Finite Group Databasebeta

← Group #489282

Character table — Group #489282

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11112222222222222244444444444444444444444488888888161616161616161616161616161616163232
order1222224444444488884488888816161616161616161616161616161616222444442444448888881616161644
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-111-11-1-11-1-1-1-11111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1111-1-11-1-1-1-1-1-111-1-1-1-11111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-111-111-1-1-1-1-1-1-1-1-1-111
χ511111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-11-1-11-1-1-1-1-1-1-1-1111111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11-1-1-1-1-1-1111111-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-111111111-1-1
χ91111-1-1-1-11-1-111111111-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111-11-1-1-1-1111-1-11-111-1-111-1-11-1
χ101111-1-1-1-11-1-111111111-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-11-1-1-11-1-1-1111-1111-1-1-1-111-11
χ111111-1-1-1-11-1-111111111-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11-1111-11-1-1-1111-1-1-11111-1-1-11
χ121111-1-1-1-11-1-111111111-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-11-1111111-1-1-1-11-1-111-1-1111-1
χ131111-1-1-1-11-1-111111111-1-1-1-1-111-1-1-1-1-1-1-1-111111111111-11-1-1-1-1111-1-11-1-1-111-1-111-11
χ141111-1-1-1-11-1-111111111-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-11-1-1-11-1-1-1111-11-1-11111-1-11-1
χ151111-1-1-1-11-1-111111111-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11-1111-11-1-1-1111-111-1-1-1-1111-1
χ161111-1-1-1-11-1-111111111-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-11-1111111-1-1-1-1111-1-111-1-1-11
χ1722222222222222-2-2-2-222-2-2-2-2-2-2000000000000000000222002000000-2-20000000000
χ1822222222222222-2-2-2-222-2-2-2-2-2-2000000000000000000-2-2-200-2000000220000000000
χ19222222-2-2222-2-220000-2-20000002222−2−2−2−22222−2−2−2−20022-200-20000000000002−22−200
χ20222222-2-2222-2-220000-2-20000002222−2−2−2−22222−2−2−2−200-2-22002000000000000−22−2200
χ21222222-2-2222-2-220000-2-2000000−2−2−2−22222−2−2−2−222220022-200-2000000000000−22−2200
χ22222222-2-2222-2-220000-2-2000000−2−2−2−22222−2−2−2−2222200-2-220020000000000002−22−200
χ23222222-2-2-2-2-222-22222-2222-2-2-2-2000000000000000022000-2-20200-200000000000000
χ24222222-2-2-2-2-222-22222-2222-2-2-2-20000000000000000-2-2000220-200200000000000000
χ25222222-2-2-2-2-222-2-2-2-2-2-22-2-2222200000000000000000000000002-202-2000000000000
χ26222222-2-2-2-2-222-2-2-2-2-2-22-2-222220000000000000000000000000-220-22000000000000
χ272222-2-2222-2-2-2-220000-220000002222−2−2−2−2−2−2−2−22222002-2-20020000000000002−2−2200
χ282222-2-2222-2-2-2-220000-220000002222−2−2−2−2−2−2−2−2222200-22200-2000000000000−222−200
χ292222-2-2222-2-2-2-220000-22000000−2−2−2−222222222−2−2−2−2002-2-2002000000000000−222−200
χ302222-2-2222-2-2-2-220000-22000000−2−2−2−222222222−2−2−2−200-22200-20000000000002−2−2200
χ312222-2-222-22222-22222-2-2-2-222-2-2000000000000000022000220-200-200000000000000
χ322222-2-222-22222-22222-2-2-2-222-2-20000000000000000-2-2000-2-20200200000000000000
χ332222-2-222-22222-2-2-2-2-2-2-222-2-22200000000000000000000000002-20-22000000000000
χ342222-2-222-22222-2-2-2-2-2-2-222-2-2220000000000000000000000000-2202-2000000000000
χ352222-2-2-2-22-2-2222-2-2-2-22-22222-2-20000000000000000002-2200-2000000-220000000000
χ362222-2-2-2-22-2-2222-2-2-2-22-22222-2-2000000000000000000-22-20020000002-20000000000
χ372-22-2002i−2i02i−2i2-2022-2-200002i−2i0022−2−222−2−2i2i2−i2−i2i2i2−i2−i22-20002i−2i0000000002−2i2−i2000000
χ382-22-2002i−2i02i−2i2-2022-2-200002i−2i0022−2−222−2−2i2i2−i2−i2i2i2−i2−i2-22000−2i2i000000000−22−i2i2000000
χ392-22-2002i−2i02i−2i2-2022-2-200002i−2i00−2−222−2−222−i2−i2i2i2−i2−i2i2i22-20002i−2i000000000−22−i2i2000000
χ402-22-2002i−2i02i−2i2-2022-2-200002i−2i00−2−222−2−222−i2−i2i2i2−i2−i2i2i2-22000−2i2i0000000002−2i2−i2000000
χ412-22-200−2i2i0−2i2i2-2022-2-20000−2i2i0022−2−222−2−2−i2−i2i2i2−i2−i2i2i22-2000−2i2i0000000002−2−i2i2000000
χ422-22-200−2i2i0−2i2i2-2022-2-20000−2i2i0022−2−222−2−2−i2−i2i2i2−i2−i2i2i2-220002i−2i000000000−22i2−i2000000
χ432-22-200−2i2i0−2i2i2-2022-2-20000−2i2i00−2−222−2−222i2i2−i2−i2i2i2−i2−i22-2000−2i2i000000000−22i2−i2000000
χ442-22-200−2i2i0−2i2i2-2022-2-20000−2i2i00−2−222−2−222i2i2−i2−i2i2i2−i2−i2-220002i−2i0000000002−2−i2i2000000
χ4544444444-4-4-4-4-4-400004-4000000000000000000000000000000000000000000000000
χ464444-4-4-4-4-444-4-4-4000044000000000000000000000000000000000000000000000000
χ4744-4-44-40000000022−2222−220022−220000ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ700000000000000000000000000
χ4844-4-44-40000000022−2222−220022−220000−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ700000000000000000000000000
χ4944-4-44-400000000−2222−222200−22220000ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ700000000000000000000000000
χ5044-4-44-400000000−2222−222200−22220000−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ700000000000000000000000000
χ5144-4-4-440000000022−2222−2200−22220000ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ700000000000000000000000000
χ5244-4-4-440000000022−2222−2200−22220000−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ700000000000000000000000000
χ5344-4-4-4400000000−2222−22220022−220000ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ700000000000000000000000000
χ5444-4-4-4400000000−2222−22220022−220000−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ700000000000000000000000000
χ554-44-4004i−4i04i−4i4-40-4-4440000−4i4i00000000000000000000000000000000000000000000
χ564-44-4004i−4i0−4i4i-44000000000000022-2-2-2-222−2i−2i2i2i2i2i−2i−2i00000000000000000000000000
χ574-44-4004i−4i0−4i4i-440000000000000-2-22222-2-22i2i−2i−2i−2i−2i2i2i00000000000000000000000000
χ584-44-400−4i4i04i−4i-44000000000000022-2-2-2-2222i2i−2i−2i−2i−2i2i2i00000000000000000000000000
χ594-44-400−4i4i04i−4i-440000000000000-2-22222-2-2−2i−2i2i2i2i2i−2i−2i00000000000000000000000000
χ604-44-400−4i4i0−4i4i4-40-4-44400004i−4i00000000000000000000000000000000000000000000
χ614-4-44000040000-422−22−222200000022−22000000002ζ3+2ζ5−2ζ3−2ζ5−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ7−2ζ−2ζ72ζ+2ζ700000000000000000000000000
χ624-4-44000040000-422−22−222200000022−2200000000−2ζ3−2ζ52ζ3+2ζ52ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ72ζ+2ζ7−2ζ−2ζ700000000000000000000000000
χ634-4-44000040000-4−222222−22000000−2222000000002ζ+2ζ7−2ζ−2ζ7−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ52ζ3+2ζ5−2ζ3−2ζ500000000000000000000000000
χ644-4-44000040000-4−222222−22000000−222200000000−2ζ−2ζ72ζ+2ζ72ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ5−2ζ3−2ζ52ζ3+2ζ500000000000000000000000000
χ654-4-440000-40000422−22−2222000000−22222ζ−2ζ7−2ζ+2ζ7−2ζ+2ζ72ζ−2ζ72ζ3−2ζ5−2ζ3+2ζ5−2ζ3+2ζ52ζ3−2ζ50000000000000000000000000000000000
χ664-4-440000-40000422−22−2222000000−2222−2ζ+2ζ72ζ−2ζ72ζ−2ζ7−2ζ+2ζ7−2ζ3+2ζ52ζ3−2ζ52ζ3−2ζ5−2ζ3+2ζ50000000000000000000000000000000000
χ674-4-440000-400004−222222−2200000022−222ζ3−2ζ5−2ζ3+2ζ5−2ζ3+2ζ52ζ3−2ζ5−2ζ+2ζ72ζ−2ζ72ζ−2ζ7−2ζ+2ζ70000000000000000000000000000000000
χ684-4-440000-400004−222222−2200000022−22−2ζ3+2ζ52ζ3−2ζ52ζ3−2ζ5−2ζ3+2ζ52ζ−2ζ7−2ζ+2ζ7−2ζ+2ζ72ζ−2ζ70000000000000000000000000000000000

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