Finite Group Databasebeta

← Group #72323121

Character table — Group #72323121

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162C163C164C165C166C167C168C169C170C171C172C173C174C175C176
size11111111222222222222222222222222444444444444444444444444444444444444448888888888888888888888888888888888888888888888161616161616161616161616161616161616161616161616161616161616161616161616323232323232323232323232323232323232323264646464
order12222222222244444444444488888888444444888888881616161616161616161616161616161616161616161616168888888888161616163232323232323232323232323232323232323232323232323232323232323232888888888888161616161616161632323232323232323232323232323232222244448888888888884444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ5111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ6111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ7111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ8111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-111111111-1-1-1-1
χ911111111111111-1-1-1-111-1-1-1-11111111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1iiii−i−i−i−i-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iiiii−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i11-1-111-1-1ii−i−iiiii−i−i−i−i11-1-1
χ1011111111111111-1-1-1-111-1-1-1-11111111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1iiii−i−i−i−i-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i−i−i−i−iiiiiiiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i-1-111-1-111−i−iii−i−i−i−iiiii-1-111
χ1111111111111111-1-1-1-111-1-1-1-11111111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1iiii−i−i−i−i-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111ii−i−iiiii−i−i−i−iiiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii11-1-111-1-1ii−i−i−i−i−i−iiiii-1-111
χ1211111111111111-1-1-1-111-1-1-1-11111111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1iiii−i−i−i−i-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111ii−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii-1-111-1-111−i−iiiiiii−i−i−i−i11-1-1
χ1311111111111111-1-1-1-111-1-1-1-11111111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1−i−i−i−iiiii-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiii-1-111-1-111ii−i−iiiii−i−i−i−i-1-111
χ1411111111111111-1-1-1-111-1-1-1-11111111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1−i−i−i−iiiii-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiii11-1-111-1-1−i−iii−i−i−i−iiiii11-1-1
χ1511111111111111-1-1-1-111-1-1-1-11111111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1−i−i−i−iiiii-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111−i−iiiiiii−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−i−i−i-1-111-1-111ii−i−i−i−i−i−iiiii11-1-1
χ1611111111111111-1-1-1-111-1-1-1-11111111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1−i−i−i−iiiii-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111−i−iii−i−i−i−iiiii−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−i−i−i11-1-111-1-1−i−iiiiiii−i−i−i−i-1-111
χ1711111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11-11111111111-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-111-1-111-1-11-11-1
χ1811111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-111-1-111-11-11
χ1911111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111-11-11111111111-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-111-1-111-11-11
χ2011111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111-11-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1111111-1-111-1-11-11-1
χ2111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1111111111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-111-1-111-1-1-11-11
χ2211111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-1111111-1-111-1-1111-11-1
χ2311111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-11-1111111111-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1111-11-1
χ2411111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-11-11-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-111-1-1-11-11
χ2511111111-1-1-1-111-1-1-1-111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111ii−i−i−i−iii111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111i−i−iiiiii−i−i−i−iii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1−i−iiiii−i−i−i−iii1-1-11
χ2611111111-1-1-1-111-1-1-1-111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111ii−i−i−i−iii111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111i−i−ii−i−i−i−iiiiiii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111ii−i−i−i−iiiii−i−i-111-1
χ2711111111-1-1-1-111-1-1-1-111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111ii−i−i−i−iii1111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1i−i−iiiiii−i−i−i−iii−i−i−i−iii−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1−i−iii−i−iiiii−i−i-111-1
χ2811111111-1-1-1-111-1-1-1-111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111ii−i−i−i−iii1111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1i−i−ii−i−i−i−iiiiiii−i−i−i−iii−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111ii−i−iii−i−i−i−iii1-1-11
χ2911111111-1-1-1-111-1-1-1-111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111−i−iiiii−i−i111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−iii−iiiii−i−i−i−i−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111−i−iiiii−i−i−i−iii-111-1
χ3011111111-1-1-1-111-1-1-1-111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111−i−iiiii−i−i111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−iii−i−i−i−i−iiiii−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1ii−i−i−i−iiiii−i−i1-1-11
χ3111111111-1-1-1-111-1-1-1-111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111−i−iiiii−i−i1111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1−iii−iiiii−i−i−i−i−i−iiiii−i−iiiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111−i−iii−i−iiiii−i−i1-1-11
χ3211111111-1-1-1-111-1-1-1-111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111−i−iiiii−i−i1111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1−iii−i−i−i−i−iiiii−i−iiiii−i−iiiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1ii−i−iii−i−i−i−iii-111-1
χ332222222222222222222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222222222-2-2-2-200000000000000000000000000000000222200000000-2-2-2-2-2-2-2-20000000000000000000000000000000000000000
χ342222222222222222222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000-2-2-2-200000000222222220000000000000000000000000000000000000000
χ35222222222222222222222222-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-2000000000000000000000000-2-22222222200002222−2−2−2−22222−2−2−2−22222−2−2−2−22222−2−2−2−2-2-2-2-2000000000000000022−2−222−2−222−2−222−2−2000000000000000000000000
χ36222222222222222222222222-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-2000000000000000000000000-2-2222222220000−2−2−2−22222−2−2−2−22222−2−2−2−22222−2−2−2−22222-2-2-2-20000000000000000−2−222−2−222−2−222−2−222000000000000000000000000
χ37222222222222222222222222-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-2000000000000000000000000-2-2-2-2-2-2-2-2-2-200002222−2−2−2−22222−2−2−2−22222−2−2−2−22222−2−2−2−222220000000000000000−2−222−2−222−2−222−2−222000000000000000000000000
χ38222222222222222222222222-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-2000000000000000000000000-2-2-2-2-2-2-2-2-2-20000−2−2−2−22222−2−2−2−22222−2−2−2−22222−2−2−2−222222222000000000000000022−2−222−2−222−2−222−2−2000000000000000000000000
χ3922222222222222-2-2-2-222-2-2-2-22222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-22222-2-22i2i2i2i−2i−2i−2i−2i2222000000000000000000000000000000002i2i−2i−2i00000000−2i−2i−2i−2i2i2i2i2i0000000000000000000000000000000000000000
χ4022222222222222-2-2-2-222-2-2-2-22222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2−2i−2i−2i−2i2i2i2i2i222200000000000000000000000000000000−2i−2i2i2i000000002i2i2i2i−2i−2i−2i−2i0000000000000000000000000000000000000000
χ4122222222222222-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-22222000000000000000000000000222i2i2i2i−2i−2i−2i−2i00002222−2−2−2−22222−2−2−2−2−2−2−2−22222−2−2−2−22222−2i−2i2i2i0000000000000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2000000000000000000000000
χ4222222222222222-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-22222000000000000000000000000222i2i2i2i−2i−2i−2i−2i0000−2−2−2−22222−2−2−2−222222222−2−2−2−22222−2−2−2−2−2i−2i2i2i0000000000000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2000000000000000000000000
χ4322222222222222-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-2222200000000000000000000000022−2i−2i−2i−2i2i2i2i2i00002222−2−2−2−22222−2−2−2−2−2−2−2−22222−2−2−2−222222i2i−2i−2i0000000000000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2000000000000000000000000
χ4422222222222222-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-2222200000000000000000000000022−2i−2i−2i−2i2i2i2i2i0000−2−2−2−22222−2−2−2−222222222−2−2−2−22222−2−2−2−22i2i−2i−2i0000000000000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2000000000000000000000000
χ4522222222-2-2-2-222222222222222222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-222-2-22222000000000000000000000000000000002-22-200000000-2-222-2-2220000000000000000000000000000000000000000
χ4622222222-2-2-2-222222222222222222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-222222200000000000000000000000000000000-22-220000000022-2-222-2-20000000000000000000000000000000000000000
χ4722222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-20000000000000000000000002222-2-222-2-200002222−2−2−2−2−2−2−2−222222222−2−2−2−2−2−2−2−22222-22-22000000000000000022−2−2−2−22222−2−2−2−222000000000000000000000000
χ4822222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-20000000000000000000000002222-2-222-2-20000−2−2−2−222222222−2−2−2−2−2−2−2−222222222−2−2−2−2-22-220000000000000000−2−22222−2−2−2−22222−2−2000000000000000000000000
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Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.