Finite Group Databasebeta

← Group #120496

Character table — Group #120496

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111111111111222222222222222244444444444444444444888888888888888888888888888888881616161616161616
order12222222444444444444444444444444224488888888888888888888888888888888888888888888888888888888
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
χ911111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-11111111111-1-1-1-1-1-1-1-1ii−i−iii−i−iiiii−i−i−i−i1111-1-1-1-11111-1-1-1-1ii−i−iii−i−i
χ1011111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-11111111111-1-1-1-1-1-1-1-1ii−i−iii−i−iiiii−i−i−i−i-1-1-1-11111-1-1-1-11111−i−iii−i−iii
χ1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-11111111111-1-1-1-1-1-1-1-1−i−iii−i−iii−i−i−i−iiiii1111-1-1-1-11111-1-1-1-1−i−iii−i−iii
χ1211111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-11111111111-1-1-1-1-1-1-1-1−i−iii−i−iii−i−i−i−iiiii-1-1-1-11111-1-1-1-11111ii−i−iii−i−i
χ1311111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-111111111ii−i−iii−i−i−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111ii−i−i−i−iii
χ1411111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-111111111ii−i−iii−i−i−i−i−i−iiiii-1-1-1-111111111-1-1-1-1−i−iiiii−i−i
χ1511111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-111111111−i−iii−i−iiiiiii−i−i−i−i1111-1-1-1-1-1-1-1-11111−i−iiiii−i−i
χ1611111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-111111111−i−iii−i−iiiiiii−i−i−i−i-1-1-1-111111111-1-1-1-1ii−i−i−i−iii
χ17222222222222222222-2-22222-2-2-2-2-2-222-2-2-2-200000000000000002222-2-2-2-200000000000000000000000000000000
χ18222222222222222222-2-22222-2-2-2-2-2-222-2-2-2-20000000000000000-2-2-2-2222200000000000000000000000000000000
χ192222222222222222-2-222-2-2-2-2222222-2-2-2-2-2-22222-2-2-2-22222-2-2-2-20000000000000000000000000000000000000000
χ202222222222222222-2-222-2-2-2-2222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-222220000000000000000000000000000000000000000
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
χ2322222222-2-2-2-2-2-2-2-222-2-2-2-2-2-222-2-2222222-2-200000000000000002i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ2422222222-2-2-2-2-2-2-2-222-2-2-2-2-2-222-2-2222222-2-20000000000000000−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-2-2-2222222-2-222-2-2-2-222-2-22222-2-2-2-2-2-2-2-222220000000000000000000000000000000000000000
χ2622222222-2-2-2-2-2-2-2-2-2-2222222-2-222-2-2-2-222-2-2-2-2-2-222222222-2-2-2-20000000000000000000000000000000000000000
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χ4022-22-2-22-22i−2i2i−2i−2i2i−2i2i2-2002i2i−2i−2i0000002-20000−i2−i2i2i2−i2i2−i2i2−2−222−22−220000−2ζ32ζ3−2ζ2ζ1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000000000000000
χ4122-22-2-22-22i−2i2i−2i−2i2i−2i2i-2200−2i−2i2i2i000000-220000i2i2−i2−i2−i2i2−i2i222−2−2−22−222ζ−2ζ2ζ3−2ζ300001−i−1+i−1+i1−i−1−i1+i1+i−1−i000000000000000000000000
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χ4322-22-2-22-22i−2i2i−2i−2i2i−2i2i-2200−2i−2i2i2i000000-220000−i2−i2i2i2i2−i2i2−i2−2−2222−22−22ζ−2ζ2ζ3−2ζ30000−1+i1−i1−i−1+i1+i−1−i−1−i1+i000000000000000000000000
χ4422-22-2-22-22i−2i2i−2i−2i2i−2i2i-2200−2i−2i2i2i000000-220000−i2−i2i2i2i2−i2i2−i2−2−2222−22−2−2ζ2ζ−2ζ32ζ300001−i−1+i−1+i1−i−1−i1+i1+i−1−i000000000000000000000000
χ4522-22-2-22-2−2i2i−2i2i2i−2i2i−2i2-200−2i−2i2i2i0000002-20000i2i2−i2−i2i2−i2i2−i2−2−222−22−2200002ζ−2ζ2ζ3−2ζ31−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000000000000000
χ4622-22-2-22-2−2i2i−2i2i2i−2i2i−2i2-200−2i−2i2i2i0000002-20000i2i2−i2−i2i2−i2i2−i2−2−222−22−220000−2ζ2ζ−2ζ32ζ3−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000000000000000
χ4722-22-2-22-2−2i2i−2i2i2i−2i2i−2i2-200−2i−2i2i2i0000002-20000−i2−i2i2i2−i2i2−i2i222−2−22−22−200002ζ−2ζ2ζ3−2ζ3−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000000000000000
χ4822-22-2-22-2−2i2i−2i2i2i−2i2i−2i2-200−2i−2i2i2i0000002-20000−i2−i2i2i2−i2i2−i2i222−2−22−22−20000−2ζ2ζ−2ζ32ζ31−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000000000000000
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χ5022-22-2-22-2−2i2i−2i2i2i−2i2i−2i-22002i2i−2i−2i000000-220000i2i2−i2−i2−i2i2−i2i2−2−2222−22−2−2ζ32ζ3−2ζ2ζ0000−1−i1+i1+i−1−i1−i−1+i−1+i1−i000000000000000000000000
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Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.