Finite Group Databasebeta

← Group #218833

Character table — Group #218833

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111111111111222222224444444444444444444444444444444488888888888888888888888888881616161616161616
order12222222444444444444444422444444888888888888888888888888224444448888888888888888888844448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111
χ511111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111
χ611111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111
χ9111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111
χ10111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ11111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-111111111-1-1-1-11111-1-111-1-1-1-1
χ12111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111
χ13111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111
χ14111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111111111-1-1-1-1111111-1-1-1-1-1-1
χ15111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1
χ16111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-111
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χ2111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1−i−iii−i−iiiiiii−i−i−i−iiiii−i−i−i−i11-1-1-1-111−ii−ii−i−iiiii−i−i-1-111-1-1111-1-11−iii−i
χ2211111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1−i−iii−i−iiiiiii−i−i−i−iiiii−i−i−i−i-1-11111-1-1−ii−iiii−i−i−i−iii-1-111-1-111-111-1i−i−ii
χ2311111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1−ii−ii−i−iii−i−iii11-1-111-1-11-11-1−ii−ii
χ2411111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111−ii−iiii−i−iii−i−i11-1-111-1-1-11-11i−ii−i
χ2511111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii11-1-111-1-1i−i−iiii−i−i−i−iii11-1-1-1-111-11-11−iii−i
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χ2711111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111ii−i−i−i−iii−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111i−i−iiii−i−iii−i−i-1-11111-1-1-111-1−ii−ii
χ2811111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111ii−i−i−i−iii−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1i−i−ii−i−iii−i−iii-1-11111-1-11-1-11i−ii−i
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χ3011111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111−i−iiiii−i−iiiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1−iii−iii−i−iii−i−i-1-11111-1-11-1-11−ii−ii
χ3111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i11-1-111-1-1−iii−i−i−iiiii−i−i11-1-1-1-111-11-11i−i−ii
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χ884-4-44-4-444-4-44-444-44000000000000000000000000−222222−2222−22−222200000000000000000000000000000000000000000000
χ894-4-4-444-4444-4-444-4-44444-4-4-4-400000000000000000000000000000000000000000000000000000000000000000000
χ904-4-4-444-4444-4-444-4-4-4-4-4-4444400000000000000000000000000000000000000000000000000000000000000000000
χ914-4-4-444-44-4-444-4-44444-4-4-4-44400000000000000000000000000000000000000000000000000000000000000000000
χ924-4-4-444-44-4-444-4-444-4-44444-4-400000000000000000000000000000000000000000000000000000000000000000000

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