Finite Group Databasebeta

← Group #102012

Character table — Group #102012

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111111111111222222222222222244444444444444444444888888888888888888888888888888881616161616161616
order12222222444444444444444444444444444488888888888888888888888888888888888888888888888844444444
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
χ5111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
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
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
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χ1011111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111
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χ1211111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1
χ1311111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111
χ1411111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1
χ1511111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1
χ1611111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111
χ1722222222222222222222-2-2-2-2-2-22222-2-2-2-2-2-2000000000000000022-2-222-2-200000000000000000000000000000000
χ1822222222222222222222-2-2-2-2-2-22222-2-2-2-2-2-20000000000000000-2-222-2-22200000000000000000000000000000000
χ192222222222222222-2-2-2-2222222-2-2-2-222-2-2-2-22222-2-2-2-22222-2-2-2-20000000000000000000000000000000000000000
χ202222222222222222-2-2-2-2222222-2-2-2-222-2-2-2-2-2-2-2-22222-2-2-2-222220000000000000000000000000000000000000000
χ212222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000000000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ2322222222-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-222-2-22200000000000000002i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ2422222222-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-222-2-2220000000000000000−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-222222222-2-200000000000000000000000022-2-2-2-222000000000000000000000000
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χ4822-2-2-2-222-2-222-2-22222-2-2000000-2-222000000−i2−i2i2i2−i2i2−i2i2i2i2−i2−i2i2−i2i2−i200-22002-2−i2i2−i2i2i2−i2i2−i2000000000000000000000000
χ4922-2-2-2-222-2-222-2-222-2-22200000022-2-2000000i2i2−i2−i2−i2i2−i2i2−i2−i2i2i2i2−i2i2−i22i−2i00−2i2i00−222−22−2−22000000000000000000000000
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χ632-2-222-2-222i−2i2i−2i−2i2i−2i2i2-22-2−2i2i2-2-222i−2i2i−2i2i−2i-22−2i2i00000000000000000000000000000000000000002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ300000000
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χ692-2-222-2-22−2i2i−2i2i2i−2i2i−2i2-22-22i−2i2-2-22−2i2i−2i2i−2i2i-222i−2i00000000000000000000000000000000000000002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ00000000
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χ874-44-4-44-44−4i4i4i−4i4i−4i−4i4i4-4-44000000−4i4i4i−4i00000000000000000000000000000000000000000000000000000000000000
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χ904-4-44-444-44i−4i−4i4i4i−4i−4i4i00000000000000000000−2i22i22i2−2i2000022−22−222200000000000000000000000000000000000000000000
χ914-4-44-444-4−4i4i4i−4i−4i4i4i−4i000000000000000000002i2−2i2−2i22i2000022−22−222200000000000000000000000000000000000000000000
χ924-4-44-444-4−4i4i4i−4i−4i4i4i−4i00000000000000000000−2i22i22i2−2i20000−222222−2200000000000000000000000000000000000000000000

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