Finite Group Databasebeta

← Group #121321

Character table — Group #121321

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111111111111222222222222222244444444444444444444888888888888888888888888888888881616161616161616
order12222222444444442222444444444444444444444444444444448888888888888888888888888888888844448888
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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χ1011111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-111-1-1111-1-1iiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-1-1-1-111111111-1-1-1-1-1-111−i−iii
χ1111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-111-1-1111-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-1-1-1-11111-1-111−i−iii
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
χ1411111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-111-1-1111-1-1−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111-1-111ii−i−i
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
χ1722222222222222222222222-2-2-2-2-2-2-2-22-2-2-2-22222-2-2-2-22222-2-2-2-20000000000000000000000000000000000000000
χ1822222222222222222222222-2-2-2-2-2-2-2-22-2-2-2-2-2-2-2-22222-2-2-2-222220000000000000000000000000000000000000000
χ192222222222222222-2-2-2-2-2-2-222222222-2-2-2-2-2000000000000000022-2-222-2-200000000000000000000000000000000
χ202222222222222222-2-2-2-2-2-2-222222222-2-2-2-2-20000000000000000-2-222-2-22200000000000000000000000000000000
χ212222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000000000002i2i−2i−2i2i2i−2i−2i00000000
χ222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000000000000000−2i−2i2i2i−2i−2i2i2i00000000
χ2322222222-2-2-2-2-2-2-2-22222-2-2-222-2-222-2-2-2-2-22200000000000000002i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ2422222222-2-2-2-2-2-2-2-22222-2-2-222-2-222-2-2-2-2-2220000000000000000−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-22222-2-2-2-2-222-2-222-222-2-200000000000000000000000000000000000000002i2i−2i−2i−2i−2i2i2i00000000
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χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222-2-222-2-2222-2-2222i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i0000000000000000000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2222-2-222-2-2222-2-222−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i0000000000000000000000000000000000000000
χ292222-2-2-2-222-2-222-2-22-22-22-2-2000000002000000002i2i−2i−2i00002i2i−2i−2i0000000022−2−222−2−2i2i2−i2−i2i2i2−i2−i20000000000000000
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χ332222-2-2-2-2-2-222-2-222-22-222-2-20000000020000000022-2-20000-2-22200000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ342222-2-2-2-2-2-222-2-222-22-222-2-20000000020000000022-2-20000-2-22200000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ352222-2-2-2-2-2-222-2-222-22-222-2-200000000200000000-2-222000022-2-200000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ362222-2-2-2-2-2-222-2-222-22-222-2-200000000200000000-2-222000022-2-200000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000000000000000
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χ4022-2-22-22-22i−2i2i−2i2i−2i2i−2i00000002-22i−2i2-22i−2i00000−1−i−1−i1+i1+i−1−i1+i−1−i1+i−1+i−1+i1−i1−i−1+i1−i−1+i1−i00−2ζ32ζ300−2ζ2ζ0000000000000000i2−i2i2−i22−22−200000000
χ4122-2-22-22-22i−2i2i−2i2i−2i2i−2i0000000-22−2i2i-22−2i2i000001+i1+i−1−i−1−i−1−i1+i−1−i1+i1−i1−i−1+i−1+i−1+i1−i−1+i1−i2ζ−2ζ002ζ3−2ζ30000000000000000002−2−22−i2i2i2−i200000000
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χ4322-2-22-22-22i−2i2i−2i2i−2i2i−2i0000000-22−2i2i-22−2i2i00000−1−i−1−i1+i1+i1+i−1−i1+i−1−i−1+i−1+i1−i1−i1−i−1+i1−i−1+i2ζ−2ζ002ζ3−2ζ3000000000000000000−222−2i2−i2−i2i200000000
χ4422-2-22-22-22i−2i2i−2i2i−2i2i−2i0000000-22−2i2i-22−2i2i00000−1−i−1−i1+i1+i1+i−1−i1+i−1−i−1+i−1+i1−i1−i1−i−1+i1−i−1+i−2ζ2ζ00−2ζ32ζ30000000000000000002−2−22−i2i2i2−i200000000
χ4522-2-22-22-2−2i2i−2i2i−2i2i−2i2i00000002-2−2i2i2-2−2i2i000001−i1−i−1+i−1+i1−i−1+i1−i−1+i1+i1+i−1−i−1−i1+i−1−i1+i−1−i002ζ−2ζ002ζ3−2ζ30000000000000000i2−i2i2−i2−22−2200000000
χ4622-2-22-22-2−2i2i−2i2i−2i2i−2i2i00000002-2−2i2i2-2−2i2i000001−i1−i−1+i−1+i1−i−1+i1−i−1+i1+i1+i−1−i−1−i1+i−1−i1+i−1−i00−2ζ2ζ00−2ζ32ζ30000000000000000−i2i2−i2i22−22−200000000
χ4722-2-22-22-2−2i2i−2i2i−2i2i−2i2i00000002-2−2i2i2-2−2i2i00000−1+i−1+i1−i1−i−1+i1−i−1+i1−i−1−i−1−i1+i1+i−1−i1+i−1−i1+i002ζ−2ζ002ζ3−2ζ30000000000000000−i2i2−i2i22−22−200000000
χ4822-2-22-22-2−2i2i−2i2i−2i2i−2i2i00000002-2−2i2i2-2−2i2i00000−1+i−1+i1−i1−i−1+i1−i−1+i1−i−1−i−1−i1+i1+i−1−i1+i−1−i1+i00−2ζ2ζ00−2ζ32ζ30000000000000000i2−i2i2−i2−22−2200000000
χ4922-2-22-22-2−2i2i−2i2i−2i2i−2i2i0000000-222i−2i-222i−2i000001−i1−i−1+i−1+i−1+i1−i−1+i1−i1+i1+i−1−i−1−i−1−i1+i−1−i1+i2ζ3−2ζ3002ζ−2ζ000000000000000000−222−2−i2i2i2−i200000000
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χ532-2-2222-2-222-2-2-2-22222-2-2-22-222-2-2-2-22222-22-2000000000000000000000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ542-2-2222-2-222-2-2-2-22222-2-2-22-222-2-2-2-22222-22-200000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000
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χ572-2-2222-2-222-2-2-2-222-2-2222-2222-2-2-2-222-2-22-2200000000000000000000000000000000000000000000000000002i−2i2i−2i
χ582-2-2222-2-222-2-2-2-222-2-2222-2222-2-2-2-222-2-22-220000000000000000000000000000000000000000000000000000−2i2i−2i2i
χ592-2-2222-2-222-2-2-2-222-2-2222-22-2-22222-2-2-22-22-20000000000000000000000000000000000000000000000002i−2i2i−2i0000
χ602-2-2222-2-222-2-2-2-222-2-2222-22-2-22222-2-2-22-22-2000000000000000000000000000000000000000000000000−2i2i−2i2i0000
χ612-2-2222-2-2-2-22222-2-222-2-22-222222-2-2-2-2-2-222-200000000000000000000000000000000000000000000000000002-2-22
χ622-2-2222-2-2-2-22222-2-222-2-22-222222-2-2-2-2-2-222-20000000000000000000000000000000000000000000000000000-222-2
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χ904-44-4-444-4−4i4i−4i4i4i−4i4i−4i00000000000000000000−2−2i2+2i2+2i−2−2i00002−2i−2+2i−2+2i2−2i00000000000000000000000000000000000000000000
χ914-4-44-4-4444444-4-4-4-4-444-444-400000000-4000000000000000000000000000000000000000000000000000000000000
χ924-4-44-4-444-4-4-4-444444-4-4444-400000000-4000000000000000000000000000000000000000000000000000000000000

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