Finite Group Databasebeta

← Group #491237

Character table — Group #491237

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111122222222224444444444444444444444448888888888888888816161616323232323232
order1222444444888822244444888888881616161616161616248881616161616161616161616168888224488
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-11-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111
χ5111111111111111-1-1111-1-11111-1-1-1-111111111-1-11-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111
χ6111111111111111-1-1111-1-11111-1-1-1-111111111-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ7111111111111111-1-1111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1111111111111-111-1-1-1
χ8111111111111111-1-1111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-111111111-1-1-1-11-1-1111
χ91111-1-111111111-1111-1-11111-1-111111111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1-11-111-1
χ101111-1-111111111-1111-1-11111-1-111111111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1111-11-1-11
χ111111-1-111111111-1111-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-111-11
χ121111-1-111111111-1111-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-11111-1-11111-1-11-1
χ131111-1-111111111-1-1-11-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-11111-1-1-1-1-1-1111111-1-11-11-11-1
χ141111-1-111111111-1-1-11-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-11111-1-1-1-1-1-11111-1-111-11-11-11
χ151111-1-111111111-1-1-11-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-111-1-1111111-1-1-1-111-1-111-1-1-11
χ161111-1-111111111-1-1-11-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-111-1-1111111-1-1-1-1-1-111-1-1111-1
χ172222222222-2-2-2-222222222-2-2-2-2-2-2-2-20000000022-2-2-20000000000000000000000
χ182222222222-2-2-2-22-2-2222-2-2-2-2-2-2222200000000-2-2-2220000000000000000000000
χ192222222-22-22222200-2-2-200-2-22200002222222200-200-2-2-2-2000000000000000000
χ202222222-22-22222200-2-2-200-2-2220000-2-2-2-2-2-2-2-200-2002222000000000000000000
χ212222222-22-2-2-2-2-2200-2-2-20022-2-20000000000000020000002i2i−2i−2i2i2i−2i−2i0000000000
χ222222222-22-2-2-2-2-2200-2-2-20022-2-2000000000000002000000−2i−2i2i2i−2i−2i2i2i0000000000
χ23222222-22-220000-222-22-2-2-20000000022−2−222−2−2-220002−22−22−22−22−22−20000000000
χ24222222-22-220000-222-22-2-2-200000000−2−222−2−222-22000−22−22−22−22−22−220000000000
χ25222222-22-220000-2-2-2-22-2220000000022−2−222−2−22-20002−22−2−22−22−22−220000000000
χ26222222-22-220000-2-2-2-22-22200000000−2−222−2−2222-2000−22−222−22−22−22−20000000000
χ27222222-2-2-2-20000-2002-220000002i2i−2i−2i22−2−222−2−20002i−2i−22−22i2−i2−i2i2i2−i2−i2i20000000000
χ28222222-2-2-2-20000-2002-220000002i2i−2i−2i−2−222−2−2220002i−2i2−22−2−i2i2i2−i2−i2i2i2−i20000000000
χ29222222-2-2-2-20000-2002-22000000−2i−2i2i2i22−2−222−2−2000−2i2i−22−22−i2i2i2−i2−i2i2i2−i20000000000
χ30222222-2-2-2-20000-2002-22000000−2i−2i2i2i−2−222−2−222000−2i2i2−22−2i2−i2−i2i2i2−i2−i2i20000000000
χ312222-2-22222-2-2-2-2-2222-2-222-2-222-2-2-2-200000000-2-22220000000000000000000000
χ322222-2-22222-2-2-2-2-2-2-22-2-2-2-2-2-222222200000000222-2-20000000000000000000000
χ332222-2-22-22-22222-200-22200-2-2-2-200002222-2-2-2-200200-2-222000000000000000000
χ342222-2-22-22-22222-200-22200-2-2-2-20000-2-2-2-222220020022-2-2000000000000000000
χ352222-2-22-22-2-2-2-2-2-200-22200222200000000000000-20000002i2i−2i−2i−2i−2i2i2i0000000000
χ362222-2-22-22-2-2-2-2-2-200-22200222200000000000000-2000000−2i−2i2i2i2i2i−2i−2i0000000000
χ372222-2-2-22-220000222-2-22-2-20000000022−2−2−2−2222-20002−2−222−22−2−22−220000000000
χ382222-2-2-22-220000222-2-22-2-200000000−2−22222−2−22-2000−222−2−22−222−22−20000000000
χ392222-2-2-22-2200002-2-2-2-22220000000022−2−2−2−222-220002−2−22−22−222−22−20000000000
χ402222-2-2-22-2200002-2-2-2-222200000000−2−22222−2−2-22000−222−22−22−2−22−220000000000
χ412222-2-2-2-2-2-2000020022-20000002i2i−2i−2i22−2−2−2−222000−2i2i−222−2i2−i2−i2i2−i2i2i2−i20000000000
χ422222-2-2-2-2-2-2000020022-20000002i2i−2i−2i−2−22222−2−2000−2i2i2−2−22−i2i2i2−i2i2−i2−i2i20000000000
χ432222-2-2-2-2-2-2000020022-2000000−2i−2i2i2i22−2−2−2−2220002i−2i−222−2−i2i2i2−i2i2−i2−i2i20000000000
χ442222-2-2-2-2-2-2000020022-2000000−2i−2i2i2i−2−22222−2−20002i−2i2−2−22i2−i2−i2i2−i2i2i2−i20000000000
χ4544-4-44i−4i00002222−22−2200000000002i2−2i200002ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ52ζ3−2ζ5−2ζ3+2ζ52ζ−2ζ7−2ζ+2ζ7000000000000000000000000000
χ4644-4-44i−4i00002222−22−2200000000002i2−2i20000−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ5−2ζ3+2ζ52ζ3−2ζ5−2ζ+2ζ72ζ−2ζ7000000000000000000000000000
χ4744-4-44i−4i0000−22−2222220000000000−2i22i200002ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ72ζ−2ζ7−2ζ+2ζ7−2ζ3+2ζ52ζ3−2ζ5000000000000000000000000000
χ4844-4-44i−4i0000−22−2222220000000000−2i22i20000−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ7−2ζ+2ζ72ζ−2ζ72ζ3−2ζ5−2ζ3+2ζ5000000000000000000000000000
χ4944-4-4−4i4i00002222−22−220000000000−2i22i200002ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ5−2ζ+2ζ72ζ−2ζ7000000000000000000000000000
χ5044-4-4−4i4i00002222−22−220000000000−2i22i20000−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ52ζ−2ζ7−2ζ+2ζ7000000000000000000000000000
χ5144-4-4−4i4i0000−22−22222200000000002i2−2i200002ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ7−2ζ+2ζ72ζ−2ζ72ζ3−2ζ5−2ζ3+2ζ5000000000000000000000000000
χ5244-4-4−4i4i0000−22−22222200000000002i2−2i20000−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ72ζ−2ζ7−2ζ+2ζ7−2ζ3+2ζ52ζ3−2ζ5000000000000000000000000000
χ534-44-400040-422−2222−220000004i−4i22−22002i2−2i22i2−2i200000000000000000000000000000000000
χ544-44-400040-422−2222−22000000−4i4i22−2200−2i22i2−2i22i200000000000000000000000000000000000
χ554-44-400040-4−2222−22220000004i−4i−222200−2i22i2−2i22i200000000000000000000000000000000000
χ564-44-400040-4−2222−2222000000−4i4i−2222002i2−2i22i2−2i200000000000000000000000000000000000
χ574-44-4000-40422−2222−2204-400000−22220022−22−222200000000000000000000000000000000000
χ584-44-4000-40422−2222−220-4400000−222200−222222−2200000000000000000000000000000000000
χ594-44-4000-404−2222−222204-40000022−2200−222222−2200000000000000000000000000000000000
χ604-44-4000-404−2222−22220-440000022−220022−22−222200000000000000000000000000000000000
χ614-4-4400-40404-4-440000000000000000000000000000000000000000022−2200000000
χ624-4-4400-40404-4-4400000000000000000000000000000000000000000−222200000000
χ634-4-4400-4040-444-4000000000000000000000000000000000000000000022−22000000
χ644-4-4400-4040-444-40000000000000000000000000000000000000000000−2222000000
χ658-8-880080-800000000000000000000000000000000000000000000000000000000

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