Finite Group Databasebeta

← Group #217185

Character table — Group #217185

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111111111111222222224444444444444444444444444444444488888888888888888888888888881616161616161616
order12222222444444444444444422444444444444448888888888888888224444444444888888888888888824448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111
χ6111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-1111-1-1
χ7111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1111111111111-111-111-1-1
χ8111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1111111111-1-11-1-111
χ9111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1
χ10111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-111
χ11111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111
χ12111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1
χ13111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111111111-1-1-1-111111-1-11-1-1-1-1
χ14111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-11111
χ15111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11-1-111111
χ16111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1111111111111-1-1-1-1-111-1-1-1-1-1
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χ1811111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-11-11-1-1-11111−i−iii−i−iiiii−i−iii−i−i-1-111−ii−ii
χ1911111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii111-11-111-1-1-1-1−i−iii−i−iii−i−iii−i−iii11-1-1−ii−ii
χ2011111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-11-11-1-1-11111ii−i−iii−i−i−i−iii−i−iii-1-111i−ii−i
χ2111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i11-11-11-1-111-1-1ii−i−i−i−iii−i−iii−i−iii-11-11−iii−i
χ2211111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-11-1111-1-111−i−iiiii−i−i−i−iii−i−iii1-11-1i−i−ii
χ2311111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii11-11-11-1-111-1-1−i−iiiii−i−iii−i−iii−i−i-11-11i−i−ii
χ2411111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-11-1111-1-111ii−i−i−i−iiiii−i−iii−i−i1-11-1−iii−i
χ2511111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii111-1-1111-1-1-1-1ii−i−i−i−iiiii−i−i−i−iii-1-111i−i−ii
χ2611111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-11-1-11-1-11111−i−iiiii−i−iii−i−i−i−iii11-1-1−iii−i
χ2711111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i111-1-1111-1-1-1-1−i−iiiii−i−i−i−iiiii−i−i-1-111−iii−i
χ2811111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-11-1-11-1-11111ii−i−i−i−iii−i−iiiii−i−i11-1-1i−i−ii
χ2911111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-111iiii−i−i−i−i−i−i−i−iiiii11-111-1-1-111-1-1ii−i−iii−i−i−i−iiiii−i−i1-11-1−ii−ii
χ3011111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-111iiii−i−i−i−i−i−i−i−iiiii-1-1-111-111-1-111−i−iii−i−iii−i−iiiii−i−i-11-11i−ii−i
χ3111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-111−i−i−i−iiiiiiiii−i−i−i−i11-111-1-1-111-1-1−i−iii−i−iiiii−i−i−i−iii1-11-1i−ii−i
χ3211111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-111−i−i−i−iiiiiiiii−i−i−i−i-1-1-111-111-1-111ii−i−iii−i−iii−i−i−i−iii-11-11−ii−ii
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χ874-4-44-4-444-4-4-444-4440000000000000000000000000000000022−22−2222−222222−22000000000000000000000000000000000000
χ884-4-44-4-444-4-4-444-44400000000000000000000000000000000−222222−2222−22−2222000000000000000000000000000000000000
χ894-4-4-444-4444-444-4-4-40000000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000000000000
χ904-4-4-444-4444-444-4-4-4000000000000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000000000000
χ914-4-4-444-44-4-44-4-444400000000000000000000000022−22−2222−222222−2200000000000000000000000000000000000000000000
χ924-4-4-444-44-4-44-4-4444000000000000000000000000−222222−2222−22−222200000000000000000000000000000000000000000000

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