Finite Group Databasebeta

← Group #143916

Character table — Group #143916

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111222222222222222222444444444444444444444488888888888888883232323232323232
order12222244444444888888884488881616161616161616161616161616161644448888161616161616161624448888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11-1-1-111
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1111-1-1
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ922222222222222-2-2-2-2-2-2-2-222-2-2-2-200000000000000002222-2-2-2-20000000000000000
χ1022222222222222-2-2-2-2-2-2-2-222-2-2-2-20000000000000000-2-2-2-222220000000000000000
χ1122222222-2-222-2-222222222-2-2-2-2-2-20000000000000000000000002222-2-2-2-200000000
χ1222222222-2-222-2-222222222-2-2-2-2-2-2000000000000000000000000-2-2-2-2222200000000
χ1322222222-2-222-2-2-2-2-2-2-2-2-2-2-2-222222i2i2i2i2i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i000000000000000000000000
χ1422222222-2-222-2-2-2-2-2-2-2-2-2-2-2-22222−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i2i2i2i2i000000000000000000000000
χ15222222-2-222-2-22200000000-2-200002222−2−2−2−22222−2−2−2−222-2-2000022−2−222−2−200000000
χ16222222-2-222-2-22200000000-2-200002222−2−2−2−22222−2−2−2−2-2-2220000−2−222−2−22200000000
χ17222222-2-222-2-22200000000-2-20000−2−2−2−22222−2−2−2−2222222-2-20000−2−222−2−22200000000
χ18222222-2-222-2-22200000000-2-20000−2−2−2−22222−2−2−2−22222-2-222000022−2−222−2−200000000
χ19222222-2-2-2-2-2-2-2-200000000220000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i200002i2i−2i−2i22−2−2−2−22200000000
χ20222222-2-2-2-2-2-2-2-200000000220000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i20000−2i−2i2i2i−2−22222−2−200000000
χ21222222-2-2-2-2-2-2-2-200000000220000−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i200002i2i−2i−2i−2−22222−2−200000000
χ22222222-2-2-2-2-2-2-2-200000000220000−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i20000−2i−2i2i2i22−2−2−2−22200000000
χ232222-2-2-2-22-2222-222-2-2-2-2222-222-2-200000000000000000000000000000000020-20000
χ242222-2-2-2-22-2222-222-2-2-2-2222-222-2-2000000000000000000000000000000000-2020000
χ252222-2-2-2-22-2222-2-2-22222-2-22-2-2-2220000000000000000000000000000000000002-200
χ262222-2-2-2-22-2222-2-2-22222-2-22-2-2-222000000000000000000000000000000000000-2200
χ272222-2-2-2-2-2222-2222-2-2-2-222-22-2-2220000000000000000000000000000000020-200000
χ282222-2-2-2-2-2222-2222-2-2-2-222-22-2-22200000000000000000000000000000000-20200000
χ292222-2-2-2-2-2222-22-2-22222-2-2-2222-2-2000000000000000000000000000000000000002-2
χ302222-2-2-2-2-2222-22-2-22222-2-2-2222-2-200000000000000000000000000000000000000-22
χ312-22-22-2002-200-222−222−2−22−2002−22−2ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5002-22−22−2ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ700000000
χ322-22-22-2002-200-222−222−2−22−2002−22−2ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ500-22−22−22−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ700000000
χ332-22-22-2002-200-222−222−2−22−2002−22−2−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5002-22−22−2−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ700000000
χ342-22-22-2002-200-222−222−2−22−2002−22−2−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ500-22−22−22ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ700000000
χ352-22-22-2002-200-22−22−2−222−2200−22−22ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7002-2−22−22−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ500000000
χ362-22-22-2002-200-22−22−2−222−2200−22−22ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ700-222−22−2ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ500000000
χ372-22-22-2002-200-22−22−2−222−2200−22−22−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7002-2−22−22ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ500000000
χ382-22-22-2002-200-22−22−2−222−2200−22−22−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ700-222−22−2−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ500000000
χ392-22-22-200-22002-22−222−2−22−200−22−22ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ52i−2i00i2−i2−i2i2−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ700000000
χ402-22-22-200-22002-22−222−2−22−200−22−22ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5−2i2i00−i2i2i2−i2ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ700000000
χ412-22-22-200-22002-22−222−2−22−200−22−22−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ52i−2i00i2−i2−i2i2ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ700000000
χ422-22-22-200-22002-22−222−2−22−200−22−22−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5−2i2i00−i2i2i2−i2−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ700000000
χ432-22-22-200-22002-2−22−2−222−22002−22−2ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ72i−2i00−i2i2i2−i2−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ500000000
χ442-22-22-200-22002-2−22−2−222−22002−22−2ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−2i2i00i2−i2−i2i2ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ500000000
χ452-22-22-200-22002-2−22−2−222−22002−22−2−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ72i−2i00−i2i2i2−i2ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ500000000
χ462-22-22-200-22002-2−22−2−222−22002−22−2−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7−2i2i00i2−i2−i2i2−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ500000000
χ474444-4-4444-4-4-44-400000000-4400000000000000000000000000000000000000000000
χ484444-4-444-44-4-4-44000000004-400000000000000000000000000000000000000000000
χ4944-4-40000004-400440000-4-40000002-22-22-22-22-22-22-22-2000000000000000000000000
χ5044-4-40000004-400440000-4-4000000-22-22-22-22-22-22-22-22000000000000000000000000
χ5144-4-40000004-400-4-40000440000002i−2i2i−2i2i−2i2i−2i−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ5244-4-40000004-400-4-4000044000000−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ5344-4-4000000-4400004i−4i4i−4i000000002ζ2−2ζ22ζ2−2ζ2−2ζ22ζ2−2ζ22ζ2−2ζ62ζ6−2ζ62ζ62ζ6−2ζ62ζ6−2ζ6000000000000000000000000
χ5444-4-4000000-4400004i−4i4i−4i00000000−2ζ22ζ2−2ζ22ζ22ζ2−2ζ22ζ2−2ζ22ζ6−2ζ62ζ6−2ζ6−2ζ62ζ6−2ζ62ζ6000000000000000000000000
χ5544-4-4000000-440000−4i4i−4i4i000000002ζ6−2ζ62ζ6−2ζ6−2ζ62ζ6−2ζ62ζ6−2ζ22ζ2−2ζ22ζ22ζ2−2ζ22ζ2−2ζ2000000000000000000000000
χ5644-4-4000000-440000−4i4i−4i4i00000000−2ζ62ζ6−2ζ62ζ62ζ6−2ζ62ζ6−2ζ62ζ2−2ζ22ζ2−2ζ2−2ζ22ζ2−2ζ22ζ2000000000000000000000000
χ574-44-4-44004400-4-422−22−22−22222222−220022−22−22220000000000000000000000000000000000000000
χ584-44-4-44004400-4-4−22222222−22−22−222200−222222−220000000000000000000000000000000000000000
χ594-44-4-4400-4-4004422−22−22−22222222−2200−222222−220000000000000000000000000000000000000000
χ604-44-4-4400-4-40044−22222222−22−22−22220022−22−22220000000000000000000000000000000000000000
χ614-4-44004i−4i00000022−222i2−2i2−2i22i2−22220000002ζ−2ζ−2ζ2ζ2ζ5−2ζ5−2ζ52ζ52ζ7−2ζ7−2ζ72ζ72ζ3−2ζ3−2ζ32ζ3000000000000000000000000
χ624-4-44004i−4i00000022−222i2−2i2−2i22i2−2222000000−2ζ2ζ2ζ−2ζ−2ζ52ζ52ζ5−2ζ5−2ζ72ζ72ζ7−2ζ7−2ζ32ζ32ζ3−2ζ3000000000000000000000000
χ634-4-44004i−4i000000−2222−2i22i22i2−2i222−220000002ζ5−2ζ5−2ζ52ζ5−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ3−2ζ72ζ72ζ7−2ζ7000000000000000000000000
χ644-4-44004i−4i000000−2222−2i22i22i2−2i222−22000000−2ζ52ζ52ζ5−2ζ52ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ32ζ7−2ζ7−2ζ72ζ7000000000000000000000000
χ654-4-4400−4i4i00000022−22−2i22i22i2−2i2−22220000002ζ7−2ζ7−2ζ72ζ72ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ2ζ5−2ζ5−2ζ52ζ5000000000000000000000000
χ664-4-4400−4i4i00000022−22−2i22i22i2−2i2−2222000000−2ζ72ζ72ζ7−2ζ7−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ−2ζ52ζ52ζ5−2ζ5000000000000000000000000
χ674-4-4400−4i4i000000−22222i2−2i2−2i22i222−220000002ζ3−2ζ3−2ζ32ζ3−2ζ72ζ72ζ7−2ζ72ζ5−2ζ5−2ζ52ζ5−2ζ2ζ2ζ−2ζ000000000000000000000000
χ684-4-4400−4i4i000000−22222i2−2i2−2i22i222−22000000−2ζ32ζ32ζ3−2ζ32ζ7−2ζ7−2ζ72ζ7−2ζ52ζ52ζ5−2ζ52ζ−2ζ−2ζ2ζ000000000000000000000000

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