Finite Group Databasebeta

← Group #6372890

Character table — Group #6372890

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162C163C164C165C166C167C168C169C170C171C172C173C174C175C176
size11111111111111112222222222222222222222222222222222222222222222222222222288888888888888881111111111111111222222222222222222222222222222222222222222222222222222228888888888888888
order12224444888888882222224444444444444444444444888888888888888888888888888822444444888888882222444488888888222222444444444444444444444488888888888888888888888888882244444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-11-111-1-111-1-1111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-11-111-1-111-1-1
χ4111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-11-1-111-1-111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-11-1-111-1-111
χ511111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1111111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111
χ611111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1
χ711111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1111-1-1-11111-1-111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1111-1-1-11111-1-1
χ811111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1111-1-1-1111-1-1-1-11111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1111-1-1-1111-1-1-1-111
χ911111111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-11-1-1-111-1-11111111111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-11-1-1-111-1-111
χ1011111111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1111-1-111-1-111111111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1111-1-111-1-1
χ1111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1
χ1211111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111
χ1311111111-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1111111111-1-1-1111-111-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1111111111-1-1-1111-111-1-1-1-111
χ1411111111-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1111-1-1-11-1-11111-1-111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1111-1-1-11-1-11111-1-1
χ1511111111-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1
χ1611111111-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111
χ171111-1-1-1-1iiii−i−i−i−i-111-1-1-1111-1-1iiii−i−i−i−iiiii−i−i−i−i1ii−i−iiiii−i−i−i−i1111-1-1-1-11111-1-1-1-1111-11-1-1-1i−ii−ii−ii−i1111-1-1-1-1iiii−i−i−i−i-111-1-1-1111-1-1iiii−i−i−i−iiiii−i−i−i−i1ii−i−iiiii−i−i−i−i1111-1-1-1-11111-1-1-1-1111-11-1-1-1i−ii−ii−ii−i
χ181111-1-1-1-1iiii−i−i−i−i-111-1-1-1111-1-1iiii−i−i−i−iiiii−i−i−i−i1ii−i−iiiii−i−i−i−i1111-1-1-1-11111-1-1-1-1-1-1-11-1111−ii−ii−ii−ii1111-1-1-1-1iiii−i−i−i−i-111-1-1-1111-1-1iiii−i−i−i−iiiii−i−i−i−i1ii−i−iiiii−i−i−i−i1111-1-1-1-11111-1-1-1-1-1-1-11-1111−ii−ii−ii−ii
χ191111-1-1-1-1iiii−i−i−i−i-111-1-1-1111-1-1−i−i−i−iiiii−i−i−i−iiiii1ii−i−iiiii−i−i−i−i-1-1-1-11111-1-1-1-111111-11-1-11-11i−i−iii−i−ii1111-1-1-1-1iiii−i−i−i−i-111-1-1-1111-1-1−i−i−i−iiiii−i−i−i−iiiii1ii−i−iiiii−i−i−i−i-1-1-1-11111-1-1-1-111111-11-1-11-11i−i−iii−i−ii
χ201111-1-1-1-1iiii−i−i−i−i-111-1-1-1111-1-1−i−i−i−iiiii−i−i−i−iiiii1ii−i−iiiii−i−i−i−i-1-1-1-11111-1-1-1-11111-11-111-11-1−iii−i−iii−i1111-1-1-1-1iiii−i−i−i−i-111-1-1-1111-1-1−i−i−i−iiiii−i−i−i−iiiii1ii−i−iiiii−i−i−i−i-1-1-1-11111-1-1-1-11111-11-111-11-1−iii−i−iii−i
χ211111-1-1-1-1iiii−i−i−i−i-1-1-111-11-1-111iiii−i−i−i−i−i−i−i−iiiii1ii−i−i−i−i−i−iiiii1111-1-1-1-1-1-1-1-1111111-11-11-1-1−ii−iii−ii−i1111-1-1-1-1iiii−i−i−i−i-1-1-111-11-1-111iiii−i−i−i−i−i−i−i−iiiii1ii−i−i−i−i−i−iiiii1111-1-1-1-1-1-1-1-1111111-11-11-1-1−ii−iii−ii−i
χ221111-1-1-1-1iiii−i−i−i−i-1-1-111-11-1-111iiii−i−i−i−i−i−i−i−iiiii1ii−i−i−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111-1-11-11-111i−ii−i−ii−ii1111-1-1-1-1iiii−i−i−i−i-1-1-111-11-1-111iiii−i−i−i−i−i−i−i−iiiii1ii−i−i−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111-1-11-11-111i−ii−i−ii−ii
χ231111-1-1-1-1iiii−i−i−i−i-1-1-111-11-1-111−i−i−i−iiiiiiiii−i−i−i−i1ii−i−i−i−i−i−iiiii-1-1-1-111111111-1-1-1-11-1-111-1-11−iii−ii−i−ii1111-1-1-1-1iiii−i−i−i−i-1-1-111-11-1-111−i−i−i−iiiiiiiii−i−i−i−i1ii−i−i−i−i−i−iiiii-1-1-1-111111111-1-1-1-11-1-111-1-11−iii−ii−i−ii
χ241111-1-1-1-1iiii−i−i−i−i-1-1-111-11-1-111−i−i−i−iiiiiiiii−i−i−i−i1ii−i−i−i−i−i−iiiii-1-1-1-111111111-1-1-1-1-111-1-111-1i−i−ii−iii−i1111-1-1-1-1iiii−i−i−i−i-1-1-111-11-1-111−i−i−i−iiiiiiiii−i−i−i−i1ii−i−i−i−i−i−iiiii-1-1-1-111111111-1-1-1-1-111-1-111-1i−i−ii−iii−i
χ251111-1-1-1-1−i−i−i−iiiii-111-1-1-1111-1-1iiii−i−i−i−iiiii−i−i−i−i1−i−iii−i−i−i−iiiii-1-1-1-11111-1-1-1-111111-11-1-11-11−iii−i−iii−i1111-1-1-1-1−i−i−i−iiiii-111-1-1-1111-1-1iiii−i−i−i−iiiii−i−i−i−i1−i−iii−i−i−i−iiiii-1-1-1-11111-1-1-1-111111-11-1-11-11−iii−i−iii−i
χ261111-1-1-1-1−i−i−i−iiiii-111-1-1-1111-1-1iiii−i−i−i−iiiii−i−i−i−i1−i−iii−i−i−i−iiiii-1-1-1-11111-1-1-1-11111-11-111-11-1i−i−iii−i−ii1111-1-1-1-1−i−i−i−iiiii-111-1-1-1111-1-1iiii−i−i−i−iiiii−i−i−i−i1−i−iii−i−i−i−iiiii-1-1-1-11111-1-1-1-11111-11-111-11-1i−i−iii−i−ii
χ271111-1-1-1-1−i−i−i−iiiii-111-1-1-1111-1-1−i−i−i−iiiii−i−i−i−iiiii1−i−iii−i−i−i−iiiii1111-1-1-1-11111-1-1-1-1111-11-1-1-1−ii−ii−ii−ii1111-1-1-1-1−i−i−i−iiiii-111-1-1-1111-1-1−i−i−i−iiiii−i−i−i−iiiii1−i−iii−i−i−i−iiiii1111-1-1-1-11111-1-1-1-1111-11-1-1-1−ii−ii−ii−ii
χ281111-1-1-1-1−i−i−i−iiiii-111-1-1-1111-1-1−i−i−i−iiiii−i−i−i−iiiii1−i−iii−i−i−i−iiiii1111-1-1-1-11111-1-1-1-1-1-1-11-1111i−ii−ii−ii−i1111-1-1-1-1−i−i−i−iiiii-111-1-1-1111-1-1−i−i−i−iiiii−i−i−i−iiiii1−i−iii−i−i−i−iiiii1111-1-1-1-11111-1-1-1-1-1-1-11-1111i−ii−ii−ii−i
χ291111-1-1-1-1−i−i−i−iiiii-1-1-111-11-1-111iiii−i−i−i−i−i−i−i−iiiii1−i−iiiiiii−i−i−i−i-1-1-1-111111111-1-1-1-11-1-111-1-11i−i−ii−iii−i1111-1-1-1-1−i−i−i−iiiii-1-1-111-11-1-111iiii−i−i−i−i−i−i−i−iiiii1−i−iiiiiii−i−i−i−i-1-1-1-111111111-1-1-1-11-1-111-1-11i−i−ii−iii−i
χ301111-1-1-1-1−i−i−i−iiiii-1-1-111-11-1-111iiii−i−i−i−i−i−i−i−iiiii1−i−iiiiiii−i−i−i−i-1-1-1-111111111-1-1-1-1-111-1-111-1−iii−ii−i−ii1111-1-1-1-1−i−i−i−iiiii-1-1-111-11-1-111iiii−i−i−i−i−i−i−i−iiiii1−i−iiiiiii−i−i−i−i-1-1-1-111111111-1-1-1-1-111-1-111-1−iii−ii−i−ii
χ311111-1-1-1-1−i−i−i−iiiii-1-1-111-11-1-111−i−i−i−iiiiiiiii−i−i−i−i1−i−iiiiiii−i−i−i−i1111-1-1-1-1-1-1-1-1111111-11-11-1-1i−ii−i−ii−ii1111-1-1-1-1−i−i−i−iiiii-1-1-111-11-1-111−i−i−i−iiiiiiiii−i−i−i−i1−i−iiiiiii−i−i−i−i1111-1-1-1-1-1-1-1-1111111-11-11-1-1i−ii−i−ii−ii
χ321111-1-1-1-1−i−i−i−iiiii-1-1-111-11-1-111−i−i−i−iiiiiiiii−i−i−i−i1−i−iiiiiii−i−i−i−i1111-1-1-1-1-1-1-1-11111-1-11-11-111−ii−iii−ii−i1111-1-1-1-1−i−i−i−iiiii-1-1-111-11-1-111−i−i−i−iiiiiiiii−i−i−i−i1−i−iiiiiii−i−i−i−i1111-1-1-1-1-1-1-1-11111-1-11-11-111−ii−iii−ii−i
χ332222222222222222-222-2-2-2-2-2-2220000000000000000-2-2-2-2-222-2-222-2-2000000000000000000000000000000002222222222222222-222-2-2-2-2-2-2220000000000000000-2-2-2-2-222-2-222-2-200000000000000000000000000000000
χ342222222222222222-2-2-222-2-222-2-20000000000000000-2-2-2-2-2-2-222-2-222000000000000000000000000000000002222222222222222-2-2-222-2-222-2-20000000000000000-2-2-2-2-2-2-222-2-22200000000000000000000000000000000
χ3522222222-2-2-2-2-2-2-2-2-222-2-2-2-2-2-2220000000000000000-22222-2-222-2-2220000000000000000000000000000000022222222-2-2-2-2-2-2-2-2-222-2-2-2-2-2-2220000000000000000-22222-2-222-2-22200000000000000000000000000000000
χ3622222222-2-2-2-2-2-2-2-2-2-2-222-2-222-2-20000000000000000-2222222-2-222-2-20000000000000000000000000000000022222222-2-2-2-2-2-2-2-2-2-2-222-2-222-2-20000000000000000-2222222-2-222-2-200000000000000000000000000000000
χ372222-2-2-2-22i2i2i2i−2i−2i−2i−2i222222-2-2-2-2-20000000000000000-2−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i000000000000000000000000000000002222-2-2-2-22i2i2i2i−2i−2i−2i−2i222222-2-2-2-2-20000000000000000-2−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ382222-2-2-2-22i2i2i2i−2i−2i−2i−2i2-2-2-2-22-222220000000000000000-2−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000002222-2-2-2-22i2i2i2i−2i−2i−2i−2i2-2-2-2-22-222220000000000000000-2−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ392222-2-2-2-2−2i−2i−2i−2i2i2i2i2i222222-2-2-2-2-20000000000000000-22i2i−2i−2i−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000002222-2-2-2-2−2i−2i−2i−2i2i2i2i2i222222-2-2-2-2-20000000000000000-22i2i−2i−2i−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ402222-2-2-2-2−2i−2i−2i−2i2i2i2i2i2-2-2-2-22-222220000000000000000-22i2i−2i−2i2i2i−2i−2i−2i−2i2i2i000000000000000000000000000000002222-2-2-2-2−2i−2i−2i−2i2i2i2i2i2-2-2-2-22-222220000000000000000-22i2i−2i−2i2i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ4122-2-22i−2i2i−2i2ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ30002-2002i−2i001+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i00000002ζ3−2ζ3002ζ−2ζ22−2−2i2i2−i2−i2i2i2−i2−i222−2−2000000000000000022-2-22i−2i2i−2i2ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ30002-2002i−2i001+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i00000002ζ3−2ζ3002ζ−2ζ22−2−2i2i2−i2−i2i2i2−i2−i222−2−20000000000000000
χ4222-2-22i−2i2i−2i2ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ30002-2002i−2i00−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000002ζ3−2ζ3002ζ−2ζ−2−222−i2−i2i2i2−i2−i2i2i2−2−222000000000000000022-2-22i−2i2i−2i2ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ30002-2002i−2i00−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000002ζ3−2ζ3002ζ−2ζ−2−222−i2−i2i2i2−i2−i2i2i2−2−2220000000000000000
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χ1762-2-22-2-222-222-2-222-2-200002-20000-222-2-222-2000000002-222-200000000-222-22-2-22000000000000000000000000-222-222-2-22-2-222-2-2220000-2200002-2-222-2-2200000000-22-2-22000000002-2-22-222-2000000000000000000000000

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