Finite Group Databasebeta

← Group #490118

Character table — Group #490118

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size1111222244444444444448888888888881616161616161616161616161616161616163232
order12224444244448888888824441616161616161616222444448888881616161644
χ111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1
χ31111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111
χ5111111111111111111111-1-1-1-11111111111-1-1-111-1-1-11111-1-1-1-1-1-1
χ6111111111111111111111-1-1-1-111111111-1-1111-1-11-1-1-1-1-1-1-1-1-1-111
χ7111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-1-1-1-1-1-1111111
χ8111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11-1-111111111-1-1
χ91111-1-111-1-11-111-1-1-1-11111-1-111111-1-1-1-11-11-111-1-11-111-1-111-1-11-1
χ101111-1-111-1-11-111-1-1-1-11111-1-111111-1-1-1-1-11-11-1-1111-1-1-11111-1-1-11
χ111111-1-111-1-11-111-1-1-1-11111-1-11-1-1-1-111111-11-111-1-11-1-1-111-1-111-11
χ121111-1-111-1-11-111-1-1-1-11111-1-11-1-1-1-11111-11-11-1-1111-111-1-1-1-1111-1
χ131111-1-111-1-11-111-1-1-1-1111-111-11111-1-1-1-11-1-11-11-11-1111-1-1-1-111-11
χ141111-1-111-1-11-111-1-1-1-1111-111-11111-1-1-1-1-111-11-11-1-11-1-111-1-1111-1
χ151111-1-111-1-11-111-1-1-1-1111-111-1-1-1-1-111111-1-11-11-11-11-1-11111-1-11-1
χ161111-1-111-1-11-111-1-1-1-1111-111-1-1-1-1-11111-111-11-11-1-1111-1-111-1-1-11
χ172222222222222-2-2-2-2-2-2-2-222220000000000000000-2-20000000000
χ182222222222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000220000000000
χ19222222222-2-2-2-2222-2-2-2-220000000000000022-200-2000000000000
χ20222222222-2-2-2-2222-2-2-2-2200000000000000-2-22002000000000000
χ21222222222-2-2-2-2-2-2-22222-20000000000002-2000-220000000000000
χ22222222222-2-2-2-2-2-2-22222-2000000000000-220002-20000000000000
χ23222222-2-2-2-2-2220000000022-2-222−2−222−2−2000000000000002−22−200
χ24222222-2-2-2-2-2220000000022-2-2−2−222−2−22200000000000000−22−2200
χ25222222-2-2-2-2-22200000000-2-22222−2−222−2−200000000000000−22−2200
χ26222222-2-2-2-2-22200000000-2-222−2−222−2−222000000000000002−22−200
χ272222-2-222-22-22-22-2-222-2-22000000000000002-2-2002000000000000
χ282222-2-222-22-22-22-2-222-2-2200000000000000-22200-2000000000000
χ292222-2-222-22-22-2-222-2-222-200000000000022000-2-20000000000000
χ302222-2-222-22-22-2-222-2-222-2000000000000-2-2000220000000000000
χ312222-2-222-2-22-22-22222-2-2-22-2-220000000000000000-220000000000
χ322222-2-222-2-22-22-22222-2-2-2-222-200000000000000002-20000000000
χ332222-2-2-2-222-2-22000000002-22-222−2−2−2−222000000000000002−2−2200
χ342222-2-2-2-222-2-22000000002-22-2−2−22222−2−200000000000000−222−200
χ352222-2-2-2-222-2-2200000000-22-2222−2−2−2−22200000000000000−222−200
χ362222-2-2-2-222-2-2200000000-22-22−2−22222−2−2000000000000002−2−2200
χ37444444-4-4-444-4-40000000000000000000000000000000000000000
χ384444-4-4-4-44-444-40000000000000000000000000000000000000000
χ394-44-44i−4i00000000002i2−2i222−2200000ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ700000000000000000000
χ404-44-44i−4i00000000002i2−2i222−2200000−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ700000000000000000000
χ414-44-44i−4i0000000000−2i22i2−222200000ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ700000000000000000000
χ424-44-44i−4i0000000000−2i22i2−222200000−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ700000000000000000000
χ434-44-4−4i4i00000000002i2−2i2−222200000ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ700000000000000000000
χ444-44-4−4i4i00000000002i2−2i2−222200000−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ700000000000000000000
χ454-44-4−4i4i0000000000−2i22i222−2200000ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ700000000000000000000
χ464-44-4−4i4i0000000000−2i22i222−2200000−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ700000000000000000000
χ474-4-44004-4000004000000-400000000000000000000002i2−2i200000000
χ484-4-44004-4000004000000-40000000000000000000000−2i22i200000000
χ494-4-44004-400000-4000000400000000000000000000000022−22000000
χ504-4-44004-400000-40000004000000000000000000000000−2222000000
χ5188-8-8000000000042−420000000000000000000000000000000000000
χ5288-8-80000000000−42420000000000000000000000000000000000000
χ538-8-8800-88000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.