Finite Group Databasebeta

← Group #489137

Character table — Group #489137

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11112222222222222244444444444444444444444488888888161616161616161616161616161616163232
order1222224444444488884488888816161616161616161616161616161616222244444444448888881616161644
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111
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
χ611111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1
χ91111-1-1-1-11-1-111111111-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-11-11-1111-1-1-11-111-1-111-1-11-1
χ101111-1-1-1-11-1-111111111-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-11-11-1-11-111-1111-1-1-1-111-11
χ111111-1-1-1-11-1-111111111-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1111-11-1-1-1-11111-1-1-11111-1-1-11
χ121111-1-1-1-11-1-111111111-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-11-1111-11-1-1-11-1-111-1-1111-1
χ131111-1-1-1-11-1-111111111-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-11-11-1111-1-1-11-1-1-111-1-111-11
χ141111-1-1-1-11-1-111111111-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-11-11-1-11-111-11-1-11111-1-11-1
χ151111-1-1-1-11-1-111111111-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1111-11-1-1-1-11111-111-1-1-1-1111-1
χ161111-1-1-1-11-1-111111111-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-11-1111-11-1-1-1111-1-111-1-1-11
χ1722222222222222-2-2-2-222-2-2-2-2-2-2000000000000000000002222000000-2-20000000000
χ1822222222222222-2-2-2-222-2-2-2-2-2-200000000000000000000-2-2-2-2000000220000000000
χ1922222222-2-2-222-22222-2-222-2-2-2-200000000000000002222000000-2-200000000000000
χ2022222222-2-2-222-22222-2-222-2-2-2-20000000000000000-2-2-2-20000002200000000000000
χ2122222222-2-2-222-2-2-2-2-2-2-2-2-222220000000000000000000000002-2002-2000000000000
χ2222222222-2-2-222-2-2-2-2-2-2-2-2-22222000000000000000000000000-2200-22000000000000
χ23222222-2-2222-2-220000-2-20000002222−2−2−2−22222−2−2−2−200002-2-220000000000002−22−200
χ24222222-2-2222-2-220000-2-20000002222−2−2−2−22222−2−2−2−20000-222-2000000000000−22−2200
χ25222222-2-2222-2-220000-2-2000000−2−2−2−22222−2−2−2−2222200002-2-22000000000000−22−2200
χ26222222-2-2222-2-220000-2-2000000−2−2−2−22222−2−2−2−222220000-222-20000000000002−22−200
χ272222-2-2222-2-2-2-220000-220000002222−2−2−2−2−2−2−2−22222000022-2-20000000000002−2−2200
χ282222-2-2222-2-2-2-220000-220000002222−2−2−2−2−2−2−2−222220000-2-222000000000000−222−200
χ292222-2-2222-2-2-2-220000-22000000−2−2−2−222222222−2−2−2−2000022-2-2000000000000−222−200
χ302222-2-2222-2-2-2-220000-22000000−2−2−2−222222222−2−2−2−20000-2-2220000000000002−2−2200
χ312222-2-2-2-22-2-2222-2-2-2-22-22222-2-2000000000000000000002-22-2000000-220000000000
χ322222-2-2-2-22-2-2222-2-2-2-22-22222-2-200000000000000000000-22-220000002-20000000000
χ332222-2-2-2-2-22222-22222-22-2-222-2-2000000000000000022-2-2000000-2200000000000000
χ342222-2-2-2-2-22222-22222-22-2-222-2-20000000000000000-2-2220000002-200000000000000
χ352222-2-2-2-2-22222-2-2-2-2-2-2222-2-2220000000000000000000000002-200-22000000000000
χ362222-2-2-2-2-22222-2-2-2-2-2-2222-2-222000000000000000000000000-22002-2000000000000
χ3722-2-22-22-20002-2022-2-2002-2000022−2−222−2−222−2−222−2−22-22-20000000000002−22−2000000
χ3822-2-22-22-20002-2022-2-2002-2000022−2−222−2−222−2−222−2−2-22-22000000000000−22−22000000
χ3922-2-22-22-20002-2022-2-2002-20000−2−222−2−222−2−222−2−2222-22-2000000000000−22−22000000
χ4022-2-22-22-20002-2022-2-2002-20000−2−222−2−222−2−222−2−222-22-220000000000002−22−2000000
χ4122-2-2-22-220002-2022-2-200-22000022−2−222−2−2−2−222−2−2222-2-220000000000002−2−22000000
χ4222-2-2-22-220002-2022-2-200-22000022−2−222−2−2−2−222−2−222-222-2000000000000−222−2000000
χ4322-2-2-22-220002-2022-2-200-220000−2−222−2−22222−2−222−2−22-2-22000000000000−222−2000000
χ4422-2-2-22-220002-2022-2-200-220000−2−222−2−22222−2−222−2−2-222-20000000000002−2−22000000
χ45444444-4-4-4-4-4-4-4-4000044000000000000000000000000000000000000000000000000
χ464444-4-444-444-4-4-400004-4000000000000000000000000000000000000000000000000
χ4744-4-44-44-40004-40-4-44400-440000000000000000000000000000000000000000000000
χ4844-4-44-4-44000-44000000000000022-2-2-2-22222-2-2-2-22200000000000000000000000000
χ4944-4-44-4-44000-440000000000000-2-22222-2-2-2-22222-2-200000000000000000000000000
χ5044-4-4-444-4000-44000000000000022-2-2-2-222-2-22222-2-200000000000000000000000000
χ5144-4-4-444-4000-440000000000000-2-22222-2-222-2-2-2-22200000000000000000000000000
χ5244-4-4-44-440004-40-4-444004-40000000000000000000000000000000000000000000000
χ534-44-4000004i−4i00022−2222−2200002i2−2i200ζ+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
χ544-44-4000004i−4i00022−2222−2200002i2−2i200−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
χ554-44-4000004i−4i000−2222−22220000−2i22i200ζ−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
χ564-44-4000004i−4i000−2222−22220000−2i22i200−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
χ574-44-400000−4i4i00022−2222−220000−2i22i200ζ+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
χ584-44-400000−4i4i00022−2222−220000−2i22i200−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
χ594-44-400000−4i4i000−2222−222200002i2−2i200ζ−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
χ604-44-400000−4i4i000−2222−222200002i2−2i200−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
χ614-4-44000040000-422−22−222200000022−22000000002ζ3+2ζ5−2ζ3−2ζ5−2ζ3−2ζ52ζ3+2ζ5−2ζ−2ζ72ζ+2ζ72ζ+2ζ7−2ζ−2ζ700000000000000000000000000
χ624-4-44000040000-422−22−222200000022−2200000000−2ζ3−2ζ52ζ3+2ζ52ζ3+2ζ5−2ζ3−2ζ52ζ+2ζ7−2ζ−2ζ7−2ζ−2ζ72ζ+2ζ700000000000000000000000000
χ634-4-44000040000-4−222222−22000000−2222000000002ζ+2ζ7−2ζ−2ζ7−2ζ−2ζ72ζ+2ζ72ζ3+2ζ5−2ζ3−2ζ5−2ζ3−2ζ52ζ3+2ζ500000000000000000000000000
χ644-4-44000040000-4−222222−22000000−222200000000−2ζ−2ζ72ζ+2ζ72ζ+2ζ7−2ζ−2ζ7−2ζ3−2ζ52ζ3+2ζ52ζ3+2ζ5−2ζ3−2ζ500000000000000000000000000
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.