Finite Group Databasebeta

← Group #72227250

Character table — Group #72227250

Order 4096.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160
size11222222222224444444444444444888888888888888888888888888888888161616161616161616161616161616161616161616161616161616161616161616161616161616161616323232323232323232323232323232323232323232323232323232323232323264646464646464646464646464646464128128128128128128128128
order1222244448888448888881616161616161616444448888888888881616161616161616161616161616161622448888888816161616161616161616161616163232323232323232323232323232323244881616161632323232323232323232323232323232323232323232323232323232323232323232323232323232224416161616
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ41111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ511111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ811111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ9111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-111111111-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-111-1-1ii−i−i
χ10111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-111111111-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111-1-111−i−iii
χ11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-111111111-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111-1-111ii−i−i
χ12111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-111111111-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-111-1-1−i−iii
χ13111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-111111111-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1-1-111−i−iii
χ14111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-111111111-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−i−i−iiiii-1-1-1-1111111-1-1ii−i−i
χ15111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-111111111-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-1111111-1-1−i−iii
χ16111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-111111111-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1-1-111ii−i−i
χ17111-1-11-11-1-1-1-1-11111-11-11iiii−i−i−i−ii−ii−i-1i−i1111-1-1-1-1i−i1-111-1-1ii−i−iii−i−i1-11-11-111-1-1ii−i−iiiii−i−i−i−i11-1-1i−iζζζζ−ζ−ζ−ζ−ζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3i−ii−i11-1-1ζζζζ−ζ−ζ−ζ−ζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ311-1-1ii−i−i1-1i−iζ−ζζ3−ζ3
χ18111-1-11-11-1-1-1-1-11111-11-11iiii−i−i−i−ii−ii−i-1i−i1111-1-1-1-1i−i1-111-1-1ii−i−iii−i−i1-11-11-111-1-1ii−i−iiiii−i−i−i−i11-1-1i−iζζζζ−ζ−ζ−ζ−ζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3i−ii−i11-1-1ζζζζ−ζ−ζ−ζ−ζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3-1-111−i−iii-11−ii−ζζ−ζ3ζ3
χ19111-1-11-11-1-1-1-1-11111-11-11iiii−i−i−i−ii−ii−i-1i−i1111-1-1-1-1i−i1-111-1-1ii−i−iii−i−i1-11-11-111-1-1ii−i−iiiii−i−i−i−i11-1-1i−i−ζ−ζ−ζ−ζζζζζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3i−ii−i11-1-1−ζ−ζ−ζ−ζζζζζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3-1-111−i−iii-11−iiζ−ζζ3−ζ3
χ20111-1-11-11-1-1-1-1-11111-11-11iiii−i−i−i−ii−ii−i-1i−i1111-1-1-1-1i−i1-111-1-1ii−i−iii−i−i1-11-11-111-1-1ii−i−iiiii−i−i−i−i11-1-1i−i−ζ−ζ−ζ−ζζζζζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3i−ii−i11-1-1−ζ−ζ−ζ−ζζζζζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ311-1-1ii−i−i1-1i−i−ζζ−ζ3ζ3
χ21111-1-11-11-1-1-1-1-11111-11-11iiii−i−i−i−ii−ii−i-1i−i1111-1-1-1-1i−i1-111-1-1ii−i−iii−i−i1-1-11-11-1-111ii−i−i−i−i−i−iiiii11-1-1i−iζζζζ−ζ−ζ−ζ−ζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3−ii−ii-1-111−ζ−ζ−ζ−ζζζζζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ311-1-1ii−i−i-11−ii−ζζ−ζ3ζ3
χ22111-1-11-11-1-1-1-1-11111-11-11iiii−i−i−i−ii−ii−i-1i−i1111-1-1-1-1i−i1-111-1-1ii−i−iii−i−i1-1-11-11-1-111ii−i−i−i−i−i−iiiii11-1-1i−iζζζζ−ζ−ζ−ζ−ζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3−ii−ii-1-111−ζ−ζ−ζ−ζζζζζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3-1-111−i−iii1-1i−iζ−ζζ3−ζ3
χ23111-1-11-11-1-1-1-1-11111-11-11iiii−i−i−i−ii−ii−i-1i−i1111-1-1-1-1i−i1-111-1-1ii−i−iii−i−i1-1-11-11-1-111ii−i−i−i−i−i−iiiii11-1-1i−i−ζ−ζ−ζ−ζζζζζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ii−ii-1-111ζζζζ−ζ−ζ−ζ−ζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3-1-111−i−iii1-1i−i−ζζ−ζ3ζ3
χ24111-1-11-11-1-1-1-1-11111-11-11iiii−i−i−i−ii−ii−i-1i−i1111-1-1-1-1i−i1-111-1-1ii−i−iii−i−i1-1-11-11-1-111ii−i−i−i−i−i−iiiii11-1-1i−i−ζ−ζ−ζ−ζζζζζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ii−ii-1-111ζζζζ−ζ−ζ−ζ−ζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ311-1-1ii−i−i-11−iiζ−ζζ3−ζ3
χ25111-1-11-11-1-1-1-1-11111-11-11−i−i−i−iiiii−ii−ii-1−ii1111-1-1-1-1−ii1-111-1-1−i−iii−i−iii1-11-11-111-1-1−i−iii−i−i−i−iiiii11-1-1−iiζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζζζζ−ζ−ζ−ζ−ζ−ii−ii11-1-1ζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζζζζ−ζ−ζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ11-1-1−i−iii1-1−iiζ3−ζ3ζ−ζ
χ26111-1-11-11-1-1-1-1-11111-11-11−i−i−i−iiiii−ii−ii-1−ii1111-1-1-1-1−ii1-111-1-1−i−iii−i−iii1-11-11-111-1-1−i−iii−i−i−i−iiiii11-1-1−iiζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζζζζ−ζ−ζ−ζ−ζ−ii−ii11-1-1ζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζζζζ−ζ−ζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ-1-111ii−i−i-11i−i−ζ3ζ3−ζζ
χ27111-1-11-11-1-1-1-1-11111-11-11−i−i−i−iiiii−ii−ii-1−ii1111-1-1-1-1−ii1-111-1-1−i−iii−i−iii1-11-11-111-1-1−i−iii−i−i−i−iiiii11-1-1−ii−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ−ζ−ζ−ζζζζζ−ii−ii11-1-1−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ−ζ−ζ−ζζζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ-1-111ii−i−i-11i−iζ3−ζ3ζ−ζ
χ28111-1-11-11-1-1-1-1-11111-11-11−i−i−i−iiiii−ii−ii-1−ii1111-1-1-1-1−ii1-111-1-1−i−iii−i−iii1-11-11-111-1-1−i−iii−i−i−i−iiiii11-1-1−ii−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ−ζ−ζ−ζζζζζ−ii−ii11-1-1−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ−ζ−ζ−ζζζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ11-1-1−i−iii1-1−ii−ζ3ζ3−ζζ
χ29111-1-11-11-1-1-1-1-11111-11-11−i−i−i−iiiii−ii−ii-1−ii1111-1-1-1-1−ii1-111-1-1−i−iii−i−iii1-1-11-11-1-111−i−iiiiiii−i−i−i−i11-1-1−iiζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζζζζ−ζ−ζ−ζ−ζi−ii−i-1-111−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ−ζ−ζ−ζζζζζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ11-1-1−i−iii-11i−i−ζ3ζ3−ζζ
χ30111-1-11-11-1-1-1-1-11111-11-11−i−i−i−iiiii−ii−ii-1−ii1111-1-1-1-1−ii1-111-1-1−i−iii−i−iii1-1-11-11-1-111−i−iiiiiii−i−i−i−i11-1-1−iiζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζζζζ−ζ−ζ−ζ−ζi−ii−i-1-111−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ−ζ−ζ−ζζζζζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ-1-111ii−i−i1-1−iiζ3−ζ3ζ−ζ
χ31111-1-11-11-1-1-1-1-11111-11-11−i−i−i−iiiii−ii−ii-1−ii1111-1-1-1-1−ii1-111-1-1−i−iii−i−iii1-1-11-11-1-111−i−iiiiiii−i−i−i−i11-1-1−ii−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ−ζ−ζ−ζζζζζi−ii−i-1-111ζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζζζζ−ζ−ζ−ζ−ζ−ζ3−ζ3ζ3ζ3−ζ−ζζζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ-1-111ii−i−i1-1−ii−ζ3ζ3−ζζ
χ32111-1-11-11-1-1-1-1-11111-11-11−i−i−i−iiiii−ii−ii-1−ii1111-1-1-1-1−ii1-111-1-1−i−iii−i−iii1-1-11-11-1-111−i−iiiiiii−i−i−i−i11-1-1−ii−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ−ζ−ζ−ζζζζζi−ii−i-1-111ζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζζζζ−ζ−ζ−ζ−ζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ11-1-1−i−iii-11i−iζ3−ζ3ζ−ζ
χ33222222222222222222222222222222222222-2-2-2-2-2-2-2-222-2-222222222-2-2-2-2-2-200000000-2-2-2-2000000002-22-2-2-22222222222222222000000000000000000000000-2-2-2-2-2-2-2-2000000000000000000000000
χ34222222222222222222222222222222222222-2-2-2-2-2-2-2-222-2-222222222-2-2-2-2-2-200000000-2-2-2-2000000002-22-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000022222222000000000000000000000000
χ3522222222222222222222222222222-2-2-2-22-2-222222222-2-2-2-2-2-2-2-222222222-2-200000000-2-2-2-200000000-2-2-2-22200000000000000000000000022-2-222-2-222-2-222-2-200000000000000000000000000000000
χ3622222222222222222222222222222-2-2-2-22-2-222222222-2-2-2-2-2-2-2-222222222-2-200000000-2-2-2-200000000-2-2-2-222000000000000000000000000-2-222-2-222-2-222-2-22200000000000000000000000000000000
χ3722222222222222222222222222222-2-2-2-22-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-22222-2-2-2-22222222222222222222222-22-22-2-20000000000000000-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000
χ3822222222222222222222222222222-2-2-2-22-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-22222-2-2-2-222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-22-22-2-2000000000000000022222222000000000000000000000000000000000000000000000000
χ39222222222222222222222-2-2-2-2-2-2-2-222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000222200000000-2-2-2-2-2-20000000000000000000000002i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000
χ40222222222222222222222-2-2-2-2-2-2-2-222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000222200000000-2-2-2-2-2-2000000000000000000000000−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000
χ41222222222222222222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-22-222200000000000000002222-2-2-2-2000000000000000000000000000000000000000000000000
χ42222222222222222222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-2-2-2-2-222222222-22-22220000000000000000-2-2-2-22222000000000000000000000000000000000000000000000000
χ43222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-22-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2000000002222000000002-22-2222i2i2i2i2i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i000000000000000000000000−2i−2i−2i−2i2i2i2i2i000000000000000000000000
χ44222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-22-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2000000002222000000002-22-222−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i2i2i2i2i0000000000000000000000002i2i2i2i−2i−2i−2i−2i000000000000000000000000
χ4522222222222-2-2-2-2222-2-2-20000000022-2-2-2-2-2000000002222000000002222222222-2-2-2-20000000000000-20-2-2-222−2−222−2−222−2−222−2−222-2-200002−22−22−22−22−22−22−22−22−22−22−22−2000000000000000000000000
χ4622222222222-2-2-2-2222-2-2-20000000022-2-2-2-2-2000000002222000000002222222222-2-2-2-20000000000000-20-2-2-2−2−222−2−222−2−222−2−22222-2-20000−22−22−22−22−22−22−22−22−22−22−22−22000000000000000000000000
χ4722222222222-2-2-2-2222-2-2-20000000022-2-2-2-2-200000000222200000000222222-2-2-2-222220000000000000-20-2-2-222−2−222−2−222−2−222−2−2-2-2220000−22−22−22−22−22−22−22−222−22−22−22−2000000000000000000000000
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Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.