Finite Group Databasebeta

← Group #507126

Character table — Group #507126

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11112222222222222222222222444444444444444444448888888888888888161616161616161632323232
order124422244444448888161616161616161644888888161616161616161616161616244488881616161616161616244488884488
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11-11-1
χ6111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-11-11
χ7111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-11-11
χ8111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111-11-1
χ91111111-1-1-1-1111111111111111-1-11-1-1-1-111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1111111-1-111-1-1-111-1
χ101111111-1-1-1-1111111111111111-1-11-1-1-1-111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-111-1-1111-1-11
χ111111111-1-1-1-1111111111111111-1-11-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-111-1-11-1-11
χ121111111-1-1-1-1111111111111111-1-11-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111-1-111-111-1
χ131111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-11111111111-1-1-1-1111111-1-1-1-111-1-1-1-111-1-111
χ141111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-11111-1-111-1-1
χ151111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-111111111-1-11111-1-1-1-1-1-1111111-1-1-1-11111-1-1
χ161111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-111111111-1-11111-1-1-1-1-1-11111-1-11111-1-1-1-111
χ1722222222222222-2-2-2-20000000022-2-2-2-2-2-200000000000022-2-222-2-200000000000000000000
χ1822222222222222-2-2-2-20000000022-2-2-2-2-2-2000000000000-2-222-2-22200000000000000000000
χ192222222-2-2-2-2222-2-2-2-200000000-2-2-22222-20000000000002222-2-2-2-200000000000000000000
χ202222222-2-2-2-2222-2-2-2-200000000-2-2-22222-2000000000000-2-2-2-2222200000000000000000000
χ2122222-2-200002-2-222222222222200-20000-2-2-2-2-2000000000000000000000000002i−2i002i−2i0000
χ2222222-2-200002-2-222222222222200-20000-2-2-2-2-200000000000000000000000000−2i2i00−2i2i0000
χ2322222-2-200002-2-22222-2-2-2-2-2-2-2-200-20000-22222000000000000000000000000002i−2i00−2i2i0000
χ2422222-2-200002-2-22222-2-2-2-2-2-2-2-200-20000-2222200000000000000000000000000−2i2i002i−2i0000
χ252222-22-22222-22-200002222−2−2−2−2-2-200000022−2−22222−2−2−2−2002i−2i002i−2ii2i2−i2−i2i2i2−i2−i2000000000000
χ262222-22-22222-22-200002222−2−2−2−2-2-200000022−2−22222−2−2−2−200−2i2i00−2i2i−i2−i2i2i2−i2−i2i2i2000000000000
χ272222-22-22222-22-20000−2−2−2−22222-2-2000000−2−222−2−2−2−22222002i−2i002i−2i−i2−i2i2i2−i2−i2i2i2000000000000
χ282222-22-22222-22-20000−2−2−2−22222-2-2000000−2−222−2−2−2−2222200−2i2i00−2i2ii2i2−i2−i2i2i2−i2−i2000000000000
χ292222-22-2-2-2-2-2-22-200002222−2−2−2−22200000022−2−2−2−2−2−22222002i−2i00−2i2ii2i2−i2−i2−i2−i2i2i2000000000000
χ302222-22-2-2-2-2-2-22-200002222−2−2−2−22200000022−2−2−2−2−2−2222200−2i2i002i−2i−i2−i2i2i2i2i2−i2−i2000000000000
χ312222-22-2-2-2-2-2-22-20000−2−2−2−2222222000000−2−2222222−2−2−2−2002i−2i00−2i2i−i2−i2i2i2i2i2−i2−i2000000000000
χ322222-22-2-2-2-2-2-22-20000−2−2−2−2222222000000−2−2222222−2−2−2−200−2i2i002i−2ii2i2−i2−i2−i2−i2i2i2000000000000
χ3322-2-22-2-22i2i−2i−2i-2220000i2i2−i2−i2i2i2−i2−i22i−2i000000i2−i2i2−i222−2−222−2−22-2002i−2i002−22−2i2−i2i2−i2000000000000
χ3422-2-22-2-22i2i−2i−2i-2220000i2i2−i2−i2i2i2−i2−i22i−2i000000i2−i2i2−i222−2−222−2−2-2200−2i2i00−22−22−i2i2−i2i2000000000000
χ3522-2-22-2-22i2i−2i−2i-2220000−i2−i2i2i2−i2−i2i2i22i−2i000000−i2i2−i2i2−2−222−2−2222-2002i−2i00−22−22−i2i2−i2i2000000000000
χ3622-2-22-2-22i2i−2i−2i-2220000−i2−i2i2i2−i2−i2i2i22i−2i000000−i2i2−i2i2−2−222−2−222-2200−2i2i002−22−2i2−i2i2−i2000000000000
χ3722-2-22-2-2−2i−2i2i2i-2220000i2i2−i2−i2i2i2−i2−i2−2i2i000000i2−i2i2−i2−2−222−2−2222-200−2i2i00−22−22i2−i2i2−i2000000000000
χ3822-2-22-2-2−2i−2i2i2i-2220000i2i2−i2−i2i2i2−i2−i2−2i2i000000i2−i2i2−i2−2−222−2−222-22002i−2i002−22−2−i2i2−i2i2000000000000
χ3922-2-22-2-2−2i−2i2i2i-2220000−i2−i2i2i2−i2−i2i2i2−2i2i000000−i2i2−i2i222−2−222−2−22-200−2i2i002−22−2−i2i2−i2i2000000000000
χ4022-2-22-2-2−2i−2i2i2i-2220000−i2−i2i2i2−i2−i2i2i2−2i2i000000−i2i2−i2i222−2−222−2−2-22002i−2i00−22−22i2−i2i2−i2000000000000
χ4122-2-2-22-200002-2222-2-22i2i−2i−2i−2i−2i2i2i0020000-2−2i2i2i−2i0000000000000000000000002-2002i−2i000000
χ4222-2-2-22-200002-2222-2-22i2i−2i−2i−2i−2i2i2i0020000-2−2i2i2i−2i000000000000000000000000-2200−2i2i000000
χ4322-2-2-22-200002-2222-2-2−2i−2i2i2i2i2i−2i−2i0020000-22i−2i−2i2i0000000000000000000000002-200−2i2i000000
χ4422-2-2-22-200002-2222-2-2−2i−2i2i2i2i2i−2i−2i0020000-22i−2i−2i2i000000000000000000000000-22002i−2i000000
χ4522-2-2-2-222i2i−2i−2i22-222-2-22i2i−2i−2i−2i−2i2i2i−2i2i-22i2i−2i−2i22i−2i−2i2i22-2-2-2-2220000000000000000000000000000
χ4622-2-2-2-222i2i−2i−2i22-222-2-2−2i−2i2i2i2i2i−2i−2i−2i2i-22i2i−2i−2i2−2i2i2i−2i-2-22222-2-20000000000000000000000000000
χ4722-2-2-2-222i2i−2i−2i22-2-2-22200000000−2i2i2−2i−2i2i2i-2000000000000000000002i−2i−2i2i-222-2000000000000
χ4822-2-2-2-222i2i−2i−2i22-2-2-22200000000−2i2i2−2i−2i2i2i-200000000000000000000−2i2i2i−2i2-2-22000000000000
χ4922-2-2-2-22−2i−2i2i2i22-222-2-22i2i−2i−2i−2i−2i2i2i2i−2i-2−2i−2i2i2i22i−2i−2i2i-2-22222-2-20000000000000000000000000000
χ5022-2-2-2-22−2i−2i2i2i22-222-2-2−2i−2i2i2i2i2i−2i−2i2i−2i-2−2i−2i2i2i2−2i2i2i−2i22-2-2-2-2220000000000000000000000000000
χ5122-2-2-2-22−2i−2i2i2i22-2-2-222000000002i−2i22i2i−2i−2i-2000000000000000000002i−2i−2i2i2-2-22000000000000
χ5222-2-2-2-22−2i−2i2i2i22-2-2-222000000002i−2i22i2i−2i−2i-200000000000000000000−2i2i2i−2i-222-2000000000000
χ5344444-4-400004-4-4-4-4-4-400000000004000040000000000000000000000000000000000000000
χ544444-4-440000-4-44000022222222−22−22−22−2200000000−22−222222000000000000000000000000000000000000
χ554444-4-440000-4-440000−22−22−22−2222222222000000002222−22−22000000000000000000000000000000000000
χ5644-4-44440000-4-4-400002i22i2−2i2−2i22i22i2−2i2−2i200000000−2i22i2−2i22i2000000000000000000000000000000000000
χ5744-4-44440000-4-4-40000−2i2−2i22i22i2−2i2−2i22i22i2000000002i2−2i22i2−2i2000000000000000000000000000000000000
χ5844-4-4-44-400004-44-4-4440000000000-4000040000000000000000000000000000000000000000
χ594-44i−4i0002+2i−2−2i2−2i−2+2i00022−222i2−2i22ζ+2ζ3−2ζ−2ζ32ζ5+2ζ7−2ζ5−2ζ72ζ−2ζ3−2ζ+2ζ32ζ5−2ζ7−2ζ5+2ζ70002ζ2−2ζ22ζ6−2ζ600000ζ+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+ζ70000000000000000000000000000
χ604-44i−4i0002+2i−2−2i2−2i−2+2i00022−222i2−2i2−2ζ−2ζ32ζ+2ζ3−2ζ5−2ζ72ζ5+2ζ7−2ζ+2ζ32ζ−2ζ3−2ζ5+2ζ72ζ5−2ζ70002ζ2−2ζ22ζ6−2ζ600000−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−ζ70000000000000000000000000000
χ614-44i−4i0002+2i−2−2i2−2i−2+2i000−2222−2i22i22ζ5−2ζ7−2ζ5+2ζ7−2ζ+2ζ32ζ−2ζ32ζ5+2ζ7−2ζ5−2ζ7−2ζ−2ζ32ζ+2ζ3000−2ζ22ζ2−2ζ62ζ600000ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ70000000000000000000000000000
χ624-44i−4i0002+2i−2−2i2−2i−2+2i000−2222−2i22i2−2ζ5+2ζ72ζ5−2ζ72ζ−2ζ3−2ζ+2ζ3−2ζ5−2ζ72ζ5+2ζ72ζ+2ζ3−2ζ−2ζ3000−2ζ22ζ2−2ζ62ζ600000−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ70000000000000000000000000000
χ634-44i−4i000−2−2i2+2i−2+2i2−2i00022−222i2−2i22ζ+2ζ3−2ζ−2ζ32ζ5+2ζ7−2ζ5−2ζ72ζ−2ζ3−2ζ+2ζ32ζ5−2ζ7−2ζ5+2ζ7000−2ζ22ζ2−2ζ62ζ600000−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−ζ70000000000000000000000000000
χ644-44i−4i000−2−2i2+2i−2+2i2−2i00022−222i2−2i2−2ζ−2ζ32ζ+2ζ3−2ζ5−2ζ72ζ5+2ζ7−2ζ+2ζ32ζ−2ζ3−2ζ5+2ζ72ζ5−2ζ7000−2ζ22ζ2−2ζ62ζ600000ζ+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+ζ70000000000000000000000000000
χ654-44i−4i000−2−2i2+2i−2+2i2−2i000−2222−2i22i22ζ5−2ζ7−2ζ5+2ζ7−2ζ+2ζ32ζ−2ζ32ζ5+2ζ7−2ζ5−2ζ7−2ζ−2ζ32ζ+2ζ30002ζ2−2ζ22ζ6−2ζ600000−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ70000000000000000000000000000
χ664-44i−4i000−2−2i2+2i−2+2i2−2i000−2222−2i22i2−2ζ5+2ζ72ζ5−2ζ72ζ−2ζ3−2ζ+2ζ3−2ζ5−2ζ72ζ5+2ζ72ζ+2ζ3−2ζ−2ζ30002ζ2−2ζ22ζ6−2ζ600000ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ70000000000000000000000000000
χ674-4−4i4i0002−2i−2+2i2+2i−2−2i00022−22−2i22i22ζ5+2ζ7−2ζ5−2ζ72ζ+2ζ3−2ζ−2ζ3−2ζ5+2ζ72ζ5−2ζ7−2ζ+2ζ32ζ−2ζ3000−2ζ62ζ6−2ζ22ζ200000−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−ζ70000000000000000000000000000
χ684-4−4i4i0002−2i−2+2i2+2i−2−2i00022−22−2i22i2−2ζ5−2ζ72ζ5+2ζ7−2ζ−2ζ32ζ+2ζ32ζ5−2ζ7−2ζ5+2ζ72ζ−2ζ3−2ζ+2ζ3000−2ζ62ζ6−2ζ22ζ200000ζ+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+ζ70000000000000000000000000000
χ694-4−4i4i0002−2i−2+2i2+2i−2−2i000−22222i2−2i22ζ−2ζ3−2ζ+2ζ3−2ζ5+2ζ72ζ5−2ζ7−2ζ−2ζ32ζ+2ζ32ζ5+2ζ7−2ζ5−2ζ70002ζ6−2ζ62ζ2−2ζ200000ζ−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−ζ70000000000000000000000000000
χ704-4−4i4i0002−2i−2+2i2+2i−2−2i000−22222i2−2i2−2ζ+2ζ32ζ−2ζ32ζ5−2ζ7−2ζ5+2ζ72ζ+2ζ3−2ζ−2ζ3−2ζ5−2ζ72ζ5+2ζ70002ζ6−2ζ62ζ2−2ζ200000−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+ζ70000000000000000000000000000
χ714-4−4i4i000−2+2i2−2i−2−2i2+2i00022−22−2i22i22ζ5+2ζ7−2ζ5−2ζ72ζ+2ζ3−2ζ−2ζ3−2ζ5+2ζ72ζ5−2ζ7−2ζ+2ζ32ζ−2ζ30002ζ6−2ζ62ζ2−2ζ200000ζ+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+ζ70000000000000000000000000000
χ724-4−4i4i000−2+2i2−2i−2−2i2+2i00022−22−2i22i2−2ζ5−2ζ72ζ5+2ζ7−2ζ−2ζ32ζ+2ζ32ζ5−2ζ7−2ζ5+2ζ72ζ−2ζ3−2ζ+2ζ30002ζ6−2ζ62ζ2−2ζ200000−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−ζ70000000000000000000000000000
χ734-4−4i4i000−2+2i2−2i−2−2i2+2i000−22222i2−2i22ζ−2ζ3−2ζ+2ζ3−2ζ5+2ζ72ζ5−2ζ7−2ζ−2ζ32ζ+2ζ32ζ5+2ζ7−2ζ5−2ζ7000−2ζ62ζ6−2ζ22ζ200000−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+ζ70000000000000000000000000000
χ744-4−4i4i000−2+2i2−2i−2−2i2+2i000−22222i2−2i2−2ζ+2ζ32ζ−2ζ32ζ5−2ζ7−2ζ5+2ζ72ζ+2ζ3−2ζ−2ζ3−2ζ5−2ζ72ζ5+2ζ7000−2ζ62ζ6−2ζ22ζ200000ζ−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−ζ70000000000000000000000000000

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