Finite Group Databasebeta

← Group #489875

Character table — Group #489875

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111122222222222244444444444448888888888888888888888888816161616161632323232
order122244444444888824444448888882244448888161616161616161616161616161616164444442488
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ311111111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111-1-11-1-11111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-11-1-111-1-1
χ6111111111111111111-1-11-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-11-1-1-1-111
χ7111111111111111111-1-11-1-1111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111-111-1-111
χ8111111111111111111-1-11-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-111-11111-1-1
χ91111-1-1-1-111111111-1-1111-1-1-1-1-1-11111-1-1-1111-1-11111-1-1-1-11111-1-1-1-1111-1-1-11-11-1
χ101111-1-1-1-111111111-1-1111-1-1-1-1-1-11111-1-1-1111-1-1-1-1-1-11111-1-1-1-11111111-1-1-1-11-11
χ111111-1-1-1-111111111-1-1111-1-1-1-1-1-111-1-111-1111-1-11111-1-1-1-11111-1-1-1-1-1-1-1111-11-11
χ121111-1-1-1-111111111-1-1111-1-1-1-1-1-111-1-111-1111-1-1-1-1-1-11111-1-1-1-11111-1-1-11111-11-1
χ131111-1-1-1-111111111-1-1-1-1111-1-1-1-11111-1-11-1-1-1111111-1-1-1-1-1-1-1-111111-1-1-1111-1-11
χ141111-1-1-1-111111111-1-1-1-1111-1-1-1-11111-1-11-1-1-111-1-1-1-111111111-1-1-1-11-1-1-111-111-1
χ151111-1-1-1-111111111-1-1-1-1111-1-1-1-111-1-1111-1-1-1111111-1-1-1-1-1-1-1-11111-1111-1-1-111-1
χ161111-1-1-1-111111111-1-1-1-1111-1-1-1-111-1-1111-1-1-111-1-1-1-111111111-1-1-1-1-1111-1-11-1-11
χ17222222222222-2-2-2-22222222-2-2-2-2-2-2000022-2-2-2-200000000000000000000000000
χ18222222222222-2-2-2-222-2-22-2-2-2-2-2-2-2-20000-2-2222200000000000000000000000000
χ1922222222-222-20000-2-222-2220000000000-2-2000022−2−222−2−222−2−222−2−20000000000
χ2022222222-222-20000-2-222-2220000000000-2-20000−2−222−2−222−2−222−2−2220000000000
χ2122222222-222-20000-2-2-2-2-2-2-2000000000022000022−2−222−2−2−2−222−2−2220000000000
χ2222222222-222-20000-2-2-2-2-2-2-20000000000220000−2−222−2−22222−2−222−2−20000000000
χ23222222-2-22-2-2222222-200-20022-2-2-2-222220000000000000000000000-200-2000000
χ24222222-2-22-2-2222222-200-20022-2-2-2-2-2-2-2-200000000000000000000002002000000
χ25222222-2-22-2-22-2-2-2-22-200-200-2-222220000000000000000000000000002-202-20000
χ26222222-2-22-2-22-2-2-2-22-200-200-2-22222000000000000000000000000000-220-220000
χ272222-2-2222-2-222222-2200-200-2-222-2-222-2-20000000000000000000000-2002000000
χ282222-2-2222-2-222222-2200-200-2-222-2-2-2-2220000000000000000000000200-2000000
χ292222-2-2222-2-22-2-2-2-2-2200-20022-2-2220000000000000000000000000002-20-220000
χ302222-2-2222-2-22-2-2-2-2-2200-20022-2-222000000000000000000000000000-2202-20000
χ312222-2-2-2-22222-2-2-2-2-2-2222-2-22222-2-20000-22-2-22200000000000000000000000000
χ322222-2-2-2-22222-2-2-2-2-2-2-2-22222222-2-200002-222-2-200000000000000000000000000
χ332222-2-2-2-2-222-200002222-2-2-200000000002-2000022−2−2−2−22222−2−2−2−2220000000000
χ342222-2-2-2-2-222-200002222-2-2-200000000002-20000−2−22222−2−2−2−22222−2−20000000000
χ352222-2-2-2-2-222-2000022-2-2-2220000000000-22000022−2−2−2−222−2−22222−2−20000000000
χ362222-2-2-2-2-222-2000022-2-2-2220000000000-220000−2−22222−2−222−2−2−2−2220000000000
χ372-22-22i−2i2i−2i02-2022−2−2002-202i−2ii2−i2i2−i22−20000002−2i2−i2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ70000000000
χ382-22-22i−2i2i−2i02-2022−2−2002-202i−2ii2−i2i2−i22−20000002−2i2−i2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ70000000000
χ392-22-22i−2i2i−2i02-2022−2−200-220−2i2ii2−i2i2−i22−2000000−22−i2i2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ70000000000
χ402-22-22i−2i2i−2i02-2022−2−200-220−2i2ii2−i2i2−i22−2000000−22−i2i2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ70000000000
χ412-22-22i−2i2i−2i02-20−2−222002-202i−2i−i2i2−i2i2−22000000−22−i2i2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ50000000000
χ422-22-22i−2i2i−2i02-20−2−222002-202i−2i−i2i2−i2i2−22000000−22−i2i2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ50000000000
χ432-22-22i−2i2i−2i02-20−2−22200-220−2i2i−i2i2−i2i2−220000002−2i2−i2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ50000000000
χ442-22-22i−2i2i−2i02-20−2−22200-220−2i2i−i2i2−i2i2−220000002−2i2−i2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ50000000000
χ452-22-2−2i2i−2i2i02-2022−2−2002-20−2i2i−i2i2−i2i22−20000002−2−i2i2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ70000000000
χ462-22-2−2i2i−2i2i02-2022−2−2002-20−2i2i−i2i2−i2i22−20000002−2−i2i2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ70000000000
χ472-22-2−2i2i−2i2i02-2022−2−200-2202i−2i−i2i2−i2i22−2000000−22i2−i2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ70000000000
χ482-22-2−2i2i−2i2i02-2022−2−200-2202i−2i−i2i2−i2i22−2000000−22i2−i2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ70000000000
χ492-22-2−2i2i−2i2i02-20−2−222002-20−2i2ii2−i2i2−i2−22000000−22i2−i2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ50000000000
χ502-22-2−2i2i−2i2i02-20−2−222002-20−2i2ii2−i2i2−i2−22000000−22i2−i2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ50000000000
χ512-22-2−2i2i−2i2i02-20−2−22200-2202i−2ii2−i2i2−i2−220000002−2−i2i2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ50000000000
χ522-22-2−2i2i−2i2i02-20−2−22200-2202i−2ii2−i2i2−i2−220000002−2−i2i2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ50000000000
χ53444444-4-4-4-4-4-40000-4400400000000000000000000000000000000000000000000
χ544444-4-444-4-4-4-400004-400400000000000000000000000000000000000000000000
χ5544-4-40000400-44-44-40000000000000004-400000000000000000000000000000000
χ5644-4-40000400-44-44-4000000000000000-4400000000000000000000000000000000
χ5744-4-40000400-4-44-4400000000000004-40000000000000000000000000000000000
χ5844-4-40000400-4-44-440000000000000-440000000000000000000000000000000000
χ594-44-44i−4i−4i4i0-4402222−22−2200000002i2−2i2−2i22i2−2222000000000000000000000000000000000000
χ604-44-44i−4i−4i4i0-440−22−2222220000000−2i22i22i2−2i222−22000000000000000000000000000000000000
χ614-44-4−4i4i4i−4i0-4402222−22−220000000−2i22i22i2−2i2−2222000000000000000000000000000000000000
χ624-44-4−4i4i4i−4i0-440−22−22222200000002i2−2i2−2i22i222−22000000000000000000000000000000000000
χ6388-8-80000-800800000000000000000000000000000000000000000000000000000
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.