Finite Group Databasebeta

← Group #353646

Character table — Group #353646

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162C163C164C165C166C167C168C169C170C171C172C173C174C175C176
size11111111111111112222222222222222222222222222222222222222222222222222222288888888888888881111111111111111222222222222222222222222222222222222222222222222222222228888888888888888
order12222222444444442222444444444444444444448888888888888888888888888888888844444444888888882222222244444444222244444444444444444444888888888888888888888888888888884444444488888888
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
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ511111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ611111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ711111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1
χ811111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111
χ911111111-1-1-1-1-1-1-1-1-1-1-1-1111iiiiiiii−i−i−i−i−i−i−i−i1iiiiiiii−i−i−i−i−i−i−i−i11111111-1-1-1-1-1-1-1-111-1-111-1-1ii−i−iii−i−i11111111-1-1-1-1-1-1-1-1-1-1-1-1111iiiiiiii−i−i−i−i−i−i−i−i1iiiiiiii−i−i−i−i−i−i−i−i11111111-1-1-1-1-1-1-1-111-1-111-1-1ii−i−iii−i−i
χ1011111111-1-1-1-1-1-1-1-1-1-1-1-1111iiiiiiii−i−i−i−i−i−i−i−i1iiiiiiii−i−i−i−i−i−i−i−i11111111-1-1-1-1-1-1-1-1-1-111-1-111−i−iii−i−iii11111111-1-1-1-1-1-1-1-1-1-1-1-1111iiiiiiii−i−i−i−i−i−i−i−i1iiiiiiii−i−i−i−i−i−i−i−i11111111-1-1-1-1-1-1-1-1-1-111-1-111−i−iii−i−iii
χ1111111111-1-1-1-1-1-1-1-1-1-1-1-1111iiiiiiii−i−i−i−i−i−i−i−i1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1-1-1-1-11111111111-1-1-1-111ii−i−i−i−iii11111111-1-1-1-1-1-1-1-1-1-1-1-1111iiiiiiii−i−i−i−i−i−i−i−i1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1-1-1-1-11111111111-1-1-1-111ii−i−i−i−iii
χ1211111111-1-1-1-1-1-1-1-1-1-1-1-1111iiiiiiii−i−i−i−i−i−i−i−i1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1-1-1-1-111111111-1-11111-1-1−i−iiiii−i−i11111111-1-1-1-1-1-1-1-1-1-1-1-1111iiiiiiii−i−i−i−i−i−i−i−i1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1-1-1-1-111111111-1-11111-1-1−i−iiiii−i−i
χ1311111111-1-1-1-1-1-1-1-1-1-1-1-1111−i−i−i−i−i−i−i−iiiiiiiii1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1-1-1-1-11111111111-1-1-1-111−i−iiiii−i−i11111111-1-1-1-1-1-1-1-1-1-1-1-1111−i−i−i−i−i−i−i−iiiiiiiii1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1-1-1-1-11111111111-1-1-1-111−i−iiiii−i−i
χ1411111111-1-1-1-1-1-1-1-1-1-1-1-1111−i−i−i−i−i−i−i−iiiiiiiii1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1-1-1-1-111111111-1-11111-1-1ii−i−i−i−iii11111111-1-1-1-1-1-1-1-1-1-1-1-1111−i−i−i−i−i−i−i−iiiiiiiii1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1-1-1-1-111111111-1-11111-1-1ii−i−i−i−iii
χ1511111111-1-1-1-1-1-1-1-1-1-1-1-1111−i−i−i−i−i−i−i−iiiiiiiii1−i−i−i−i−i−i−i−iiiiiiiii11111111-1-1-1-1-1-1-1-111-1-111-1-1−i−iii−i−iii11111111-1-1-1-1-1-1-1-1-1-1-1-1111−i−i−i−i−i−i−i−iiiiiiiii1−i−i−i−i−i−i−i−iiiiiiiii11111111-1-1-1-1-1-1-1-111-1-111-1-1−i−iii−i−iii
χ1611111111-1-1-1-1-1-1-1-1-1-1-1-1111−i−i−i−i−i−i−i−iiiiiiiii1−i−i−i−i−i−i−i−iiiiiiiii11111111-1-1-1-1-1-1-1-1-1-111-1-111ii−i−iii−i−i11111111-1-1-1-1-1-1-1-1-1-1-1-1111−i−i−i−i−i−i−i−iiiiiiiii1−i−i−i−i−i−i−i−iiiiiiiii11111111-1-1-1-1-1-1-1-1-1-111-1-111ii−i−iii−i−i
χ17111-1-11-1-111-1-111-1-11-1-111-1-11111-1-1-1-11111-1-1-1-111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1i−ii−ii−ii−ii−ii−ii−ii−i111-1-11-1-111-1-111-1-11-1-111-1-11111-1-1-1-11111-1-1-1-111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1i−ii−ii−ii−ii−ii−ii−ii−i
χ18111-1-11-1-111-1-111-1-11-1-111-1-11111-1-1-1-11111-1-1-1-111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1−ii−ii−ii−ii−ii−ii−ii−ii111-1-11-1-111-1-111-1-11-1-111-1-11111-1-1-1-11111-1-1-1-111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1−ii−ii−ii−ii−ii−ii−ii−ii
χ19111-1-11-1-111-1-111-1-11-1-111-1-11111-1-1-1-11111-1-1-1-11-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111i−ii−i−ii−iii−ii−i−ii−ii111-1-11-1-111-1-111-1-11-1-111-1-11111-1-1-1-11111-1-1-1-11-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111i−ii−i−ii−iii−ii−i−ii−ii
χ20111-1-11-1-111-1-111-1-11-1-111-1-11111-1-1-1-11111-1-1-1-11-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111−ii−iii−ii−i−ii−iii−ii−i111-1-11-1-111-1-111-1-11-1-111-1-11111-1-1-1-11111-1-1-1-11-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111−ii−iii−ii−i−ii−iii−ii−i
χ21111-1-11-1-111-1-111-1-11-1-111-1-1-1-1-1-11111-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111i−ii−i−ii−ii−ii−iii−ii−i111-1-11-1-111-1-111-1-11-1-111-1-1-1-1-1-11111-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111i−ii−i−ii−ii−ii−iii−ii−i
χ22111-1-11-1-111-1-111-1-11-1-111-1-1-1-1-1-11111-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111−ii−iii−ii−ii−ii−i−ii−ii111-1-11-1-111-1-111-1-11-1-111-1-1-1-1-1-11111-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111−ii−iii−ii−ii−ii−i−ii−ii
χ23111-1-11-1-111-1-111-1-11-1-111-1-1-1-1-1-11111-1-1-1-111111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1i−ii−ii−ii−i−ii−ii−ii−ii111-1-11-1-111-1-111-1-11-1-111-1-1-1-1-1-11111-1-1-1-111111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1i−ii−ii−ii−i−ii−ii−ii−ii
χ24111-1-11-1-111-1-111-1-11-1-111-1-1-1-1-1-11111-1-1-1-111111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1−ii−ii−ii−iii−ii−ii−ii−i111-1-11-1-111-1-111-1-11-1-111-1-1-1-1-1-11111-1-1-1-111111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1−ii−ii−ii−iii−ii−ii−ii−i
χ25111-1-11-1-1-1-111-1-111-111-11-1-1iiii−i−i−i−i−i−i−i−iiiii1iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111i−i−iii−i−ii-111-1-111-1111-1-11-1-1-1-111-1-111-111-11-1-1iiii−i−i−i−i−i−i−i−iiiii1iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111i−i−iii−i−ii-111-1-111-1
χ26111-1-11-1-1-1-111-1-111-111-11-1-1iiii−i−i−i−i−i−i−i−iiiii1iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111−iii−i−iii−i1-1-111-1-11111-1-11-1-1-1-111-1-111-111-11-1-1iiii−i−i−i−i−i−i−i−iiiii1iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111−iii−i−iii−i1-1-111-1-11
χ27111-1-11-1-1-1-111-1-111-111-11-1-1iiii−i−i−i−i−i−i−i−iiiii1−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-111111111-1-1-1-1i−i−ii−iii−i-111-11-1-11111-1-11-1-1-1-111-1-111-111-11-1-1iiii−i−i−i−i−i−i−i−iiiii1−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-111111111-1-1-1-1i−i−ii−iii−i-111-11-1-11
χ28111-1-11-1-1-1-111-1-111-111-11-1-1iiii−i−i−i−i−i−i−i−iiiii1−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-111111111-1-1-1-1−iii−ii−i−ii1-1-11-111-1111-1-11-1-1-1-111-1-111-111-11-1-1iiii−i−i−i−i−i−i−i−iiiii1−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-111111111-1-1-1-1−iii−ii−i−ii1-1-11-111-1
χ29111-1-11-1-1-1-111-1-111-111-11-1-1−i−i−i−iiiiiiiii−i−i−i−i1iiii−i−i−i−i−i−i−i−iiiii-1-1-1-111111111-1-1-1-1i−i−ii−iii−i1-1-11-111-1111-1-11-1-1-1-111-1-111-111-11-1-1−i−i−i−iiiiiiiii−i−i−i−i1iiii−i−i−i−i−i−i−i−iiiii-1-1-1-111111111-1-1-1-1i−i−ii−iii−i1-1-11-111-1
χ30111-1-11-1-1-1-111-1-111-111-11-1-1−i−i−i−iiiiiiiii−i−i−i−i1iiii−i−i−i−i−i−i−i−iiiii-1-1-1-111111111-1-1-1-1−iii−ii−i−ii-111-11-1-11111-1-11-1-1-1-111-1-111-111-11-1-1−i−i−i−iiiiiiiii−i−i−i−i1iiii−i−i−i−i−i−i−i−iiiii-1-1-1-111111111-1-1-1-1−iii−ii−i−ii-111-11-1-11
χ31111-1-11-1-1-1-111-1-111-111-11-1-1−i−i−i−iiiiiiiii−i−i−i−i1−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-1-1-1-11111i−i−iii−i−ii1-1-111-1-11111-1-11-1-1-1-111-1-111-111-11-1-1−i−i−i−iiiiiiiii−i−i−i−i1−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-1-1-1-11111i−i−iii−i−ii1-1-111-1-11
χ32111-1-11-1-1-1-111-1-111-111-11-1-1−i−i−i−iiiiiiiii−i−i−i−i1−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-1-1-1-11111−iii−i−iii−i-111-1-111-1111-1-11-1-1-1-111-1-111-111-11-1-1−i−i−i−iiiiiiiii−i−i−i−i1−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-1-1-1-11111−iii−i−iii−i-111-1-111-1
χ332222222222222222-2-2-2-2-2-2-20000000000000000-222-2-222-2-222-2-222-2-2000000000000000000000000000000002222222222222222-2-2-2-2-2-2-20000000000000000-222-2-222-2-222-2-222-2-200000000000000000000000000000000
χ342222222222222222-2-2-2-2-2-2-20000000000000000-2-2-222-2-222-2-222-2-222000000000000000000000000000000002222222222222222-2-2-2-2-2-2-20000000000000000-2-2-222-2-222-2-222-2-22200000000000000000000000000000000
χ3522222222-2-2-2-2-2-2-2-22222-2-2-20000000000000000-22i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000022222222-2-2-2-2-2-2-2-22222-2-2-20000000000000000-22i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000
χ3622222222-2-2-2-2-2-2-2-22222-2-2-20000000000000000-2−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000022222222-2-2-2-2-2-2-2-22222-2-2-20000000000000000-2−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000
χ37222-2-22-2-222-2-222-2-2-222-2-2220000000000000000-222-2-2-2-22222-2-2-2-22200000000000000000000000000000000222-2-22-2-222-2-222-2-2-222-2-2220000000000000000-222-2-2-2-22222-2-2-2-22200000000000000000000000000000000
χ38222-2-22-2-222-2-222-2-2-222-2-2220000000000000000-2-2-22222-2-2-2-22222-2-200000000000000000000000000000000222-2-22-2-222-2-222-2-2-222-2-2220000000000000000-2-2-22222-2-2-2-22222-2-200000000000000000000000000000000
χ39222-2-22-2-2-2-222-2-2222-2-22-2220000000000000000-22i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000222-2-22-2-2-2-222-2-2222-2-22-2220000000000000000-22i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ40222-2-22-2-2-2-222-2-2222-2-22-2220000000000000000-2−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000222-2-22-2-2-2-222-2-2222-2-22-2220000000000000000-2−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
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Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.