Finite Group Databasebeta

← Group #207697

Character table — Group #207697

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size11111111222222222222222222222222222288888888888888888888888888888888888888888888888888888888
order12222222222244444444444444444444444422224444444444444444444488888888888888888888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111
χ5111111111111111111111111111111111111-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111111111-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ911111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i
χ1011111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii
χ1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1-1-111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii
χ1211111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1-1-111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-1-1-111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1111111-1-1iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1111111-1-1−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii
χ17111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-1ii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−i
χ18111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii
χ19111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111-1-1-1-11111ii−i−iii−i−iii−i−iii−i−i−i−iii−i−iii−i−iii−i−iii
χ20111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111-1-1-1-11111−i−iii−i−iii−i−iii−i−iiiii−i−iii−i−iii−i−iii−i−i
χ21111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-111-1-11111ii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iii
χ22111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-111-1-11111−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i
χ23111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1ii−i−iii−i−i−i−iii−i−iii−i−iii−i−iiiii−i−iii−i−i
χ24111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1−i−iii−i−iiiii−i−iii−i−iii−i−iii−i−i−i−iii−i−iii
χ25111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111
χ26111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1
χ27111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1111111-1-111-1-111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-1
χ28111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1111111-1-111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-111
χ29111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-11111-1-111-1-1-1-111-1-11111-1-1
χ30111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-111-1-11111-1-111-1-1-1-111
χ31111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111-1-1111111-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-111-1-1-1-111
χ32111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111-1-1111111-1-111-1-11111-1-111-1-1-1-11111-1-1-1-111-1-11111-1-1
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Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.