Finite Group Databasebeta

← Group #489694

Character table — Group #489694

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111122222222222244444444444448888888888888888888888888816161616161632323232
order122222444444888844444448888882222228888161616161616161616161616161616164444442488
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ31111111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111-1-1-1-1111111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1
χ61111111111111111111-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111
χ71111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-111
χ81111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-1
χ91111-1-11-1-111111111-1-111-1-1-1-1-1-1111-111-1-111-1-11111-1-1-1-11111-1-1-1-11-111-1-11-11-1
χ101111-1-11-1-111111111-1-111-1-1-1-1-1-1111-111-1-111-1-1-1-1-1-11111-1-1-1-111111-111-1-1-11-11
χ111111-1-11-1-111111111-1-111-1-1-1-1-1-1111-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-11-1-111-11-11
χ121111-1-11-1-111111111-1-111-1-1-1-1-1-1111-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-11-1-1111-11-1
χ131111-1-11-1-111111111-1-1-1-111-1-1-1-111-1111-1-1-1-1111111-1-1-1-1-1-1-1-111111-1-1-1111-1-11
χ141111-1-11-1-111111111-1-1-1-111-1-1-1-111-1111-1-1-1-111-1-1-1-111111111-1-1-1-11-1-1-111-111-1
χ151111-1-11-1-111111111-1-1-1-111-1-1-1-111-11-1-111-1-1111111-1-1-1-1-1-1-1-11111-1111-1-1-111-1
χ161111-1-11-1-111111111-1-1-1-111-1-1-1-111-11-1-111-1-111-1-1-1-111111111-1-1-1-1-1111-1-11-1-11
χ17222222222222-2-2-2-22222222-2-2-2-2-2-2220000-2-2-2-200000000000000000000000000
χ18222222222222-2-2-2-2222-2-2-2-2-2-2-2-2-2-2-2-20000222200000000000000000000000000
χ19222222222-2-220000-2-2-22222000000-2-20000000022−2−222−2−222−2−222−2−20000000000
χ20222222222-2-220000-2-2-22222000000-2-200000000−2−222−2−222−2−222−2−2220000000000
χ21222222222-2-220000-2-2-2-2-2-2-2000000220000000022−2−222−2−2−2−222−2−2220000000000
χ22222222222-2-220000-2-2-2-2-2-2-20000002200000000−2−222−2−22222−2−222−2−20000000000
χ23222222-2-2-222-22222-2-220000-2-222-2-200222200000000000000000000-2-200000000
χ24222222-2-2-222-22222-2-220000-2-222-2-200-2-2-2-2000000000000000000002200000000
χ25222222-2-2-222-2-2-2-2-2-2-22000022-2-22200000000000000000000000000002-22-20000
χ26222222-2-2-222-2-2-2-2-2-2-22000022-2-2220000000000000000000000000000-22-220000
χ272222-2-22-2-2222-2-2-2-22-2-222-2-22222-2-22-20000-2-22200000000000000000000000000
χ282222-2-22-2-2222-2-2-2-22-2-2-2-2222222-2-2-22000022-2-200000000000000000000000000
χ292222-2-22-2-2-2-220000-22222-2-2000000-220000000022−2−2−2−22222−2−2−2−2220000000000
χ302222-2-22-2-2-2-220000-22222-2-2000000-2200000000−2−22222−2−2−2−22222−2−20000000000
χ312222-2-22-2-2-2-220000-222-2-2220000002-20000000022−2−2−2−222−2−22222−2−20000000000
χ322222-2-22-2-2-2-220000-222-2-2220000002-200000000−2−22222−2−222−2−2−2−2220000000000
χ332222-2-2-22222-22222-22-2000022-2-2-2-20022-2-200000000000000000000-2200000000
χ342222-2-2-22222-22222-22-2000022-2-2-2-200-2-222000000000000000000002-200000000
χ352222-2-2-22222-2-2-2-2-2-22-20000-2-2222200000000000000000000000000002-2-220000
χ362222-2-2-22222-2-2-2-2-2-22-20000-2-222220000000000000000000000000000-222-20000
χ372-22-22-222-200-222−2−20002i−2i2i−2i2−22−22−2000000i2−i2i2−i2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ70000000000
χ382-22-22-222-200-222−2−20002i−2i2i−2i2−22−22−2000000i2−i2i2−i2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ70000000000
χ392-22-22-222-200-222−2−2000−2i2i−2i2i2−22−22−2000000−i2i2−i2i2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ70000000000
χ402-22-22-222-200-222−2−2000−2i2i−2i2i2−22−22−2000000−i2i2−i2i2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ70000000000
χ412-22-22-222-200-2−2−2220002i−2i2i−2i−22−22−22000000−i2i2−i2i2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ50000000000
χ422-22-22-222-200-2−2−2220002i−2i2i−2i−22−22−22000000−i2i2−i2i2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ50000000000
χ432-22-22-222-200-2−2−222000−2i2i−2i2i−22−22−22000000i2−i2i2−i2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ50000000000
χ442-22-22-222-200-2−2−222000−2i2i−2i2i−22−22−22000000i2−i2i2−i2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ50000000000
χ452-22-2-222-2200-222−2−20002i−2i−2i2i−22−222−2000000i2−i2−i2i2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ70000000000
χ462-22-2-222-2200-222−2−20002i−2i−2i2i−22−222−2000000i2−i2−i2i2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ70000000000
χ472-22-2-222-2200-222−2−2000−2i2i2i−2i−22−222−2000000−i2i2i2−i2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ70000000000
χ482-22-2-222-2200-222−2−2000−2i2i2i−2i−22−222−2000000−i2i2i2−i2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ70000000000
χ492-22-2-222-2200-2−2−2220002i−2i−2i2i2−22−2−22000000−i2i2i2−i2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ50000000000
χ502-22-2-222-2200-2−2−2220002i−2i−2i2i2−22−2−22000000−i2i2i2−i2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ50000000000
χ512-22-2-222-2200-2−2−222000−2i2i2i−2i2−22−2−22000000i2−i2−i2i2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ50000000000
χ522-22-2-222-2200-2−2−222000−2i2i2i−2i2−22−2−22000000i2−i2−i2i2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ50000000000
χ53444444-4-4-4-4-4-4000044-40000000000000000000000000000000000000000000000
χ544444-4-4-444-4-4-400004-440000000000000000000000000000000000000000000000
χ554-44-44-4-4-440042222−22−220000000−222222−22−2222000000000000000000000000000000000000
χ564-44-44-4-4-44004−22−222222000000022−22−222222−22000000000000000000000000000000000000
χ574-44-4-44-44-40042222−22−22000000022−22−2222−2222000000000000000000000000000000000000
χ584-44-4-44-44-4004−22−2222220000000−222222−2222−22000000000000000000000000000000000000
χ594-4-4400000-4404-44-4000000000000000004-4000000000000000000000000000000
χ604-4-4400000-4404-44-400000000000000000-44000000000000000000000000000000
χ614-4-4400000-440-44-440000000000000004-400000000000000000000000000000000
χ624-4-4400000-440-44-44000000000000000-4400000000000000000000000000000000
χ6388-8-80000000042−42−42420000000000000000000000000000000000000000000000000
χ6488-8-800000000−424242−420000000000000000000000000000000000000000000000000
χ658-8-88000008-8000000000000000000000000000000000000000000000000000000

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