Finite Group Databasebeta

← Group #119889

Character table — Group #119889

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111111111111222222222222222244444444444444444444888888888888888888888888888888881616161616161616
order12222222444444444444444444444444224488888888888888888888888888888888888888888888888822448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ6111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
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χ1211111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiii-1-1-1-11111−i−i−i−iiiii-1-1-1-1111111-1-1ii−i−i
χ1311111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i-1-1-1-11111iiii−i−i−i−i-1-1-1-1111111-1-1−i−iii
χ1411111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii1111-1-1-1-1-1-111ii−i−i
χ1511111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii1111-1-1-1-1iiii−i−i−i−i-1-1-1-11111-1-111ii−i−i
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χ17222222222222222222-2-222-2-222-2-222-2-2-2-2-2-2000000000000000022-2-222-2-200000000000000000000000000000000
χ18222222222222222222-2-222-2-222-2-222-2-2-2-2-2-20000000000000000-2-222-2-22200000000000000000000000000000000
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χ914-4-4444-4-44i−4i−4i−4i4i4i4i−4i00-4400−4i4i004-4004i−4i000000000000000000000000000000000000000000000000000000000000
χ924-4-4444-4-4−4i4i4i4i−4i−4i−4i4i00-44004i−4i004-400−4i4i000000000000000000000000000000000000000000000000000000000000

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