Finite Group Databasebeta

← Group #489963

Character table — Group #489963

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size1111222222222244444444444488888888888888888881616161616161616161632323232
order12224444448888222444448888224444888881616161616161616222444161616162488
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-111-1-11111111111111-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111-1-111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111-1-1111-1-1111111-1-1111-1-1-1-1111111111-1-11-1-1-1-1-1-1-1-111
χ6111111111111111-1-1111-1-1111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1111111-1-1
χ7111111111111111-1-1111-1-11111-1-1-1-1-1-11-1-1-1-111111111-111-111-1-1-1-111-1-1
χ8111111111111111-1-1111-1-11111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-111-1111111-1-111
χ91111-1-111111111-1111-1-1-1-1-1-11111-11-1-1-111-1-11111-1-1-1-1-1111-1-111-1-11-11-1
χ101111-1-111111111-1111-1-1-1-1-1-11111-11-1-1-111-1-1-1-1-1-11111-1111-1-1-1-111-11-11
χ111111-1-111111111-1111-1-1-1-1-1-111-1-1-1111-111-1-11111-1-1-1-11-1-1-11111-1-1-11-11
χ121111-1-111111111-1111-1-1-1-1-1-111-1-1-1111-111-1-1-1-1-1-111111-1-1-111-1-1111-11-1
χ131111-1-111111111-1-1-11-1-111-1-111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1111-1-111-111-1
χ141111-1-111111111-1-1-11-1-111-1-111111-1-1-1-1-1-111-1-1-1-11111-1-1-111111-1-11-1-11
χ151111-1-111111111-1-1-11-1-111-1-111-1-11-111-1-1-1111111-1-1-1-1111-1-1-1-1-1111-1-11
χ161111-1-111111111-1-1-11-1-111-1-111-1-11-111-1-1-111-1-1-1-11111111-1-1-111-1-1-111-1
χ172222222222-2-2-2-222222222-2-2-2-2002200-2-2-2-2-20000000000000000000000
χ182222222222-2-2-2-22-2-2222-2-2-2-2-2-200-2-200-222220000000000000000000000
χ1922222222-2-22222-200-22-20022-2-2220022-2000000000000-200-20000000000
χ2022222222-2-22222-200-22-20022-2-2-2-200-2-2-200000000000020020000000000
χ2122222222-2-2-2-2-2-2-200-22-200-2-222000000200000000000002-202-200000000
χ2222222222-2-2-2-2-2-2-200-22-200-2-22200000020000000000000-220-2200000000
χ23222222-2-2220000222-2-2-222000000-2-2000000022−2−222−2−20000002−22−20000
χ24222222-2-2220000222-2-2-222000000-2-20000000−2−222−2−222000000−22−220000
χ25222222-2-22200002-2-2-2-2-2-2-200000022000000022−2−222−2−2000000−22−220000
χ26222222-2-22200002-2-2-2-2-2-2-2000000220000000−2−222−2−2220000002−22−20000
χ272222-2-22222-2-2-2-2-2222-2-2-2-222-2-200-22002-2-2220000000000000000000000
χ282222-2-22222-2-2-2-2-2-2-22-2-22222-2-2002-200222-2-20000000000000000000000
χ292222-2-222-2-22222200-2-2200-2-2-2-22200-2-22000000000000200-20000000000
χ302222-2-222-2-22222200-2-2200-2-2-2-2-2-200222000000000000-20020000000000
χ312222-2-222-2-2-2-2-2-2200-2-22002222000000-200000000000002-20-2200000000
χ322222-2-222-2-2-2-2-2-2200-2-22002222000000-20000000000000-2202-200000000
χ332222-2-2-2-2220000-222-222-2-20000002-2000000022−2−2−2−2220000002−2−220000
χ342222-2-2-2-2220000-222-222-2-20000002-20000000−2−22222−2−2000000−222−20000
χ352222-2-2-2-2220000-2-2-2-22222000000-22000000022−2−2−2−222000000−222−20000
χ362222-2-2-2-2220000-2-2-2-22222000000-220000000−2−22222−2−20000002−2−220000
χ37444444-4-4-4-40000-4004-44000000000000000000000000000000000000000
χ384444-4-4-4-4-4-4000040044-4000000000000000000000000000000000000000
χ3944-4-44i−4i000022−2222−22000000002i2−2i20000000000000ζ+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−ζ700000000000000
χ4044-4-44i−4i000022−2222−22000000002i2−2i20000000000000−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+ζ700000000000000
χ4144-4-44i−4i0000−2222−222200000000−2i22i20000000000000ζ−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−ζ700000000000000
χ4244-4-44i−4i0000−2222−222200000000−2i22i20000000000000−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+ζ700000000000000
χ4344-4-4−4i4i000022−2222−2200000000−2i22i20000000000000ζ+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+ζ700000000000000
χ4444-4-4−4i4i000022−2222−2200000000−2i22i20000000000000−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−ζ700000000000000
χ4544-4-4−4i4i0000−2222−2222000000002i2−2i20000000000000ζ−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+ζ700000000000000
χ4644-4-4−4i4i0000−2222−2222000000002i2−2i20000000000000−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−ζ700000000000000
χ474-44-4004-40044-4-400000000000000004i−4i000000000000000000000000000
χ484-44-4004-40044-4-40000000000000000−4i4i000000000000000000000000000
χ494-44-4004-400-4-4440000000000004-40000000000000000000000000000000
χ504-44-4004-400-4-444000000000000-440000000000000000000000000000000
χ514-4-4400004-422−22−22220000004-40022−2200000000022−220000000000000000000000
χ524-4-4400004-422−22−2222000000-440022−22000000000−22220000000000000000000000
χ534-4-4400004-4−222222−220000004-400−2222000000000−22220000000000000000000000
χ544-4-4400004-4−222222−22000000-4400−222200000000022−220000000000000000000000
χ554-4-440000-4422−22−222204-40000000−2222000000022−22000000000000000000000000
χ564-4-440000-4422−22−22220-440000000−22220000000−2222000000000000000000000000
χ574-4-440000-44−222222−2204-4000000022−220000000−2222000000000000000000000000
χ584-4-440000-44−222222−220-44000000022−22000000022−22000000000000000000000000
χ598-88-800-88000000000000000000000000000000000000000000000000000

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