2-2-2-2-2-22-2-2-2-22222-2-2-2-2-2-2-2-2-2-22222-2-2-2-222222222000000000000000000000000-2-2-2-20000000022000000000000000000000000000000002i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ3622222222222222222222222222222-2-2-2-2-2-2-2-2-2-22-2-2-2-22222-2-2-2-2-2-2-2-2-2-22222-2-2-2-222222222000000000000000000000000-2-2-2-2000000002200000000000000000000000000000000−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ37222222222222222-2-2-2-2-2-2-2-2222222222222222222222-2-2-2-222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2222222222222222200000000-2-2-2-2000000002222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000
χ38222222222222222-2-2-2-2-2-2-2-2222222222222222222222-2-2-2-222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000-2-2-2-20000000022-2-2-2-2-2-2-2-22222222222222222000000000000000000000000000000000000000000000000
χ39222222222222222-2-2-2-2-2-2-2-222222222222222-2-22-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222222222222222-2-2-2-2-2-2-2-200000000222200000000-2-22222-2-2-2-2-2-2-2-2-2-2-2-222222222000000000000000000000000000000000000000000000000
χ40222222222222222-2-2-2-2-2-2-2-222222222222222-2-22-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-22222222200000000222200000000-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000
χ41222222222222222-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-22222222-2-2-2-22222222222-2-2-2-2-2-2-2-222222222000000000000000022222222-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000002222-2-2-2-20000000000000000000000000000000000000000
χ42222222222222222-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-22222222-2-2-2-22222222222-2-2-2-2-2-2-2-2222222220000000000000000-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2000000000000000000000000-2-2-2-222220000000000000000000000000000000000000000
χ43222222222222222-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-2-2-22-2-2-2-2-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000222222222222-2-2-2-2-2-2-2-222000000000000000000000000-2-2-2-222220000000000000000000000000000000000000000
χ44222222222222222-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-2-2-22-2-2-2-2-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000-2-2-2-2-2-2-2-2222222222222220000000000000000000000002222-2-2-2-20000000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.