Finite Group Databasebeta

← Group #491297

Character table — Group #491297

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111122222222224444444444444444444444448888888888888888816161616323232323232
order1222224444888844444444888888881616161616161616448881616161616161616161616168888222488
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111-1-111-1-11111-1-1-1-111111111-1-11-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111
χ61111111111111111-1-111-1-11111-1-1-1-111111111-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ71111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1111111111111-1-111-1-1
χ81111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-111111111-1-1-1-111-1-111
χ91111-1-111111111-1-1111-111-1-11111111111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-11-11-1-11
χ101111-1-111111111-1-1111-111-1-11111111111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111-11-111-1
χ111111-1-111111111-1-1111-111-1-1111111-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-1111111-1-11-1-111-1
χ121111-1-111111111-1-1111-111-1-1111111-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-11111-1-111-111-1-11
χ131111-1-111111111-1-1-1-11-1-1-1-1-111-1-1-1-11111-1-1-1-111-11111-1-1-1-1-1-1111111-1-1-11-11-11
χ141111-1-111111111-1-1-1-11-1-1-1-1-111-1-1-1-11111-1-1-1-111-11111-1-1-1-1-1-11111-1-1111-11-11-1
χ151111-1-111111111-1-1-1-11-1-1-1-1-111-1-1-1-1-1-1-1-1111111-111-1-1111111-1-1-1-111-1-1-111-11-1
χ161111-1-111111111-1-1-1-11-1-1-1-1-111-1-1-1-1-1-1-1-1111111-111-1-1111111-1-1-1-1-1-1111-1-11-11
χ172222222222-2-2-2-222222222-2-2-2-2-2-2-2-20000000022-2-2-20000000000000000000000
χ182222222222-2-2-2-222-2-222-2-2-2-2-2-2222200000000-2-2-2220000000000000000000000
χ192222222-22-222222-200-2-20022-2-200002222222200-200-2-2-2-2000000000000000000
χ202222222-22-222222-200-2-20022-2-20000-2-2-2-2-2-2-2-200-2002222000000000000000000
χ212222222-22-2-2-2-2-22-200-2-200-2-2220000000000000020000002i2i−2i−2i2i2i−2i−2i0000000000
χ222222222-22-2-2-2-2-22-200-2-200-2-222000000000000002000000−2i−2i2i2i−2i−2i2i2i0000000000
χ23222222-22-220000-2222-2-2-2-20000000022−2−222−2−22-20002−22−22−22−22−22−20000000000
χ24222222-22-220000-2222-2-2-2-200000000−2−222−2−2222-2000−22−22−22−22−22−220000000000
χ25222222-22-220000-22-2-2-2-2220000000022−2−222−2−2-220002−22−2−22−22−22−220000000000
χ26222222-22-220000-22-2-2-2-22200000000−2−222−2−222-22000−22−222−22−22−22−20000000000
χ27222222-2-2-2-20000-2-200220000002i2i−2i−2i22−2−222−2−20002i−2i−22−22i2−i2−i2i2i2−i2−i2i20000000000
χ28222222-2-2-2-20000-2-200220000002i2i−2i−2i−2−222−2−2220002i−2i2−22−2−i2i2i2−i2−i2i2i2−i20000000000
χ29222222-2-2-2-20000-2-20022000000−2i−2i2i2i22−2−222−2−2000−2i2i−22−22−i2i2i2−i2−i2i2i2−i20000000000
χ30222222-2-2-2-20000-2-20022000000−2i−2i2i2i−2−222−2−222000−2i2i2−22−2i2−i2−i2i2i2−i2−i2i20000000000
χ312222-2-22222-2-2-2-2-2-2222-22222-2-2-2-2-2-200000000-2-22220000000000000000000000
χ322222-2-22222-2-2-2-2-2-2-2-22-2-2-222-2-2222200000000222-2-20000000000000000000000
χ332222-2-22-22-22222-2200-2200-2-2-2-200002222-2-2-2-200200-2-222000000000000000000
χ342222-2-22-22-22222-2200-2200-2-2-2-20000-2-2-2-222220020022-2-2000000000000000000
χ352222-2-22-22-2-2-2-2-2-2200-2200222200000000000000-20000002i2i−2i−2i−2i−2i2i2i0000000000
χ362222-2-22-22-2-2-2-2-2-2200-2200222200000000000000-2000000−2i−2i2i2i2i2i−2i−2i0000000000
χ372222-2-2-22-2200002-222-22-2-20000000022−2−2−2−222-220002−2−222−22−2−22−220000000000
χ382222-2-2-22-2200002-222-22-2-200000000−2−22222−2−2-22000−222−2−22−222−22−20000000000
χ392222-2-2-22-2200002-2-2-2-22220000000022−2−2−2−2222-20002−2−22−22−222−22−20000000000
χ402222-2-2-22-2200002-2-2-2-222200000000−2−22222−2−22-2000−222−22−22−2−22−220000000000
χ412222-2-2-2-2-2-2000022002-20000002i2i−2i−2i22−2−2−2−222000−2i2i−222−2i2−i2−i2i2−i2i2i2−i20000000000
χ422222-2-2-2-2-2-2000022002-20000002i2i−2i−2i−2−22222−2−2000−2i2i2−2−22−i2i2i2−i2i2−i2−i2i20000000000
χ432222-2-2-2-2-2-2000022002-2000000−2i−2i2i2i22−2−2−2−2220002i−2i−222−2−i2i2i2−i2i2−i2−i2i20000000000
χ442222-2-2-2-2-2-2000022002-2000000−2i−2i2i2i−2−22222−2−20002i−2i2−2−22i2−i2−i2i2−i2i2i2−i20000000000
χ4544-4-40040-4044-4-4000000000000000000000000000000000000000002i2−2i200000000
χ4644-4-40040-4044-4-400000000000000000000000000000000000000000−2i22i200000000
χ4744-4-40040-40-4-44400000000000000000000000000000000000000000002i2−2i2000000
χ4844-4-40040-40-4-4440000000000000000000000000000000000000000000−2i22i2000000
χ494-44-400040-422−2222−220000004i−4i0022−222i2−2i22i2−2i200000000000000000000000000000000000
χ504-44-400040-422−2222−22000000−4i4i0022−22−2i22i2−2i22i200000000000000000000000000000000000
χ514-44-400040-4−2222−22220000004i−4i00−2222−2i22i2−2i22i200000000000000000000000000000000000
χ524-44-400040-4−2222−2222000000−4i4i00−22222i2−2i22i2−2i200000000000000000000000000000000000
χ534-44-4000-40422−2222−22004-4000000−222222−22−222200000000000000000000000000000000000
χ544-44-4000-40422−2222−2200-44000000−2222−222222−2200000000000000000000000000000000000
χ554-44-4000-404−2222−2222004-400000022−22−222222−2200000000000000000000000000000000000
χ564-44-4000-404−2222−222200-4400000022−2222−22−222200000000000000000000000000000000000
χ574-4-444-4000022−22−22220000000022−220000002ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ52ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ5000000000000000000000000000
χ584-4-444-4000022−22−22220000000022−22000000−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ5−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ5000000000000000000000000000
χ594-4-444-40000−222222−2200000000−22220000002ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ72ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ7000000000000000000000000000
χ604-4-444-40000−222222−2200000000−2222000000−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ7−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ7000000000000000000000000000
χ614-4-44-44000022−22−222200000000−22220000002ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ5000000000000000000000000000
χ624-4-44-44000022−22−222200000000−2222000000−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ5000000000000000000000000000
χ634-4-44-440000−222222−220000000022−220000002ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ7000000000000000000000000000
χ644-4-44-440000−222222−220000000022−22000000−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ7000000000000000000000000000
χ6588-8-800-80800000000000000000000000000000000000000000000000000000000

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