Finite Group Databasebeta

← Group #117566

Character table — Group #117566

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111111111111222222222222222244444444444444444444888888888888888888888888888888881616161616161616
order12222222444444444444444444444444224444444444444444448888888888888888888888888888888844448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
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
χ5111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
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
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1
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χ1311111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−iii−i−iii−i−i-1-1-1-11111-1-1-1-1111111-1-1−i−iii
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χ192222222222222222-2-222-2-2-2-22222-2-222-2-2-2-2000000000000000022-2-222-2-200000000000000000000000000000000
χ202222222222222222-2-222-2-2-2-22222-2-222-2-2-2-20000000000000000-2-222-2-22200000000000000000000000000000000
χ212222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000000000000000000000002-22-20000
χ222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000000000000000000000000000000000000-22-220000
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χ2822222222-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2-2-222000000000000000000000000000000000000000000000000-222-20000
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χ854-444-44-4-44-444-44-4-4000000000000000000002-22-2-22-222-22-2-22-220000000000000000000000000000000000000000
χ864-444-44-4-44-444-44-4-400000000000000000000-22-222-22-2-22-222-22-20000000000000000000000000000000000000000
χ874-444-44-4-4-44-4-44-444000000000000000000002i−2i2i−2i−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000000000000000
χ884-444-44-4-4-44-4-44-44400000000000000000000−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i−2i2i−2i2i0000000000000000000000000000000000000000
χ894-44-44-4-444i−4i4i−4i4i−4i−4i4i-4400−4i4i−4i4i00004-400000000000000000000000000000000000000000000000000000000000000
χ904-44-44-4-44−4i4i−4i4i−4i4i4i−4i-44004i−4i4i−4i00004-400000000000000000000000000000000000000000000000000000000000000
χ914-4-444-44-44i−4i−4i4i4i−4i4i−4i004-40000−4i4i−4i4i00-44000000000000000000000000000000000000000000000000000000000000
χ924-4-444-44-4−4i4i4i−4i−4i4i−4i4i004-400004i−4i4i−4i00-44000000000000000000000000000000000000000000000000000000000000

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