Finite Group Databasebeta

← Group #72323027

Character table — Group #72323027

Order 4096.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162C163C164C165C166C167C168C169C170C171C172C173C174C175C176C177C178C179C180C181C182C183C184C185C186C187C188C189C190C191C192C193C194C195C196C197C198C199C200C201C202C203C204C205C206C207C208
size112222222224444444444444888888888888816161616161616161616161616161616161616161616161616323232323232323232323232323232323232323232323232323232323232323232323232323264646464112222222224444444444444888888888888816161616161616161616161616161616161616161616161616323232323232323232323232323232323232323232323232323232323232323232323232323264646464
order122224444882244448888888444881616161616161616222244448888888881616161616161616222444888888888816161616161632323232323232323232323232323232481616222224444882244448888888444881616161616161616222244448888888881616161616161616222444888888888816161616161632323232323232323232323232323232481616
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111111111111111111111111111111111111111111111-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-111
χ51111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ61111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111111111-1-1-1-11111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111111111-1-1-1-1
χ71111111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1
χ81111111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111111111-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111111111-1-1-1-1-1-1-1-1-1-111
χ91111111111111-1-1-1-1111-1-1-1-11-1-1111111-1-1-1-11111-1-1-1-1-1iiii−i−i−i−i11-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−ii−iii−i−i1111-1-1-1-1iiii−i−i−i−i1-1i−i1111111111111-1-1-1-1111-1-1-1-11-1-1111111-1-1-1-11111-1-1-1-1-1iiii−i−i−i−i11-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−ii−iii−i−i1111-1-1-1-1iiii−i−i−i−i1-1i−i
χ101111111111111-1-1-1-1111-1-1-1-11-1-1111111-1-1-1-11111-1-1-1-1-1iiii−i−i−i−i11-1-1ii−i−i11-1-1-1-111iiii−i−i−i−ii−i−i−iii-1-1-1-11111−i−i−i−iiiii-11−ii1111111111111-1-1-1-1111-1-1-1-11-1-1111111-1-1-1-11111-1-1-1-1-1iiii−i−i−i−i11-1-1ii−i−i11-1-1-1-111iiii−i−i−i−ii−i−i−iii-1-1-1-11111−i−i−i−iiiii-11−ii
χ111111111111111-1-1-1-1111-1-1-1-11-1-1111111-1-1-1-11111-1-1-1-1-1−i−i−i−iiiii11-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii−ii−i−iii1111-1-1-1-1−i−i−i−iiiii1-1−ii1111111111111-1-1-1-1111-1-1-1-11-1-1111111-1-1-1-11111-1-1-1-1-1−i−i−i−iiiii11-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii−ii−i−iii1111-1-1-1-1−i−i−i−iiiii1-1−ii
χ121111111111111-1-1-1-1111-1-1-1-11-1-1111111-1-1-1-11111-1-1-1-1-1−i−i−i−iiiii11-1-1−i−iii11-1-1-1-111−i−i−i−iiiii−iiii−i−i-1-1-1-11111iiii−i−i−i−i-11i−i1111111111111-1-1-1-1111-1-1-1-11-1-1111111-1-1-1-11111-1-1-1-1-1−i−i−i−iiiii11-1-1−i−iii11-1-1-1-111−i−i−i−iiiii−iiii−i−i-1-1-1-11111iiii−i−i−i−i-11i−i
χ131111111111111-1-1-1-1111-1-1-1-11-1-1111111-1-1-1-1-1-1-1-11111-1iiii−i−i−i−i11-1-1ii−i−i-1-11111-1-1−i−i−i−iiiiii−iii−i−i-1-1-1-11111−i−i−i−iiiii1-1i−i1111111111111-1-1-1-1111-1-1-1-11-1-1111111-1-1-1-1-1-1-1-11111-1iiii−i−i−i−i11-1-1ii−i−i-1-11111-1-1−i−i−i−iiiiii−iii−i−i-1-1-1-11111−i−i−i−iiiii1-1i−i
χ141111111111111-1-1-1-1111-1-1-1-11-1-1111111-1-1-1-1-1-1-1-11111-1iiii−i−i−i−i11-1-1ii−i−i-1-1-1-11111−i−i−i−iiiiii−i−i−iii1111-1-1-1-1iiii−i−i−i−i-11−ii1111111111111-1-1-1-1111-1-1-1-11-1-1111111-1-1-1-1-1-1-1-11111-1iiii−i−i−i−i11-1-1ii−i−i-1-1-1-11111−i−i−i−iiiiii−i−i−iii1111-1-1-1-1iiii−i−i−i−i-11−ii
χ151111111111111-1-1-1-1111-1-1-1-11-1-1111111-1-1-1-1-1-1-1-11111-1−i−i−i−iiiii11-1-1−i−iii-1-11111-1-1iiii−i−i−i−i−ii−i−iii-1-1-1-11111iiii−i−i−i−i1-1−ii1111111111111-1-1-1-1111-1-1-1-11-1-1111111-1-1-1-1-1-1-1-11111-1−i−i−i−iiiii11-1-1−i−iii-1-11111-1-1iiii−i−i−i−i−ii−i−iii-1-1-1-11111iiii−i−i−i−i1-1−ii
χ161111111111111-1-1-1-1111-1-1-1-11-1-1111111-1-1-1-1-1-1-1-11111-1−i−i−i−iiiii11-1-1−i−iii-1-1-1-11111iiii−i−i−i−i−iiii−i−i1111-1-1-1-1−i−i−i−iiiii-11i−i1111111111111-1-1-1-1111-1-1-1-11-1-1111111-1-1-1-1-1-1-1-11111-1−i−i−i−iiiii11-1-1−i−iii-1-1-1-11111iiii−i−i−i−i−iiii−i−i1111-1-1-1-1−i−i−i−iiiii-11i−i
χ1711111111111-1-111111111111-1-1-1-1-11111111111111111-111-1-111-1-1-1-1-1-11111-1-111-1-11111-1-111-1-1-1-1111111-1-111-1-111-1-111-1-1-1-1-1-111111111111-1-111111111111-1-1-1-1-11111111111111111-111-1-111-1-1-1-1-1-11111-1-111-1-11111-1-111-1-1-1-1111111-1-111-1-111-1-111-1-1-1-1-1-1
χ1811111111111-1-111111111111-1-1-1-1-11111111111111111-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111111111111111111-1-111111111111-1-1-1-1-11111111111111111-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1111111
χ1911111111111-1-111111111111-1-1-1-1-11111111111111111-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-11111-1-1-1-111-1-111-1-1-1-111-1-111-1-11111111111111-1-111111111111-1-1-1-1-11111111111111111-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-11111-1-1-1-111-1-111-1-1-1-111-1-111-1-111
χ2011111111111-1-111111111111-1-1-1-1-11111111111111111-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-111-1-11111-1-111-1-111-1-111111111111-1-111111111111-1-1-1-1-11111111111111111-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-111-1-11111-1-111-1-111-1-1
χ2111111111111-1-111111111111-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1111111111111-1-111-1-111-1-11111-1-111-1-111-1-111-1-111-1-1-1-111111111111-1-111111111111-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1111111111111-1-111-1-111-1-11111-1-111-1-111-1-111-1-111-1-1-1-1
χ2211111111111-1-111111111111-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1111111-1-111-1-1-1-111-1-111-1-1-1-1-1-111-1-111-1-111-1-111-1-1111111111111111-1-111111111111-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1111111-1-111-1-1-1-111-1-111-1-1-1-1-1-111-1-111-1-111-1-111-1-11111
χ2311111111111-1-111111111111-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-11111111111-1-111-1-111-1-1-1-1-1-111-1-11111-1-111-1-1-1-11111111111111-1-111111111111-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-11111111111-1-111-1-111-1-1-1-1-1-111-1-11111-1-111-1-1-1-111
χ2411111111111-1-111111111111-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-111111111-1-111-1-1-1-111-1-11111-1-111111111111-1-111111111111-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-111111111-1-111-1-1-1-111-1-11111-1-1
χ2511111111111-1-1-1-1-1-1111-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11ii−i−i−i−iii-1-111ii−i−i-1-11111-1-1ii−i−i−i−iii−iiii−i−i11-1-1-1-111ii−i−i−i−iii-11−ii11111111111-1-1-1-1-1-1111-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11ii−i−i−i−iii-1-111ii−i−i-1-11111-1-1ii−i−i−i−iii−iiii−i−i11-1-1-1-111ii−i−i−i−iii-11−ii
χ2611111111111-1-1-1-1-1-1111-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11ii−i−i−i−iii-1-111ii−i−i-1-1-1-11111ii−i−i−i−iii−ii−i−iii-1-11111-1-1−i−iiiii−i−i1-1i−i11111111111-1-1-1-1-1-1111-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11ii−i−i−i−iii-1-111ii−i−i-1-1-1-11111ii−i−i−i−iii−ii−i−iii-1-11111-1-1−i−iiiii−i−i1-1i−i
χ2711111111111-1-1-1-1-1-1111-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11−i−iiiii−i−i-1-111−i−iii-1-11111-1-1−i−iiiii−i−ii−i−i−iii11-1-1-1-111−i−iiiii−i−i-11i−i11111111111-1-1-1-1-1-1111-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11−i−iiiii−i−i-1-111−i−iii-1-11111-1-1−i−iiiii−i−ii−i−i−iii11-1-1-1-111−i−iiiii−i−i-11i−i
χ2811111111111-1-1-1-1-1-1111-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11−i−iiiii−i−i-1-111−i−iii-1-1-1-11111−i−iiiii−i−ii−iii−i−i-1-11111-1-1ii−i−i−i−iii1-1−ii11111111111-1-1-1-1-1-1111-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11−i−iiiii−i−i-1-111−i−iii-1-1-1-11111−i−iiiii−i−ii−iii−i−i-1-11111-1-1ii−i−i−i−iii1-1−ii
χ2911111111111-1-1-1-1-1-1111-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-111111ii−i−i−i−iii-1-111ii−i−i1111-1-1-1-1−i−iiiii−i−i−iiii−i−i-1-11111-1-1−i−iiiii−i−i-11−ii11111111111-1-1-1-1-1-1111-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-111111ii−i−i−i−iii-1-111ii−i−i1111-1-1-1-1−i−iiiii−i−i−iiii−i−i-1-11111-1-1−i−iiiii−i−i-11−ii
χ3011111111111-1-1-1-1-1-1111-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-111111ii−i−i−i−iii-1-111ii−i−i11-1-1-1-111−i−iiiii−i−i−ii−i−iii11-1-1-1-111ii−i−i−i−iii1-1i−i11111111111-1-1-1-1-1-1111-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-111111ii−i−i−i−iii-1-111ii−i−i11-1-1-1-111−i−iiiii−i−i−ii−i−iii11-1-1-1-111ii−i−i−i−iii1-1i−i
χ3111111111111-1-1-1-1-1-1111-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-111111−i−iiiii−i−i-1-111−i−iii1111-1-1-1-1ii−i−i−i−iiii−i−i−iii-1-11111-1-1ii−i−i−i−iii-11i−i11111111111-1-1-1-1-1-1111-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-111111−i−iiiii−i−i-1-111−i−iii1111-1-1-1-1ii−i−i−i−iiii−i−i−iii-1-11111-1-1ii−i−i−i−iii-11i−i
χ3211111111111-1-1-1-1-1-1111-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-111111−i−iiiii−i−i-1-111−i−iii11-1-1-1-111ii−i−i−i−iiii−iii−i−i11-1-1-1-111−i−iiiii−i−i1-1−ii11111111111-1-1-1-1-1-1111-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-111111−i−iiiii−i−i-1-111−i−iii11-1-1-1-111ii−i−i−i−iiii−iii−i−i11-1-1-1-111−i−iiiii−i−i1-1−ii
χ3322222222222222222222222222222-2-2-2-2-2-2-2-200000000222222222-2-2-2-2-2-2-2-20000000000000000-2-200000000000000000000000022222222222222222222222222222-2-2-2-2-2-2-2-200000000222222222-2-2-2-2-2-2-2-20000000000000000-2-2000000000000000000000000
χ3422222222222222222222222222222-2-2-2-2-2-2-2-2000000002-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000002200000000000000000000000022222222222222222222222222222-2-2-2-2-2-2-2-2000000002-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000022000000000000000000000000
χ352222222222222-2-2-2-2222-2-2-2-22-2-222-2-2-2-2222200000000-22i2i2i2i−2i−2i−2i−2i-2-222−2i−2i2i2i0000000000000000−2i2i0000000000000000000000002222222222222-2-2-2-2222-2-2-2-22-2-222-2-2-2-2222200000000-22i2i2i2i−2i−2i−2i−2i-2-222−2i−2i2i2i0000000000000000−2i2i000000000000000000000000
χ362222222222222-2-2-2-2222-2-2-2-22-2-222-2-2-2-2222200000000-2−2i−2i−2i−2i2i2i2i2i-2-2222i2i−2i−2i00000000000000002i−2i0000000000000000000000002222222222222-2-2-2-2222-2-2-2-22-2-222-2-2-2-2222200000000-2−2i−2i−2i−2i2i2i2i2i-2-2222i2i−2i−2i00000000000000002i−2i000000000000000000000000
χ3722222222222-2-222222222222-2-2-2-2-2-2-2-2-2-2-2-2-200000000-222-2-222-2-22222-2-2-2-200000000000000002200000000000000000000000022222222222-2-222222222222-2-2-2-2-2-2-2-2-2-2-2-2-200000000-222-2-222-2-22222-2-2-2-2000000000000000022000000000000000000000000
χ3822222222222-2-222222222222-2-2-2-2-2-2-2-2-2-2-2-2-200000000-2-2-222-2-222222222220000000000000000-2-200000000000000000000000022222222222-2-222222222222-2-2-2-2-2-2-2-2-2-2-2-2-200000000-2-2-222-2-222222222220000000000000000-2-2000000000000000000000000
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χ199888-8-88-8-88000000000000000000000000000000000000000000000004i2−4i20000000000000000000000000000000000000000000000-8-8-888-888-800000000000000000000000000000000000000000000000−4i24i20000000000000000000000000000000000000000000000
χ200888-8-88-8-8800000000000000000000000000000000000000000000000−4i24i20000000000000000000000000000000000000000000000-8-8-888-888-8000000000000000000000000000000000000000000000004i2−4i20000000000000000000000000000000000000000000000
χ20188-88-8-8-88800000000000000000000000000000000000000000000042−42000000000000000000000000000000000000000000000000-8-88-8888-8-8000000000000000000000000000000000000000000000−4242000000000000000000000000000000000000000000000000
χ20288-88-8-8-888000000000000000000000000000000000000000000000−4242000000000000000000000000000000000000000000000000-8-88-8888-8-800000000000000000000000000000000000000000000042−42000000000000000000000000000000000000000000000000
χ20388-8-888-88-800000000000000008-800000000000000000000000000000000000000000000000000000000000000000000000000000-8-888-8-88-880000000000000000-8800000000000000000000000000000000000000000000000000000000000000000000000000000
χ20488-8-888-88-80000000000000000-8800000000000000000000000000000000000000000000000000000000000000000000000000000-8-888-8-88-8800000000000000008-800000000000000000000000000000000000000000000000000000000000000000000000000000
χ20516-16000000082−828-80000000000000042−42000000000000000000000000000000000000000000000000000000000000000000000000000-16160000000−8282-8800000000000000−4242000000000000000000000000000000000000000000000000000000000000000000000000000
χ20616-16000000082−82-8800000000000000−4242000000000000000000000000000000000000000000000000000000000000000000000000000-16160000000−82828-80000000000000042−42000000000000000000000000000000000000000000000000000000000000000000000000000
χ20716-160000000−82828-800000000000000−4242000000000000000000000000000000000000000000000000000000000000000000000000000-1616000000082−82-880000000000000042−42000000000000000000000000000000000000000000000000000000000000000000000000000
χ20816-160000000−8282-880000000000000042−42000000000000000000000000000000000000000000000000000000000000000000000000000-1616000000082−828-800000000000000−4242000000000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.