Finite Group Databasebeta

← Group #489402

Character table — Group #489402

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size1111222222444444444444888888888888888888881616161616161616161632323232
order122244444424448888888824441616161616161616161616161616161622244444882488
χ111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-111-1-1-111-1-1
χ61111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111-1-11-1-1-1-111
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-111-1-1-1-1-111
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111-1-11-1-111-1-1
χ91111-1-1-1-111-11-11-1-1-1-111111-1-111111-1-1-1-11111-1-1-1-11-111-11-1-11-11-11-1
χ101111-1-1-1-111-11-11-1-1-1-111111-1-111111-1-1-1-11111-1-1-1-1-11-1-11-1111-1-11-11
χ111111-1-1-1-111-11-11-1-1-1-111111-1-11-1-1-1-11111-1-1-1-111111-111-11-1-11-1-11-11
χ121111-1-1-1-111-11-11-1-1-1-111111-1-11-1-1-1-11111-1-1-1-11111-11-1-11-1111-11-11-1
χ131111-1-1-1-111-11-11-1-1-1-11111-111-11111-1-1-1-1-1-1-1-111111-1-1-111-11-111-1-11
χ141111-1-1-1-111-11-11-1-1-1-11111-111-11111-1-1-1-1-1-1-1-11111-1111-1-11-1-11-111-1
χ151111-1-1-1-111-11-11-1-1-1-11111-111-1-1-1-1-111111111-1-1-1-11-1-1-111-11-11-111-1
χ161111-1-1-1-111-11-11-1-1-1-11111-111-1-1-1-1-111111111-1-1-1-1-1111-1-11-1-111-1-11
χ1722222222222222-2-2-2-2-2-2-2-22222000000000000000000000000-2-20000
χ1822222222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000220000
χ192222222222-2-2-2-222-2-222-2-2000000000000000000002-2000-220000000
χ202222222222-2-2-2-222-2-222-2-200000000000000000000-220002-20000000
χ212222222222-2-2-2-2-2-222-2-22200000000000000000000002-2-2002000000
χ222222222222-2-2-2-2-2-222-2-2220000000000000000000000-22200-2000000
χ23222222-2-2-2-22-2-220000000022-2-222−2−222−2−222−2−222−2−200000000000000
χ24222222-2-2-2-22-2-220000000022-2-2−2−222−2−222−2−222−2−22200000000000000
χ25222222-2-2-2-22-2-2200000000-2-22222−2−222−2−2−2−222−2−22200000000000000
χ26222222-2-2-2-22-2-2200000000-2-222−2−222−2−22222−2−222−2−200000000000000
χ272222-2-222-2-2-2-222000000002-22-222−2−2−2−22222−2−2−2−22200000000000000
χ282222-2-222-2-2-2-222000000002-22-2−2−22222−2−2−2−22222−2−200000000000000
χ292222-2-222-2-2-2-22200000000-22-2222−2−2−2−222−2−22222−2−200000000000000
χ302222-2-222-2-2-2-22200000000-22-22−2−22222−2−222−2−2−2−22200000000000000
χ312222-2-2-2-2222-22-222-2-2-2-22200000000000000000000002-2200-2000000
χ322222-2-2-2-2222-22-222-2-2-2-2220000000000000000000000-22-2002000000
χ332222-2-2-2-2222-22-2-2-22222-2-20000000000000000000022000-2-20000000
χ342222-2-2-2-2222-22-2-2-22222-2-200000000000000000000-2-2000220000000
χ352222-2-2-2-222-22-222222-2-2-2-22-2-22000000000000000000000000-220000
χ362222-2-2-2-222-22-222222-2-2-2-2-222-20000000000000000000000002-20000
χ37444444-4-4-4-4-444-4000000000000000000000000000000000000000000
χ384444-4-444-4-444-4-4000000000000000000000000000000000000000000
χ3944-4-44i−4i000000002i2−2i20022−2200000000000000ζ+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−4i000000002i2−2i20022−2200000000000000−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−4i00000000−2i22i200−222200000000000000ζ−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−4i00000000−2i22i200−222200000000000000−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
χ4344-4-4−4i4i000000002i2−2i200−222200000000000000ζ−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
χ4444-4-4−4i4i000000002i2−2i200−222200000000000000−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
χ4544-4-4−4i4i00000000−2i22i20022−2200000000000000ζ+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
χ4644-4-4−4i4i00000000−2i22i20022−2200000000000000−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
χ474-4-4400004-400000000004-40000000022−2222−220000000000000000000000
χ484-4-4400004-400000000004-400000000−2222−22220000000000000000000000
χ494-4-4400004-40000000000-44000022−2222−2200000000000000000000000000
χ504-4-4400004-40000000000-440000−2222−222200000000000000000000000000
χ514-4-440000-440000004-4000000002-2-222-2-220000000000000000000000
χ524-4-440000-440000004-400000000-222-2-222-20000000000000000000000
χ534-4-440000-44000000-44000000002-2-22-222-20000000000000000000000
χ544-4-440000-44000000-4400000000-222-22-2-220000000000000000000000
χ558-88-8008i−8i000000000000000000000000000000000000000000000000
χ568-88-800−8i8i000000000000000000000000000000000000000000000000

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