Finite Group Databasebeta

← Group #120613

Character table — Group #120613

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111111111111222222222222222244444444444444444444888888888888888888888888888888881616161616161616
order12222222444444442222444444444444444488888888888888884444444488888888888888888888888888888888
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
χ911111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-11111-1-1-1-1ii−i−iii−i−i
χ1011111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111-1-1-1-11111−i−iii−i−iii
χ1111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-11111-1-1-1-1−i−iii−i−iii
χ1211111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111-1-1-1-11111ii−i−iii−i−i
χ1311111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111ii−i−i−i−iii
χ1411111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiii-1-1-1-111111111-1-1-1-1−i−iiiii−i−i
χ1511111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-1-1-1-11111−i−iiiii−i−i
χ1611111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-111111111-1-1-1-1ii−i−i−i−iii
χ172222222222222222222222-2-2-2-222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-20000000000000000000000000000000000000000
χ182222222222222222222222-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-222220000000000000000000000000000000000000000
χ192222222222222222-2-2-2-2-2-22222-2-22222-2-2-2-200000000000000000000000022-2-222-2-2000000000000000000000000
χ202222222222222222-2-2-2-2-2-22222-2-22222-2-2-2-2000000000000000000000000-2-222-2-222000000000000000000000000
χ212222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000002i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000
χ222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000
χ2322222222-2-2-2-2-2-2-2-22222-2-22222-2-2-2-2-2-222-2-2000000000000000022-2-2-2-22200000000000000000000000000000000
χ2422222222-2-2-2-2-2-2-2-22222-2-22222-2-2-2-2-2-222-2-20000000000000000-2-22222-2-200000000000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-22222-2-2220000000000000000000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ2622222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-22222-2-222000000000000000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2222222-2-2-2-2-2-2-2-222220000000000000000000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2-2-222-2-2-2-222222222-2-2-2-20000000000000000000000000000000000000000
χ29222-2-22-2-22222-2-2-2-222-2-22-200002-200000000000022-2-2000022-2-2000000000000000022−2−222−2−222−2−222−2−200000000
χ30222-2-22-2-22222-2-2-2-222-2-22-200002-200000000000022-2-2000022-2-20000000000000000−2−222−2−222−2−222−2−22200000000
χ31222-2-22-2-22222-2-2-2-222-2-22-200002-2000000000000-2-2220000-2-222000000000000000022−2−222−2−2−2−222−2−22200000000
χ32222-2-22-2-22222-2-2-2-222-2-22-200002-2000000000000-2-2220000-2-2220000000000000000−2−222−2−22222−2−222−2−200000000
χ33222-2-22-2-2-2-2-2-22222-2-2222-200002-200000000000022-2-20000-2-222000000000000000022−2−2−2−22222−2−2−2−22200000000
χ34222-2-22-2-2-2-2-2-22222-2-2222-200002-200000000000022-2-20000-2-2220000000000000000−2−22222−2−2−2−22222−2−200000000
χ35222-2-22-2-2-2-2-2-22222-2-2222-200002-2000000000000-2-222000022-2-2000000000000000022−2−2−2−222−2−22222−2−200000000
χ36222-2-22-2-2-2-2-2-22222-2-2222-200002-2000000000000-2-222000022-2-20000000000000000−2−22222−2−222−2−2−2−22200000000
χ3722-22-2-22-22i2i−2i−2i2i−2i2i−2i0000002i2i−2i−2i0022-2-20000i2i2−i2−i2i2−i2i2−i222−2−22−22−21+i−1−i1+i−1−i1−i−1+i1−i−1+i002ζ3−2ζ3002ζ−2ζ000000000000000000000000
χ3822-22-2-22-22i2i−2i−2i2i−2i2i−2i0000002i2i−2i−2i0022-2-20000i2i2−i2−i2i2−i2i2−i222−2−22−22−2−1−i1+i−1−i1+i−1+i1−i−1+i1−i00−2ζ32ζ300−2ζ2ζ000000000000000000000000
χ3922-22-2-22-22i2i−2i−2i2i−2i2i−2i0000002i2i−2i−2i0022-2-20000−i2−i2i2i2−i2i2−i2i2−2−222−22−221+i−1−i1+i−1−i1−i−1+i1−i−1+i00−2ζ32ζ300−2ζ2ζ000000000000000000000000
χ4022-22-2-22-22i2i−2i−2i2i−2i2i−2i0000002i2i−2i−2i0022-2-20000−i2−i2i2i2−i2i2−i2i2−2−222−22−22−1−i1+i−1−i1+i−1+i1−i−1+i1−i002ζ3−2ζ3002ζ−2ζ000000000000000000000000
χ4122-22-2-22-22i2i−2i−2i2i−2i2i−2i000000−2i−2i2i2i00-2-2220000i2i2−i2−i2−i2i2−i2i222−2−2−22−221−i−1+i−1+i1−i−1−i1+i1+i−1−i2ζ−2ζ002ζ3−2ζ300000000000000000000000000
χ4222-22-2-22-22i2i−2i−2i2i−2i2i−2i000000−2i−2i2i2i00-2-2220000i2i2−i2−i2−i2i2−i2i222−2−2−22−22−1+i1−i1−i−1+i1+i−1−i−1−i1+i−2ζ2ζ00−2ζ32ζ300000000000000000000000000
χ4322-22-2-22-22i2i−2i−2i2i−2i2i−2i000000−2i−2i2i2i00-2-2220000−i2−i2i2i2i2−i2i2−i2−2−2222−22−21−i−1+i−1+i1−i−1−i1+i1+i−1−i−2ζ2ζ00−2ζ32ζ300000000000000000000000000
χ4422-22-2-22-22i2i−2i−2i2i−2i2i−2i000000−2i−2i2i2i00-2-2220000−i2−i2i2i2i2−i2i2−i2−2−2222−22−2−1+i1−i1−i−1+i1+i−1−i−1−i1+i2ζ−2ζ002ζ3−2ζ300000000000000000000000000
χ4522-22-2-22-2−2i−2i2i2i−2i2i−2i2i0000002i2i−2i−2i00-2-2220000i2i2−i2−i2−i2i2−i2i2−2−2222−22−21+i−1−i−1−i1+i−1+i1−i1−i−1+i2ζ3−2ζ3002ζ−2ζ00000000000000000000000000
χ4622-22-2-22-2−2i−2i2i2i−2i2i−2i2i0000002i2i−2i−2i00-2-2220000i2i2−i2−i2−i2i2−i2i2−2−2222−22−2−1−i1+i1+i−1−i1−i−1+i−1+i1−i−2ζ32ζ300−2ζ2ζ00000000000000000000000000
χ4722-22-2-22-2−2i−2i2i2i−2i2i−2i2i0000002i2i−2i−2i00-2-2220000−i2−i2i2i2i2−i2i2−i222−2−2−22−221+i−1−i−1−i1+i−1+i1−i1−i−1+i−2ζ32ζ300−2ζ2ζ00000000000000000000000000
χ4822-22-2-22-2−2i−2i2i2i−2i2i−2i2i0000002i2i−2i−2i00-2-2220000−i2−i2i2i2i2−i2i2−i222−2−2−22−22−1−i1+i1+i−1−i1−i−1+i−1+i1−i2ζ3−2ζ3002ζ−2ζ00000000000000000000000000
χ4922-22-2-22-2−2i−2i2i2i−2i2i−2i2i000000−2i−2i2i2i0022-2-20000i2i2−i2−i2i2−i2i2−i2−2−222−22−221−i−1+i1−i−1+i1+i−1−i1+i−1−i002ζ−2ζ002ζ3−2ζ3000000000000000000000000
χ5022-22-2-22-2−2i−2i2i2i−2i2i−2i2i000000−2i−2i2i2i0022-2-20000i2i2−i2−i2i2−i2i2−i2−2−222−22−22−1+i1−i−1+i1−i−1−i1+i−1−i1+i00−2ζ2ζ00−2ζ32ζ3000000000000000000000000
χ5122-22-2-22-2−2i−2i2i2i−2i2i−2i2i000000−2i−2i2i2i0022-2-20000−i2−i2i2i2−i2i2−i2i222−2−22−22−21−i−1+i1−i−1+i1+i−1−i1+i−1−i00−2ζ2ζ00−2ζ32ζ3000000000000000000000000
χ5222-22-2-22-2−2i−2i2i2i−2i2i−2i2i000000−2i−2i2i2i0022-2-20000−i2−i2i2i2−i2i2−i2i222−2−22−22−2−1+i1−i−1+i1−i−1−i1+i−1−i1+i002ζ−2ζ002ζ3−2ζ3000000000000000000000000
χ532-2-2222-2-22-22-222-2-22-2-222-20000-22000000002-22-200002-22-200000000000000000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i200000000
χ542-2-2222-2-22-22-222-2-22-2-222-20000-22000000002-22-200002-22-200000000000000000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i200000000
χ552-2-2222-2-22-22-222-2-22-2-222-20000-2200000000-22-220000-22-2200000000000000000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i200000000
χ562-2-2222-2-22-22-222-2-22-2-222-20000-2200000000-22-220000-22-2200000000000000000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i200000000
χ572-2-2222-2-2-22-22-2-222-222-22-20000-22000000002-22-20000-22-2200000000000000000000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i200000000
χ582-2-2222-2-2-22-22-2-222-222-22-20000-22000000002-22-20000-22-2200000000000000000000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i200000000
χ592-2-2222-2-2-22-22-2-222-222-22-20000-2200000000-22-2200002-22-200000000000000000000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i200000000
χ602-2-2222-2-2-22-22-2-222-222-22-20000-2200000000-22-2200002-22-200000000000000000000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i200000000
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χ622-2-2-2-22222-22-2-2-2222-22-2222-22-2-2-22-22-22-22-20000000000000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000
χ632-2-2-2-22222-22-2-2-2222-22-222-22-22-2-2-22-22-22-22000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ642-2-2-2-22222-22-2-2-2222-22-222-22-22-2-2-22-22-22-2200000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ652-2-2-2-22222-22-2-2-222-22-22-2-22-22-2222-22-2-22-220000000000000000000000000000000000000000000000002-22-20000
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χ682-2-2-2-22222-22-2-2-222-22-22-2-2-22-2222-22-222-22-20000000000000000000000000000000000000000000000000000-22-22
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χ752-2-2-2-2222-22-2222-2-2-22-2222-22-22-2-22-22-22-2-2200000000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000
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χ904-44-44-44-4−4i4i4i−4i4i−4i−4i4i000000−4i4i4i−4i004-4-44000000000000000000000000000000000000000000000000000000000000
χ914-4-4444-4-44-44-444-4-4-444-4-4400004-40000000000000000000000000000000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.