Finite Group Databasebeta

← Group #512099

Character table — Group #512099

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111222222222222444444444444444888888888888888888888888888881616161632323232
order12222244444488882244444444488882222444444444444888881616161616161616161616164488
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-1
χ41111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111-1-1-1-11-1-1-1-111111111-1-1-1-11111-1-1-1-11-1-1-1-111111111-1-1-1-111-1-1
χ6111111111111111111-1-1-1-11-1-1-1-111111111-1-1-1-11111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111111-1-1-1-11-1-1-1-11111-1-1-1-11111-1-1-1-111111-1-1-1-111111111-1-1-1-1-1-111
χ8111111111111111111-1-1-1-11-1-1-1-11111-1-1-1-11111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ9111111-1-111111111-1-111-1-1-111-1-1-1-111111111-1-1-1-1-1-111-1-1-111-1-11111-1-1-1-111-1-11-11-1
χ10111111-1-111111111-1-111-1-1-111-1-1-1-111111111-1-1-1-1-1-111-1-1-111-1-1-1-1-1-11111-1-111-11-11
χ11111111-1-111111111-1-111-1-1-111-1-1-1-111-1-1-1-1-1-1111111-1-111-111-1-11111-1-1-1-111-1-1-11-11
χ12111111-1-111111111-1-111-1-1-111-1-1-1-111-1-1-1-1-1-1111111-1-111-111-1-1-1-1-1-11111-1-1111-11-1
χ13111111-1-111111111-1-1-1-111-1-1-111-1-1111111-1-111-1-1-1-1-1-111-1-1-1111111-1-1-1-1-1-1111-1-11
χ14111111-1-111111111-1-1-1-111-1-1-111-1-1111111-1-111-1-1-1-1-1-111-1-1-111-1-1-1-1111111-1-1-111-1
χ15111111-1-111111111-1-1-1-111-1-1-111-1-111-1-1-1-111-1-1111111-1-1-1-1-1111111-1-1-1-1-1-111-111-1
χ16111111-1-111111111-1-1-1-111-1-1-111-1-111-1-1-1-111-1-1111111-1-1-1-1-111-1-1-1-1111111-1-11-1-11
χ17222222222222-2-2-2-222222222222-2-2-2-20000000000000000-2-2-2-2-20000000000000000
χ18222222222222-2-2-2-222-2-2-2-22-2-2-2-2-2-2-2-20000000000000000-222220000000000000000
χ19222222-2-22222-2-2-2-2-2-222-2-2-222-2-222-2-200000000000000002-2-2220000000000000000
χ20222222-2-22222-2-2-2-2-2-2-2-222-2-2-22222-2-20000000000000000222-2-20000000000000000
χ212222-2-22222-2-200002-222-2-2-2-2-222000000000000000000000000022−2−222−2−22−22−20000
χ222222-2-22222-2-200002-222-2-2-2-2-2220000000000000000000000000−2−222−2−222−22−220000
χ232222-2-22222-2-200002-2-2-222-222-2-2000000000000000000000000022−2−222−2−2−22−220000
χ242222-2-22222-2-200002-2-2-222-222-2-20000000000000000000000000−2−222−2−2222−22−20000
χ252222-2-222-2-2222222-220000-2000022-2-2000022-2-20000-2-222-200000000000000000000
χ262222-2-222-2-2222222-220000-2000022-2-20000-2-222000022-2-2-200000000000000000000
χ272222-2-222-2-222-2-2-2-2-220000-20000-2-22222-2-2000022-2-20000200000000000000000000
χ282222-2-222-2-222-2-2-2-2-220000-20000-2-222-2-2220000-2-2220000200000000000000000000
χ292222-2-2-2-222-2-20000-2222222-2-2-2-2000000000000000000000000022−2−2−2−2222−2−220000
χ302222-2-2-2-222-2-20000-2222222-2-2-2-20000000000000000000000000−2−22222−2−2−222−20000
χ312222-2-2-2-222-2-20000-22-2-2-2-222222000000000000000000000000022−2−2−2−222−222−20000
χ322222-2-2-2-222-2-20000-22-2-2-2-2222220000000000000000000000000−2−22222−2−22−2−220000
χ332222-2-2-2-2-2-22222222-2000020000-2-2-2-2000022220000-2-2-2-2200000000000000000000
χ342222-2-2-2-2-2-22222222-2000020000-2-2-2-20000-2-2-2-200002222200000000000000000000
χ352222-2-2-2-2-2-222-2-2-2-22-2000020000222222-2-20000-2-2220000-200000000000000000000
χ362222-2-2-2-2-2-222-2-2-2-22-20000200002222-2-222000022-2-20000-200000000000000000000
χ372-22-22-2002-22-222-2-200002i−2i0002i−2i002-200002i−2i002-22-22i−2i000002i−2i0000000000000000
χ382-22-22-2002-22-222-2-200002i−2i0002i−2i002-20000−2i2i00-22-22−2i2i000002i−2i0000000000000000
χ392-22-22-2002-22-222-2-20000−2i2i000−2i2i002-200002i−2i00-22-222i−2i00000−2i2i0000000000000000
χ402-22-22-2002-22-222-2-20000−2i2i000−2i2i002-20000−2i2i002-22-2−2i2i00000−2i2i0000000000000000
χ412-22-22-2002-22-2-2-22200002i−2i0002i−2i00-222-22-2002i−2i0000002i−2i000−2i2i0000000000000000
χ422-22-22-2002-22-2-2-22200002i−2i0002i−2i00-22-22-2200−2i2i000000−2i2i000−2i2i0000000000000000
χ432-22-22-2002-22-2-2-2220000−2i2i000−2i2i00-222-22-200−2i2i000000−2i2i0002i−2i0000000000000000
χ442-22-22-2002-22-2-2-2220000−2i2i000−2i2i00-22-22-22002i−2i0000002i−2i0002i−2i0000000000000000
χ452-22-2-2200-222-222-2-2002i−2i0002i−2i0000-222-2-222i−2i000000−2i2i0002i−2i000000000000000000
χ462-22-2-2200-222-222-2-2002i−2i0002i−2i0000-22-222-2−2i2i0000002i−2i0002i−2i000000000000000000
χ472-22-2-2200-222-222-2-200−2i2i000−2i2i0000-222-2-22−2i2i0000002i−2i000−2i2i000000000000000000
χ482-22-2-2200-222-222-2-200−2i2i000−2i2i0000-22-222-22i−2i000000−2i2i000−2i2i000000000000000000
χ492-22-2-2200-222-2-2-222002i−2i0002i−2i00002-20000002i−2i-222-200−2i2i0−2i2i000000000000000000
χ502-22-2-2200-222-2-2-222002i−2i0002i−2i00002-2000000−2i2i2-2-22002i−2i0−2i2i000000000000000000
χ512-22-2-2200-222-2-2-22200−2i2i000−2i2i00002-20000002i−2i2-2-2200−2i2i02i−2i000000000000000000
χ522-22-2-2200-222-2-2-22200−2i2i000−2i2i00002-2000000−2i2i-222-2002i−2i02i−2i000000000000000000
χ5344444444-4-4-4-40000-4-400004000000000000000000000000000000000000000000000
χ54444444-4-4-4-4-4-40000440000-4000000000000000000000000000000000000000000000
χ554-44-44-400-44-440000004i−4i000−4i4i0000000000000000000000000000000000000000000
χ564-44-44-400-44-44000000−4i4i0004i−4i0000000000000000000000000000000000000000000
χ574-44-4-44004-4-44000000004i−4i000−4i4i00000000000000000000000000000000000000000
χ584-44-4-44004-4-4400000000−4i4i0004i−4i00000000000000000000000000000000000000000
χ594-4-44004i−4i000022−2222−22000000000002i2−2i200000000000000000000000ζ+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−ζ700000000
χ604-4-44004i−4i000022−2222−22000000000002i2−2i200000000000000000000000−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+ζ700000000
χ614-4-44004i−4i0000−2222−222200000000000−2i22i200000000000000000000000ζ−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−ζ700000000
χ624-4-44004i−4i0000−2222−222200000000000−2i22i200000000000000000000000−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+ζ700000000
χ634-4-4400−4i4i000022−2222−2200000000000−2i22i200000000000000000000000ζ+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+ζ700000000
χ644-4-4400−4i4i000022−2222−2200000000000−2i22i200000000000000000000000−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−ζ700000000
χ654-4-4400−4i4i0000−2222−2222000000000002i2−2i200000000000000000000000ζ−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+ζ700000000
χ664-4-4400−4i4i0000−2222−2222000000000002i2−2i200000000000000000000000−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−ζ700000000
χ6788-8-80000000042−42−42420000000000000000000000000000000000000000000000000000
χ6888-8-800000000−424242−420000000000000000000000000000000000000000000000000000

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