Finite Group Databasebeta

← Group #72321305

Character table — Group #72321305

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162C163C164C165C166C167C168C169C170C171C172C173C174C175C176C177C178C179C180C181C182C183C184C185C186C187C188C189C190C191C192C193C194C195C196C197C198C199C200C201C202C203C204C205C206C207C208C209C210C211C212
size1122222222244444444444444444444444444444444444888888888888888888888888888888888888888888883232323232323232323232323232323211222222222444444444444444444444444444444444448888888888888888888888888888888888888888888832323232323232323232323232323232
order122224444882244444488888888888161616161616161616161616161616164488161616161616161632323232323232323232323232323232323232323232323232323232323232324444888888888888222224444882244444488888888888161616161616161616161616161616164488161616161616161632323232323232323232323232323232323232323232323232323232323232324444888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111-1-1-1-1111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111iiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i1111-1-1-1-1iiii−i−i−i−i111111111111111-1-1-1-1111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111iiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i1111-1-1-1-1iiii−i−i−i−i
χ6111111111111111-1-1-1-1111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111iiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i-1-1-1-11111−i−i−i−iiiii111111111111111-1-1-1-1111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111iiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i-1-1-1-11111−i−i−i−iiiii
χ7111111111111111-1-1-1-1111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii1111-1-1-1-1−i−i−i−iiiii111111111111111-1-1-1-1111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii1111-1-1-1-1−i−i−i−iiiii
χ8111111111111111-1-1-1-1111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii-1-1-1-11111iiii−i−i−i−i111111111111111-1-1-1-1111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii-1-1-1-11111iiii−i−i−i−i
χ911111111111-1-1-1-1111111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-111111111111-1-1-1-1111111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-1
χ1011111111111-1-1-1-1111111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-11111111111111-1-1-1-1111111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111
χ1111111111111-1-1-1-1111111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-111-1-11111111111111-1-1-1-1111111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-111-1-111
χ1211111111111-1-1-1-1111111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-111-1-111111111111-1-1-1-1111111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-111-1-1
χ1311111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-111111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii11-1-1-1-111ii−i−i−i−iii11111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-111111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii11-1-1-1-111ii−i−i−i−iii
χ1411111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-111111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii-1-11111-1-1−i−iiiii−i−i11111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-111111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii-1-11111-1-1−i−iiiii−i−i
χ1511111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-111111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i11-1-1-1-111−i−iiiii−i−i11111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-111111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i11-1-1-1-111−i−iiiii−i−i
χ1611111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-111111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i-1-11111-1-1ii−i−i−i−iii11111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-111111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i-1-11111-1-1ii−i−i−i−iii
χ17111-1-111-1-1111-11-111-1-1-1-111-1-111-1-11-1-1-1-11111-1-1-1-111111-11-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1i−ii−ii−ii−ii−ii−ii−ii−i111-1-111-1-1111-11-111-1-1-1-111-1-111-1-11-1-1-1-11111-1-1-1-111111-11-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1i−ii−ii−ii−ii−ii−ii−ii−i
χ18111-1-111-1-1111-11-111-1-1-1-111-1-111-1-11-1-1-1-11111-1-1-1-111111-11-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1−ii−ii−ii−ii−ii−ii−ii−ii111-1-111-1-1111-11-111-1-1-1-111-1-111-1-11-1-1-1-11111-1-1-1-111111-11-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1−ii−ii−ii−ii−ii−ii−ii−ii
χ19111-1-111-1-1111-11-111-1-1-1-111-1-111-1-11-1-1-1-11111-1-1-1-111111-11-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111i−ii−ii−ii−i−ii−ii−ii−ii111-1-111-1-1111-11-111-1-1-1-111-1-111-1-11-1-1-1-11111-1-1-1-111111-11-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111i−ii−ii−ii−i−ii−ii−ii−ii
χ20111-1-111-1-1111-11-111-1-1-1-111-1-111-1-11-1-1-1-11111-1-1-1-111111-11-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111−ii−ii−ii−iii−ii−ii−ii−i111-1-111-1-1111-11-111-1-1-1-111-1-111-1-11-1-1-1-11111-1-1-1-111111-11-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111−ii−ii−ii−iii−ii−ii−ii−i
χ21111-1-111-1-1111-11-1-1-111-1-111-1-1-1-11111111-1-1-1-11111-1-1-1-1-11-1111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiii−ii−i−ii−ii-11-111-11-1111-1-111-1-1111-11-1-1-111-1-111-1-1-1-11111111-1-1-1-11111-1-1-1-1-11-1111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiii−ii−i−ii−ii-11-111-11-1
χ22111-1-111-1-1111-11-1-1-111-1-111-1-1-1-11111111-1-1-1-11111-1-1-1-1-11-1111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii−ii−iii−ii−i1-11-1-11-11111-1-111-1-1111-11-1-1-111-1-111-1-1-1-11111111-1-1-1-11111-1-1-1-1-11-1111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii−ii−iii−ii−i1-11-1-11-11
χ23111-1-111-1-1111-11-1-1-111-1-111-1-1-1-11111111-1-1-1-11111-1-1-1-1-11-1111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−ii−ii−i−ii−ii1-11-1-11-11111-1-111-1-1111-11-1-1-111-1-111-1-1-1-11111111-1-1-1-11111-1-1-1-1-11-1111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−ii−ii−i−ii−ii1-11-1-11-11
χ24111-1-111-1-1111-11-1-1-111-1-111-1-1-1-11111111-1-1-1-11111-1-1-1-1-11-1111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−ii−iii−ii−i-11-111-11-1111-1-111-1-1111-11-1-1-111-1-111-1-1-1-11111111-1-1-1-11111-1-1-1-1-11-1111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−ii−iii−ii−i-11-111-11-1
χ25111-1-111-1-111-11-1111-1-1-1-1-1-11111-1-11-1-1-1-1-1-1-1-111111111-11-1111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111i−i−iii−i−iii−i−iii−i−ii111-1-111-1-111-11-1111-1-1-1-1-1-11111-1-11-1-1-1-1-1-1-1-111111111-11-1111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111i−i−iii−i−iii−i−iii−i−ii
χ26111-1-111-1-111-11-1111-1-1-1-1-1-11111-1-11-1-1-1-1-1-1-1-111111111-11-1111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111−iii−i−iii−i−iii−i−iii−i111-1-111-1-111-11-1111-1-1-1-1-1-11111-1-11-1-1-1-1-1-1-1-111111111-11-1111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111−iii−i−iii−i−iii−i−iii−i
χ27111-1-111-1-111-11-1111-1-1-1-1-1-11111-1-11-1-1-1-1-1-1-1-111111111-11-1111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1i−i−iii−i−ii−iii−i−iii−i111-1-111-1-111-11-1111-1-1-1-1-1-11111-1-11-1-1-1-1-1-1-1-111111111-11-1111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1i−i−iii−i−ii−iii−i−iii−i
χ28111-1-111-1-111-11-1111-1-1-1-1-1-11111-1-11-1-1-1-1-1-1-1-111111111-11-1111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1−iii−i−iii−ii−i−iii−i−ii111-1-111-1-111-11-1111-1-1-1-1-1-11111-1-11-1-1-1-1-1-1-1-111111111-11-1111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1−iii−i−iii−ii−i−iii−i−ii
χ29111-1-111-1-111-11-11-1-111-1-1-1-111-1-111111111111-1-1-1-1-1-1-1-11-11-111-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−ii−i−ii−iii−i-111-11-1-11111-1-111-1-111-11-11-1-111-1-1-1-111-1-111111111111-1-1-1-1-1-1-1-11-11-111-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−ii−i−ii−iii−i-111-11-1-11
χ30111-1-111-1-111-11-11-1-111-1-1-1-111-1-111111111111-1-1-1-1-1-1-1-11-11-111-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i−iii−ii−i−ii1-1-11-111-1111-1-111-1-111-11-11-1-111-1-1-1-111-1-111111111111-1-1-1-1-1-1-1-11-11-111-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i−iii−ii−i−ii1-1-11-111-1
χ31111-1-111-1-111-11-11-1-111-1-1-1-111-1-111111111111-1-1-1-1-1-1-1-11-11-111-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiii−i−ii−iii−i1-1-11-111-1111-1-111-1-111-11-11-1-111-1-1-1-111-1-111111111111-1-1-1-1-1-1-1-11-11-111-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiii−i−ii−iii−i1-1-11-111-1
χ32111-1-111-1-111-11-11-1-111-1-1-1-111-1-111111111111-1-1-1-1-1-1-1-11-11-111-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−iii−ii−i−ii-111-11-1-11111-1-111-1-111-11-11-1-111-1-1-1-111-1-111111111111-1-1-1-1-1-1-1-11-11-111-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−iii−ii−i−ii-111-11-1-11
χ33222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000
χ34222222222222222-2-2-2-2222222-2-2-2-222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000222222222222222-2-2-2-2222222-2-2-2-222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.