Finite Group Databasebeta

← Group #490075

Character table — Group #490075

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111222222222222444444444444488888888888888888888881616161616161616161616163232
order122244444444888822244448888884488881616161616161616161616161616161622244444888824
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ411111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111-1-111-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1
χ611111111111111111-1-111-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111
χ711111111111111111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-111
χ811111111111111111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1
χ91111-1-1-1-111111111-111-11-1-1-1-1-1-111-1111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11-1
χ101111-1-1-1-111111111-111-11-1-1-1-1-1-111-1111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-11
χ111111-1-1-1-111111111-111-11-1-1-1-1-1-111-1111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-11
χ121111-1-1-1-111111111-111-11-1-1-1-1-1-111-1111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-11-1
χ131111-1-1-1-111111111-1-1-1-1111-1-1-1-1111-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-11
χ141111-1-1-1-111111111-1-1-1-1111-1-1-1-1111-1-1-1111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1111-1
χ151111-1-1-1-111111111-1-1-1-1111-1-1-1-1111-1-1-111-1-1-1-111111111-1-1-1-111-1-1-1-111-1-1111-1
χ161111-1-1-1-111111111-1-1-1-1111-1-1-1-1111-1-1-111-1-1-1-111111111-1-1-1-1-1-11111-1-111-1-1-11
χ17222222222222-2-2-2-22222222-2-2-2-2-2-222-2-2-2-2000000000000000000000000000000
χ18222222222222-2-2-2-22-2-222-2-2-2-2-2-2-2-2-2-22222000000000000000000000000000000
χ192222222222-2-20000-222-2-222000000-2-2000022−2−222−2−222−2−222−2−200000000000000
χ202222222222-2-20000-222-2-222000000-2-20000−2−222−2−222−2−222−2−22200000000000000
χ212222222222-2-20000-2-2-2-2-2-2-200000022000022−2−222−2−2−2−222−2−22200000000000000
χ222222222222-2-20000-2-2-2-2-2-2-2000000220000−2−222−2−22222−2−222−2−200000000000000
χ23222222-2-2-2-2222222200-2-20022-2-2-2-20000000000000000000000002-2002-2000000
χ24222222-2-2-2-2222222200-2-20022-2-2-2-2000000000000000000000000-2200-22000000
χ25222222-2-2-2-222-2-2-2-2200-2-200-2-2222200000000000000000000002-2002-200000000
χ26222222-2-2-2-222-2-2-2-2200-2-200-2-222220000000000000000000000-2200-2200000000
χ272222-2-222-2-2222222-2002-200-2-222-2-20000000000000000000000002-200-22000000
χ282222-2-222-2-2222222-2002-200-2-222-2-2000000000000000000000000-22002-2000000
χ292222-2-222-2-222-2-2-2-2-2002-20022-2-22200000000000000000000002-200-2200000000
χ302222-2-222-2-222-2-2-2-2-2002-20022-2-2220000000000000000000000-22002-200000000
χ312222-2-2-2-22222-2-2-2-2-222-22-2-22222-2-2-22-2-222000000000000000000000000000000
χ322222-2-2-2-22222-2-2-2-2-2-2-2-22222222-2-22-222-2-2000000000000000000000000000000
χ332222-2-2-2-222-2-200002222-2-2-20000002-2000022−2−2−2−22222−2−2−2−22200000000000000
χ342222-2-2-2-222-2-200002222-2-2-20000002-20000−2−22222−2−2−2−22222−2−200000000000000
χ352222-2-2-2-222-2-200002-2-22-222000000-22000022−2−2−2−222−2−22222−2−200000000000000
χ362222-2-2-2-222-2-200002-2-22-222000000-220000−2−22222−2−222−2−2−2−22200000000000000
χ3722-2-22i−2i2i−2i2-2002−22−202-2002i−2ii2−i2i2−i22−2002−2i2−i2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ700000000000000
χ3822-2-22i−2i2i−2i2-2002−22−202-2002i−2ii2−i2i2−i22−2002−2i2−i2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ700000000000000
χ3922-2-22i−2i2i−2i2-2002−22−20-2200−2i2ii2−i2i2−i22−200−22−i2i2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ700000000000000
χ4022-2-22i−2i2i−2i2-2002−22−20-2200−2i2ii2−i2i2−i22−200−22−i2i2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ700000000000000
χ4122-2-22i−2i2i−2i2-200−22−2202-2002i−2i−i2i2−i2i2−2200−22−i2i2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ500000000000000
χ4222-2-22i−2i2i−2i2-200−22−2202-2002i−2i−i2i2−i2i2−2200−22−i2i2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ500000000000000
χ4322-2-22i−2i2i−2i2-200−22−220-2200−2i2i−i2i2−i2i2−22002−2i2−i2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ500000000000000
χ4422-2-22i−2i2i−2i2-200−22−220-2200−2i2i−i2i2−i2i2−22002−2i2−i2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ500000000000000
χ4522-2-2−2i2i−2i2i2-2002−22−202-200−2i2i−i2i2−i2i22−2002−2−i2i2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ700000000000000
χ4622-2-2−2i2i−2i2i2-2002−22−202-200−2i2i−i2i2−i2i22−2002−2−i2i2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ700000000000000
χ4722-2-2−2i2i−2i2i2-2002−22−20-22002i−2i−i2i2−i2i22−200−22i2−i2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ700000000000000
χ4822-2-2−2i2i−2i2i2-2002−22−20-22002i−2i−i2i2−i2i22−200−22i2−i2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ700000000000000
χ4922-2-2−2i2i−2i2i2-200−22−2202-200−2i2ii2−i2i2−i2−2200−22i2−i2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ500000000000000
χ5022-2-2−2i2i−2i2i2-200−22−2202-200−2i2ii2−i2i2−i2−2200−22i2−i2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ500000000000000
χ5122-2-2−2i2i−2i2i2-200−22−220-22002i−2ii2−i2i2−i2−22002−2−i2i2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ500000000000000
χ5222-2-2−2i2i−2i2i2-200−22−220-22002i−2ii2−i2i2−i2−22002−2−i2i2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ500000000000000
χ53444444-4-4-4-4-4-40000-4004400000000000000000000000000000000000000000000
χ544444-4-444-4-4-4-40000400-4400000000000000000000000000000000000000000000
χ5544-4-44i−4i−4i4i-440022−2222−2200000002i2−2i2−2i22i2−2222000000000000000000000000000000000000
χ5644-4-44i−4i−4i4i-4400−2222−22220000000−2i22i22i2−2i222−22000000000000000000000000000000000000
χ5744-4-4−4i4i4i−4i-440022−2222−220000000−2i22i22i2−2i2−2222000000000000000000000000000000000000
χ5844-4-4−4i4i4i−4i-4400−2222−222200000002i2−2i2−2i22i222−22000000000000000000000000000000000000
χ594-44-40000004-444-4-40000000000000000000000000000000000000000000002i2−2i200
χ604-44-40000004-444-4-4000000000000000000000000000000000000000000000−2i22i200
χ614-44-40000004-4-4-444000000000000000000000000000000000000000000022−220000
χ624-44-40000004-4-4-4440000000000000000000000000000000000000000000−22220000
χ638-88-8000000-8800000000000000000000000000000000000000000000000000000
χ648-8-880000000042−42−42420000000000000000000000000000000000000000000000000
χ658-8-8800000000−424242−420000000000000000000000000000000000000000000000000

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