Finite Group Databasebeta

← Group #490003

Character table — Group #490003

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111122222222222244444444444448888888888888888888888888816161616161632323232
order122222444444888822444448888882244448888161616161616161616161616161616162224444488
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ311111111111111111111111111111-1-111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111-1-1111-1-111111111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11-1-11-1-111-1-1
χ61111111111111111-1-1111-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-11-1-1-1-111
χ71111111111111111-1-1111-1-1111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111-111-1-111
χ81111111111111111-1-1111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-111-11111-1-1
χ91111-1-11-1-11111111111-1-1-1-1-1-1-1-111111-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1111-1-11-11-1
χ101111-1-11-1-11111111111-1-1-1-1-1-1-1-111111-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1111-1-1-11-11
χ111111-1-11-1-11111111111-1-1-1-1-1-1-1-111-1-11-11111-1-11111-1-1-1-11111-1-1-1-11-1-1-111-11-11
χ121111-1-11-1-11111111111-1-1-1-1-1-1-1-111-1-11-11111-1-1-1-1-1-11111-1-1-1-111111-1-1-1111-11-1
χ131111-1-11-1-11111111-1-11-1-111-1-1-1-11111-11-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-11111-1-11
χ141111-1-11-1-11111111-1-11-1-111-1-1-1-11111-11-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1111-111-1
χ151111-1-11-1-11111111-1-11-1-111-1-1-1-111-1-1-1111-1-1111111-1-1-1-1-1-1-1-11111111-1-1-1-111-1
χ161111-1-11-1-11111111-1-11-1-111-1-1-1-111-1-1-1111-1-111-1-1-1-111111111-1-1-1-1111-1-1-11-1-11
χ17222222222222-2-2-2-22222222-2-2-2-2-2-2002200-2-2-2-200000000000000000000000000
χ18222222222222-2-2-2-2-2-2222-2-2-2-2-2-2-2-200-2-200222200000000000000000000000000
χ19222222222-2-22000022-2-2-22200000000-2-200000022−2−222−2−222−2−222−2−20000000000
χ20222222222-2-22000022-2-2-22200000000-2-2000000−2−222−2−222−2−222−2−2220000000000
χ21222222222-2-220000-2-2-2-2-2-2-2000000002200000022−2−222−2−2−2−222−2−2220000000000
χ22222222222-2-220000-2-2-2-2-2-2-20000000022000000−2−222−2−22222−2−222−2−20000000000
χ23222222-2-2-222-2222200-22-20022-2-2-2-22200-2-200000000000000000000200-2000000
χ24222222-2-2-222-2222200-22-20022-2-2-2-2-2-2002200000000000000000000-2002000000
χ25222222-2-2-222-2-2-2-2-200-22-200-2-222220000000000000000000000000002-202-20000
χ26222222-2-2-222-2-2-2-2-200-22-200-2-22222000000000000000000000000000-220-220000
χ272222-2-22-2-2222-2-2-2-2222-2-2-2-22222-2-2002-200-2-22200000000000000000000000000
χ282222-2-22-2-2222-2-2-2-2-2-22-2-2222222-2-200-220022-2-200000000000000000000000000
χ292222-2-22-2-2-2-22000022-222-2-200000000-2200000022−2−2−2−22222−2−2−2−2220000000000
χ302222-2-22-2-2-2-22000022-222-2-200000000-22000000−2−22222−2−2−2−22222−2−20000000000
χ312222-2-22-2-2-2-220000-2-2-22222000000002-200000022−2−2−2−222−2−22222−2−20000000000
χ322222-2-22-2-2-2-220000-2-2-22222000000002-2000000−2−22222−2−222−2−2−2−2220000000000
χ332222-2-2-22222-2222200-2-2200-2-222-2-222002200000000000000000000-200-2000000
χ342222-2-2-22222-2222200-2-2200-2-222-2-2-2-200-2-2000000000000000000002002000000
χ352222-2-2-22222-2-2-2-2-200-2-220022-2-2220000000000000000000000000002-20-220000
χ362222-2-2-22222-2-2-2-2-200-2-220022-2-222000000000000000000000000000-2202-20000
χ372-2-222-2-22-20022−22−22-20002-22−22−22−20000002−22−2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ50000000000
χ382-2-222-2-22-20022−22−22-20002-22−22−22−20000002−22−2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ50000000000
χ392-2-222-2-22-20022−22−2-22000-222−22−22−2000000−22−22ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ50000000000
χ402-2-222-2-22-20022−22−2-22000-222−22−22−2000000−22−22−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ50000000000
χ412-2-222-2-22-2002−22−222-20002-2−22−22−22000000−22−22ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ70000000000
χ422-2-222-2-22-2002−22−222-20002-2−22−22−22000000−22−22−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ70000000000
χ432-2-222-2-22-2002−22−22-22000-22−22−22−220000002−22−2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ70000000000
χ442-2-222-2-22-2002−22−22-22000-22−22−22−220000002−22−2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ70000000000
χ452-2-22-22-2-220022−22−22-2000-22−22−222−20000002−2−22ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ50000000000
χ462-2-22-22-2-220022−22−22-2000-22−22−222−20000002−2−22−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ50000000000
χ472-2-22-22-2-220022−22−2-220002-2−22−222−2000000−222−2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ50000000000
χ482-2-22-22-2-220022−22−2-220002-2−22−222−2000000−222−2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ50000000000
χ492-2-22-22-2-22002−22−222-2000-222−22−2−22000000−222−2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ70000000000
χ502-2-22-22-2-22002−22−222-2000-222−22−2−22000000−222−2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ70000000000
χ512-2-22-22-2-22002−22−22-220002-22−22−2−220000002−2−22ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ70000000000
χ522-2-22-22-2-22002−22−22-220002-22−22−2−220000002−2−22−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ70000000000
χ53444444-4-4-4-4-4-40000004-4400000000000000000000000000000000000000000000
χ544444-4-4-444-4-4-400000044-400000000000000000000000000000000000000000000
χ5544-4-4000004-4044-4-400000000000004-40000000000000000000000000000000000
χ5644-4-4000004-4044-4-40000000000000-440000000000000000000000000000000000
χ5744-4-4000004-40-4-444000000000000000004i−4i000000000000000000000000000000
χ5844-4-4000004-40-4-44400000000000000000−4i4i000000000000000000000000000000
χ594-4-444-44-4400-422−2222−22000000022−22−2222−2222000000000000000000000000000000000000
χ604-4-444-44-4400-4−2222−22220000000−222222−2222−22000000000000000000000000000000000000
χ614-4-44-4444-400-422−2222−220000000−222222−22−2222000000000000000000000000000000000000
χ624-4-44-4444-400-4−2222−2222000000022−22−222222−22000000000000000000000000000000000000
χ6388-8-800000-88000000000000000000000000000000000000000000000000000000
χ648-88-80000000042−42−42420000000000000000000000000000000000000000000000000
χ658-88-800000000−424242−420000000000000000000000000000000000000000000000000

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