Finite Group Databasebeta

← Group #119978

Character table — Group #119978

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111111111111222222222222222244444444444444444444888888888888888888888888888888881616161616161616
order12222222444444442222444444444444444488888888888888884444444444444444888888888888888844448888
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
χ5111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ6111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ911111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-111-1-1ii−i−i
χ1011111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111-1-111−i−iii
χ1111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-1-111−i−iii
χ1211111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii-1-1-1-1111111-1-1ii−i−i
χ1311111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111-1-111ii−i−i
χ1411111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-111-1-1−i−iii
χ1511111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i-1-1-1-1111111-1-1−i−iii
χ1611111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-1-111ii−i−i
χ17222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000022-2-222-2-20000000000000000
χ18222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000-2-222-2-2220000000000000000
χ192222222222222222-2-2-2-2-2-2-2-222222222-2-2-2-2000000000000000022-2-222-2-200000000000000000000000000000000
χ202222222222222222-2-2-2-2-2-2-2-222222222-2-2-2-20000000000000000-2-222-2-22200000000000000000000000000000000
χ212222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000000000000000000000002-22-2
χ222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000000000000000000000000000-22-22
χ2322222222-2-2-2-2-2-2-2-22222-2-2-2-222-2-2-2-222-2-222000000000000000022-2-2-2-22200000000000000000000000000000000
χ2422222222-2-2-2-2-2-2-2-22222-2-2-2-222-2-2-2-222-2-2220000000000000000-2-22222-2-200000000000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-22222-2-222-2-200000000000000000000000000000000000000000000000000002i−2i−2i2i
χ2622222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-22222-2-222-2-20000000000000000000000000000000000000000000000000000−2i2i2i−2i
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-22222-2-2-2-222000000000000000000000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-22222-2-2-2-22200000000000000000000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ292222-2-2-2-22222-2-2-2-222-2-222-2-20000000000002222−2−2−2−22222−2−2−2−20000000000000000002-2002-222−2−222−2−200000000
χ302222-2-2-2-22222-2-2-2-222-2-222-2-20000000000002222−2−2−2−22222−2−2−2−2000000000000000000-2200-22−2−222−2−22200000000
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χ322222-2-2-2-22222-2-2-2-222-2-222-2-2000000000000−2−2−2−22222−2−2−2−22222000000000000000000-2200-2222−2−222−2−200000000
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χ4022-2-22-22-22i−2i2i−2i2i−2i2i−2i000000002-22i2i−2i−2i2-20000−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i00−2i2i00-221−i1−i−1+i−1+i1+i1+i−1−i−1−i000000000000000000000000
χ4122-2-22-22-2−2i2i−2i2i−2i2i−2i2i000000002-2−2i−2i2i2i2-200001−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i002i−2i00-22−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000000000000000000000
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χ462-22-2-222-22i−2i−2i2i−2i2i2i−2i00000000-222i−2i2i−2i2-200001−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i-2200−2i2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000000000000000
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χ482-22-2-222-22i−2i−2i2i−2i2i2i−2i00000000-222i−2i2i−2i2-20000−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i-2200−2i2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000000000000000
χ492-22-2-222-2−2i2i2i−2i2i−2i−2i2i00000000-22−2i2i−2i2i2-200001+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i2-200−2i2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000000000000000
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χ532-2-2222-2-222-2-222-2-22-2-222-22-2000000000000i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i200000000000000002-2002-200i2−i2i2−i2i2−i2i2−i200000000
χ542-2-2222-2-222-2-222-2-22-2-222-22-2000000000000i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i20000000000000000-2200-2200−i2i2−i2i2−i2i2−i2i200000000
χ552-2-2222-2-222-2-222-2-22-2-222-22-2000000000000−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i200000000000000002-2002-200−i2i2−i2i2−i2i2−i2i200000000
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χ8144-4-4-44-444i−4i4i−4i−4i4i−4i4i000000000000000000002ζ2ζ−2ζ−2ζ−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ32ζ32ζ3−2ζ3−2ζ30000000000000000000000000000000000000000
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χ8444-4-4-44-44−4i4i−4i4i4i−4i4i−4i00000000000000000000−2ζ3−2ζ32ζ32ζ32ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ−2ζ−2ζ2ζ2ζ0000000000000000000000000000000000000000
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χ864-44-44-4-444i−4i−4i4i4i−4i−4i4i00000000000000000000−2ζ32ζ3−2ζ32ζ32ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ−2ζ2ζ−2ζ2ζ0000000000000000000000000000000000000000
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χ904-44-4-444-4−4i4i4i−4i4i−4i−4i4i000000004-44i−4i4i−4i-44000000000000000000000000000000000000000000000000000000000000
χ914-4-4444-4-444-4-444-4-4-444-4-44-4400000000000000000000000000000000000000000000000000000000000000000000
χ924-4-4444-4-4-4-444-4-4444-4-44-44-4400000000000000000000000000000000000000000000000000000000000000000000

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