Finite Group Databasebeta

← Group #490084

Character table — Group #490084

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111222222222222444444444444488888888888888888888881616161616161616161616163232
order122222444444888822444448888884488881616161616161616161616161616161644444444888844
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
χ51111111111111111-1-1-1-1111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ61111111111111111-1-1-1-1111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ71111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1
χ81111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111
χ91111-1-11-1-1111111111-1-11-1-1-1-1-1-111-1111-1-11111-1-1-1-11111-1-1-1-11-11-111-1-111-1-11-1
χ101111-1-11-1-1111111111-1-11-1-1-1-1-1-111-1111-1-11111-1-1-1-11111-1-1-1-1-11-11-1-111-1-111-11
χ111111-1-11-1-1111111111-1-11-1-1-1-1-1-111-1111-1-1-1-1-1-11111-1-1-1-111111-11-111-1-1-1-111-11
χ121111-1-11-1-1111111111-1-11-1-1-1-1-1-111-1111-1-1-1-1-1-11111-1-1-1-11111-11-11-1-11111-1-11-1
χ131111-1-11-1-11111111-1-1111-1-1-1-1-1-1111-1-1-1111111-1-1-1-1-1-1-1-111111-11-1-1-111-1-1111-1
χ141111-1-11-1-11111111-1-1111-1-1-1-1-1-1111-1-1-1111111-1-1-1-1-1-1-1-11111-11-1111-1-111-1-1-11
χ151111-1-11-1-11111111-1-1111-1-1-1-1-1-1111-1-1-111-1-1-1-111111111-1-1-1-11-11-1-1-11111-1-1-11
χ161111-1-11-1-11111111-1-1111-1-1-1-1-1-1111-1-1-111-1-1-1-111111111-1-1-1-1-11-1111-1-1-1-1111-1
χ17222222222222-2-2-2-22222222-2-2-2-2-2-222-2-2-2-2000000000000000000000000000000
χ18222222222222-2-2-2-2-2-2-2-2222-2-2-2-2-2-2-2-22222000000000000000000000000000000
χ19222222222-2-2200002222-2-2-2000000-2-2000022−2−222−2−222−2−222−2−200000000000000
χ20222222222-2-2200002222-2-2-2000000-2-20000−2−222−2−222−2−222−2−22200000000000000
χ21222222222-2-220000-2-2-2-2-2-2-200000022000022−2−222−2−2−2−222−2−22200000000000000
χ22222222222-2-220000-2-2-2-2-2-2-2000000220000−2−222−2−22222−2−222−2−200000000000000
χ23222222-2-2-222-222220000-2-2222-2-2-2-200000000000000000000002-2-220000000000
χ24222222-2-2-222-222220000-2-2222-2-2-2-20000000000000000000000-222-20000000000
χ25222222-2-2-222-2-2-2-2-20000-2-22-2-22222000000000000000000000000002-22-2000000
χ26222222-2-2-222-2-2-2-2-20000-2-22-2-2222200000000000000000000000000-22-22000000
χ272222-2-22-2-2222-2-2-2-222-2-22-2-22222-2-2-22-2-222000000000000000000000000000000
χ282222-2-22-2-2222-2-2-2-2-2-2222-2-22222-2-22-222-2-2000000000000000000000000000000
χ292222-2-22-2-2-2-22000022-2-2-2220000002-2000022−2−2−2−22222−2−2−2−22200000000000000
χ302222-2-22-2-2-2-22000022-2-2-2220000002-20000−2−22222−2−2−2−22222−2−200000000000000
χ312222-2-22-2-2-2-220000-2-222-222000000-22000022−2−2−2−222−2−22222−2−200000000000000
χ322222-2-22-2-2-2-220000-2-222-222000000-220000−2−22222−2−222−2−2−2−22200000000000000
χ332222-2-2-22222-222220000-22-2-2-222-2-2000000000000000000000022-2-20000000000
χ342222-2-2-22222-222220000-22-2-2-222-2-20000000000000000000000-2-2220000000000
χ352222-2-2-22222-2-2-2-2-20000-22-222-2-222000000000000000000000000002-2-22000000
χ362222-2-2-22222-2-2-2-2-20000-22-222-2-22200000000000000000000000000-222-2000000
χ3722-2-22-222-200-22−22−22-22-20002−22−22−2002−22−2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ500000000000000
χ3822-2-22-222-200-22−22−22-22-20002−22−22−2002−22−2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ500000000000000
χ3922-2-22-222-200-22−22−2-22-220002−22−22−200−22−22ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ500000000000000
χ4022-2-22-222-200-22−22−2-22-220002−22−22−200−22−22−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ500000000000000
χ4122-2-22-222-200-2−22−222-22-2000−22−22−2200−22−22ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ700000000000000
χ4222-2-22-222-200-2−22−222-22-2000−22−22−2200−22−22−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ700000000000000
χ4322-2-22-222-200-2−22−22-22-22000−22−22−22002−22−2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ700000000000000
χ4422-2-22-222-200-2−22−22-22-22000−22−22−22002−22−2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ700000000000000
χ4522-2-2-222-2200-22−22−22-2-22000−22−222−2002−2−22ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ500000000000000
χ4622-2-2-222-2200-22−22−22-2-22000−22−222−2002−2−22−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ500000000000000
χ4722-2-2-222-2200-22−22−2-222-2000−22−222−200−222−2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ500000000000000
χ4822-2-2-222-2200-22−22−2-222-2000−22−222−200−222−2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ500000000000000
χ4922-2-2-222-2200-2−22−222-2-220002−22−2−2200−222−2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ700000000000000
χ5022-2-2-222-2200-2−22−222-2-220002−22−2−2200−222−2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ700000000000000
χ5122-2-2-222-2200-2−22−22-222-20002−22−2−22002−2−22ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ700000000000000
χ5222-2-2-222-2200-2−22−22-222-20002−22−2−22002−2−22−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ700000000000000
χ53444444-4-4-4-4-4-40000000044-4000000000000000000000000000000000000000000
χ544444-4-4-444-4-4-4000000004-44000000000000000000000000000000000000000000
χ5544-4-44-4-4-4400422−2222−22000000022−22−2222−2222000000000000000000000000000000000000
χ5644-4-44-4-4-44004−2222−22220000000−222222−2222−22000000000000000000000000000000000000
χ5744-4-4-44-44-400422−2222−220000000−222222−22−2222000000000000000000000000000000000000
χ5844-4-4-44-44-4004−2222−2222000000022−22−222222−22000000000000000000000000000000000000
χ594-4-44000004-4044-4-400000000000000000000000000000000000000000002i2−2i20000
χ604-4-44000004-4044-4-40000000000000000000000000000000000000000000−2i22i20000
χ614-4-44000004-40-4-44400000000000000000000000000000000000000000000022−2200
χ624-4-44000004-40-4-444000000000000000000000000000000000000000000000−222200
χ638-88-80000000042−42−42420000000000000000000000000000000000000000000000000
χ648-88-800000000−424242−420000000000000000000000000000000000000000000000000
χ658-8-8800000-88000000000000000000000000000000000000000000000000000000

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