Finite Group Databasebeta

← Group #121315

Character table — Group #121315

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111111111111222222222222222244444444444444444444888888888888888888888888888888881616161616161616
order12222222444444442222444444444444444488888888888888884444444488888888888888888888888844448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
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
χ6111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111
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
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χ1211111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-111-1-1111-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111-1-1-1-1111111-1-1ii−i−i
χ1311111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-111-1-1111-1-1−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111-1-1-1-1111111-1-1−i−iii
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χ1511111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-111-1-1111-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-111111111-1-1-1-1-1-111ii−i−i
χ1611111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-111-1-1111-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-11111-1-1-1-111-1-1−i−iii
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χ342222-2-2-2-22222-2-2-2-2-2-222-2-22000000002000022−2−2−2−22222−2−2−2−22200000000−2i2i00−2i2i00−i2i2i2−i2−i2i2i2−i20000000000000000
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χ4622-2-22-22-22i−2i2i−2i2i−2i2i−2i00000002-22i−2i2-22i−2i0000000002ζ3−2ζ32ζ3−2ζ300002ζ−2ζ2ζ−2ζ−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000000000000000−i2−i2i2i2−2−22200000000
χ4722-2-22-22-22i−2i2i−2i2i−2i2i−2i00000002-22i−2i2-22i−2i000000000−2ζ32ζ3−2ζ32ζ30000−2ζ2ζ−2ζ2ζ1+i1+i−1−i−1−i1−i1−i−1+i−1+i0000000000000000−i2−i2i2i2−2−22200000000
χ4822-2-22-22-22i−2i2i−2i2i−2i2i−2i00000002-22i−2i2-22i−2i000000000−2ζ32ζ3−2ζ32ζ30000−2ζ2ζ−2ζ2ζ−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000000000000000i2i2−i2−i222−2−200000000
χ4922-2-22-22-2−2i2i−2i2i−2i2i−2i2i00000002-2−2i2i2-2−2i2i0000000002ζ−2ζ2ζ−2ζ00002ζ3−2ζ32ζ3−2ζ31−i1−i−1+i−1+i1+i1+i−1−i−1−i0000000000000000i2i2−i2−i2−2−22200000000
χ5022-2-22-22-2−2i2i−2i2i−2i2i−2i2i00000002-2−2i2i2-2−2i2i0000000002ζ−2ζ2ζ−2ζ00002ζ3−2ζ32ζ3−2ζ3−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000000000000000−i2−i2i2i222−2−200000000
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χ582-22-22-2-22−2i2i2i−2i2i−2i−2i2i0000000-222i−2i2-2−2i2i000002ζ3−2ζ32ζ3−2ζ300002ζ−2ζ2ζ−2ζ0000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000000002−22−2−i2i2−i2i200000000
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χ612-2-2222-2-222-2-2-2-2222-22-22-222222-2-2-2-2-22-22-200000000000000000000000000000000000000000000000000002-22-2
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χ924-4-44-4-444-4-444-4-444-444-44-4-4000000004000000000000000000000000000000000000000000000000000000000000

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