Finite Group Databasebeta

← Group #99613

Character table — Group #99613

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111111111111222222222222222244444444444444444444888888888888888888888888888888881616161616161616
order12222222444444444444444444444444444488888888888888888888888888888888888888888888888844444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
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
χ6111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
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
χ911111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1ii−i−iii−i−iii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1
χ1011111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1ii−i−i−i−iiiii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii-1-111-1-111
χ1111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1−i−iiiii−i−i−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-111-1-111
χ1211111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1−i−iii−i−iii−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1
χ1311111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111ii−i−iii−i−iii−i−iii−i−i−i−i−i−iiiii−i−i−i−iiiii11-1-1-1-111
χ1411111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111ii−i−i−i−iiiii−i−i−i−iii−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1
χ1511111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111−i−iiiii−i−i−i−iiiii−i−iiiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1
χ1611111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111−i−iii−i−iii−i−iii−i−iiiiiii−i−i−i−iiiii−i−i−i−i11-1-1-1-111
χ172222222222222222222222-2-2-2-2-2-222-2-2-2-2-2-20000000000000000000022220000-2-2-2-2000000000000000000000000
χ182222222222222222222222-2-2-2-2-2-222-2-2-2-2-2-200000000000000000000-2-2-2-200002222000000000000000000000000
χ192222222222222222-2-2-2-2-2-2222222-2-222-2-2-2-2000000000000000022220000-2-2-2-20000000000000000000000000000
χ202222222222222222-2-2-2-2-2-2222222-2-222-2-2-2-20000000000000000-2-2-2-2000022220000000000000000000000000000
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
χ2322222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-222-2-22222-2-2000000000000000000002i2i−2i−2i0000−2i−2i2i2i000000000000000000000000
χ2422222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-222-2-22222-2-200000000000000000000−2i−2i2i2i00002i2i−2i−2i000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2-222-2-222-2-200000000000000002i2i−2i−2i0000−2i−2i2i2i0000000000000000000000000000
χ2622222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2-222-2-222-2-20000000000000000−2i−2i2i2i00002i2i−2i−2i0000000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-2222222-2-2220000000000000000000000000000000000000000000000002-2-220000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-2222222-2-222000000000000000000000000000000000000000000000000-222-20000
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χ302222-2-2-2-22222-2-2-2-222-2-222000000-2-20000002222−2−2−2−22222−2−2−2−20000-22-220000000000000000−2−222−2−22200000000
χ312222-2-2-2-22222-2-2-2-222-2-222000000-2-2000000−2−2−2−22222−2−2−2−2222200002-22-20000000000000000−2−222−2−22200000000
χ322222-2-2-2-22222-2-2-2-222-2-222000000-2-2000000−2−2−2−22222−2−2−2−222220000-22-22000000000000000022−2−222−2−200000000
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χ462-22-22-22-22i−2i2i−2i2i−2i2i−2i0000002-22-22i−2i002i−2i0000i2−i2i2−i2i2−i2i2−i22−22−22−22−2−2ζ2ζ−2ζ32ζ3000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
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χ482-22-22-22-22i−2i2i−2i2i−2i2i−2i0000002-22-22i−2i002i−2i0000−i2i2−i2i2−i2i2−i2i2−22−22−22−22−2ζ2ζ−2ζ32ζ30000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ492-22-22-22-2−2i2i−2i2i−2i2i−2i2i0000002-22-2−2i2i00−2i2i0000i2−i2i2−i2i2−i2i2−i2−22−22−22−222ζ3−2ζ32ζ−2ζ0000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
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χ532-2-222-2-222i−2i−2i2i2i−2i−2i2i2-22-22i−2i2-2-22−2i2i2i−2i2i−2i2i−2i2-2000000000000000000000000000000002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ0000000000000000
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χ622-2-222-2-22−2i2i2i−2i−2i2i2i−2i2-22-2−2i2i2-2-222i−2i−2i2i−2i2i−2i2i2-200000000000000000000000000000000−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ30000000000000000
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χ652-2-222-2-22−2i2i2i−2i−2i2i2i−2i-22-222i−2i2-2-222i−2i2i−2i−2i2i2i−2i-222-2-222-2-222i−2i−2i2i2i−2i−2i2i0000000000000000000000000000000000000000
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χ672-2-222-2-22−2i2i2i−2i−2i2i2i−2i-22-222i−2i-222-2−2i2i2i−2i2i−2i−2i2i2-200000000000000000000000000000000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ00000000
χ682-2-222-2-22−2i2i2i−2i−2i2i2i−2i-22-222i−2i-222-2−2i2i2i−2i2i−2i−2i2i2-20000000000000000000000000000000000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ00000000
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χ774444-4-4-4-44444-4-4-4-4-4-444-4-40000004400000000000000000000000000000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.