Finite Group Databasebeta

← Group #72225251

Character table — Group #72225251

Order 4096.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162C163C164C165C166C167C168C169C170C171C172C173C174C175C176C177C178C179C180C181C182C183C184
size111122222222222222444444444444444444444444444488888888888888888888888888888888888888888888888888888888888888161616161616161616161616161616161616161616161616323232323232323232323232323232326464646464646464646464646464646464646464646464646464646464646464128128128128
order12222244448888888844444444888888888888888888884488881616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616888816161616161616161616161616161616161616168888888888888888222244441616161616161616323232323232323232323232323232322244
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ711111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ811111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ91111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-1
χ101111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii-1-111
χ111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-111
χ121111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii11-1-1
χ131111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1ii−i−iii−i−i−i−i−i−iiiii−i−i−i−iiiii-1-111
χ141111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111iiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111ii−i−i−i−iii−i−i−i−iiiiiiiii−i−i−i−i11-1-1
χ151111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111−i−iiiii−i−iiiii−i−i−i−i−i−i−i−iiiii11-1-1
χ161111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1−i−iii−i−iiiiiii−i−i−i−iiiii−i−i−i−i-1-111
χ1711-1-11-111-1-11111-1-1-1-111-1-1ii−i−i11-1-111111111-1-1-1-1-1-1-1-1i−iii−i−i1111-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iii−i−iii−i−iiiiiiiii−i−i−i−i−i−i−i−iζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ311-1-1ii−i−iζ−ζζ3−ζ3ζ−ζζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ31-1i−i
χ1811-1-11-111-1-11111-1-1-1-111-1-1ii−i−i11-1-111111111-1-1-1-1-1-1-1-1i−iii−i−i1111-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iii−i−iii−i−iiiiiiiii−i−i−i−i−i−i−i−iζζ−ζ−ζζ3ζ3−ζ3−ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3-1-111−i−iiiζ−ζζ3−ζ3−ζζ−ζ3ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3-11−ii
χ1911-1-11-111-1-11111-1-1-1-111-1-1ii−i−i11-1-111111111-1-1-1-1-1-1-1-1i−iii−i−i1111-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iii−i−iii−i−iiiiiiiii−i−i−i−i−i−i−i−i−ζ−ζζζ−ζ3−ζ3ζ3ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3-1-111−i−iii−ζζ−ζ3ζ3ζ−ζζ3−ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3-11−ii
χ2011-1-11-111-1-11111-1-1-1-111-1-1ii−i−i11-1-111111111-1-1-1-1-1-1-1-1i−iii−i−i1111-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iii−i−iii−i−iiiiiiiii−i−i−i−i−i−i−i−i−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ311-1-1ii−i−i−ζζ−ζ3ζ3−ζζ−ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ31-1i−i
χ2111-1-11-111-1-11111-1-1-1-111-1-1ii−i−i11-1-111111111-1-1-1-1-1-1-1-1i−iii−i−i1111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111iiii−i−i−i−iii−i−iii−i−i−i−i−i−i−i−i−i−iiiiiiiiiζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ311-1-1ii−i−iζ−ζζ3−ζ3ζ−ζζ3−ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3-11−ii
χ2211-1-11-111-1-11111-1-1-1-111-1-1ii−i−i11-1-111111111-1-1-1-1-1-1-1-1i−iii−i−i1111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111iiii−i−i−i−iii−i−iii−i−i−i−i−i−i−i−i−i−iiiiiiiiiζζ−ζ−ζζ3ζ3−ζ3−ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3-1-111−i−iiiζ−ζζ3−ζ3−ζζ−ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ31-1i−i
χ2311-1-11-111-1-11111-1-1-1-111-1-1ii−i−i11-1-111111111-1-1-1-1-1-1-1-1i−iii−i−i1111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111iiii−i−i−i−iii−i−iii−i−i−i−i−i−i−i−i−i−iiiiiiiii−ζ−ζζζ−ζ3−ζ3ζ3ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3-1-111−i−iii−ζζ−ζ3ζ3ζ−ζζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ31-1i−i
χ2411-1-11-111-1-11111-1-1-1-111-1-1ii−i−i11-1-111111111-1-1-1-1-1-1-1-1i−iii−i−i1111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111iiii−i−i−i−iii−i−iii−i−i−i−i−i−i−i−i−i−iiiiiiiii−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ311-1-1ii−i−i−ζζ−ζ3ζ3−ζζ−ζ3ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3-11−ii
χ2511-1-11-111-1-11111-1-1-1-111-1-1−i−iii11-1-111111111-1-1-1-1-1-1-1-1−ii−i−iii1111-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−iii−i−iii−i−i−i−i−i−i−i−iiiiiiiiiζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ11-1-1−i−iiiζ3−ζ3ζ−ζζ3−ζ3ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ1-1−ii
χ2611-1-11-111-1-11111-1-1-1-111-1-1−i−iii11-1-111111111-1-1-1-1-1-1-1-1−ii−i−iii1111-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−iii−i−iii−i−i−i−i−i−i−i−iiiiiiiiiζ3ζ3−ζ3−ζ3ζζ−ζ−ζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ-1-111ii−i−iζ3−ζ3ζ−ζ−ζ3ζ3−ζζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ-11i−i
χ2711-1-11-111-1-11111-1-1-1-111-1-1−i−iii11-1-111111111-1-1-1-1-1-1-1-1−ii−i−iii1111-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−iii−i−iii−i−i−i−i−i−i−i−iiiiiiiii−ζ3−ζ3ζ3ζ3−ζ−ζζζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ-1-111ii−i−i−ζ3ζ3−ζζζ3−ζ3ζ−ζ−ζ3−ζ3ζ3ζ3−ζ−ζζζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ-11i−i
χ2811-1-11-111-1-11111-1-1-1-111-1-1−i−iii11-1-111111111-1-1-1-1-1-1-1-1−ii−i−iii1111-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−iii−i−iii−i−i−i−i−i−i−i−iiiiiiiii−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ11-1-1−i−iii−ζ3ζ3−ζζ−ζ3ζ3−ζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ1-1−ii
χ2911-1-11-111-1-11111-1-1-1-111-1-1−i−iii11-1-111111111-1-1-1-1-1-1-1-1−ii−i−iii1111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111−i−i−i−iiiii−i−iii−i−iiiiiiiiiii−i−i−i−i−i−i−i−iζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ11-1-1−i−iiiζ3−ζ3ζ−ζζ3−ζ3ζ−ζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ-11i−i
χ3011-1-11-111-1-11111-1-1-1-111-1-1−i−iii11-1-111111111-1-1-1-1-1-1-1-1−ii−i−iii1111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111−i−i−i−iiiii−i−iii−i−iiiiiiiiiii−i−i−i−i−i−i−i−iζ3ζ3−ζ3−ζ3ζζ−ζ−ζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ-1-111ii−i−iζ3−ζ3ζ−ζ−ζ3ζ3−ζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ1-1−ii
χ3111-1-11-111-1-11111-1-1-1-111-1-1−i−iii11-1-111111111-1-1-1-1-1-1-1-1−ii−i−iii1111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111−i−i−i−iiiii−i−iii−i−iiiiiiiiiii−i−i−i−i−i−i−i−i−ζ3−ζ3ζ3ζ3−ζ−ζζζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ-1-111ii−i−i−ζ3ζ3−ζζζ3−ζ3ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ1-1−ii
χ3211-1-11-111-1-11111-1-1-1-111-1-1−i−iii11-1-111111111-1-1-1-1-1-1-1-1−ii−i−iii1111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111−i−i−i−iiiii−i−iii−i−iiiiiiiiiii−i−i−i−i−i−i−i−i−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ11-1-1−i−iii−ζ3ζ3−ζζ−ζ3ζ3−ζζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ-11i−i
χ332222222222222222222222222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000-2-2-2-2-2-2-2-22222-2-2-2-2000000000000000000000000000000002-22-22-22-20000000000000000000000000000
χ342222222222222222222222222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000-2-2-2-2-2-2-2-22222-2-2-2-200000000000000000000000000000000-22-22-22-220000000000000000000000000000
χ35222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222-2-222-2-222-2-222-2-20000000000000000000000000000000022-2-222-2-2-2-2-2-22-22-200000000000000000000000022222222000000000000-2-2-2-200000000000000000000
χ36222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222-2-222-2-222-2-222-2-20000000000000000000000000000000022-2-222-2-2-2-2-2-22-22-2000000000000000000000000-2-2-2-2-2-2-2-2000000000000222200000000000000000000
χ37222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222-2-222-2-222-2-222-2-22200000000000000000000000000000000-2-222-2-222-2-2-2-2-22-220000000000000000222222220000000000000000-2-2-2-2000000000000000000000000
χ38222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222-2-222-2-222-2-222-2-22200000000000000000000000000000000-2-222-2-222-2-2-2-2-22-220000000000000000-2-2-2-2-2-2-2-200000000000000002222000000000000000000000000
χ392222222222222222222222-2-2-2-222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000022222222-2-2-2-22222000000000000000000000000000000002-22-2-22-220000000000000000000000000000
χ402222222222222222222222-2-2-2-222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000022222222-2-2-2-2222200000000000000000000000000000000-22-222-22-20000000000000000000000000000
χ412222222222222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-222-2-222-2-222-2-200000000000000000000000000000000-2-222-2-2222222-22-220000000000000000000000002i2i2i2i−2i−2i−2i−2i000000000000−2i−2i2i2i00000000000000000000
χ422222222222222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-222-2-222-2-222-2-200000000000000000000000000000000-2-222-2-2222222-22-22000000000000000000000000−2i−2i−2i−2i2i2i2i2i0000000000002i2i−2i−2i00000000000000000000
χ432222222222222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-222-2-222-2-2220000000000000000000000000000000022-2-222-2-222222-22-200000000000000002i2i2i2i−2i−2i−2i−2i0000000000000000−2i−2i2i2i000000000000000000000000
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χ552222222222-2-222-2-222-2-2-2-22222-22-220000000000000000-2-2-22-2222002200-2-200-2-200−2−2−2−22222−2−2−2−22222−2−2−2−22222−2−2−2−22222220022000000-20-20−2−222−2−222−2−222−2−222000000002-22-22-22-2000000000000000000000000−22−22−22−220000
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Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.