Finite Group Databasebeta

← Group #511757

Character table — Group #511757

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111222222222222444444444444444888888888888888888888888888881616161632323232
order12222244444488882222224444488882222222244444444888881616161616161616161616162488
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
χ91111111-1-11111111-1-111-1-1-111-1-1-1-111111111-1-1-1-1-1-111-1-1-111-1-11111-1-1-1-111-1-11-11-1
χ101111111-1-11111111-1-111-1-1-111-1-1-1-111111111-1-1-1-1-1-111-1-1-111-1-1-1-1-1-11111-1-111-11-11
χ111111111-1-11111111-1-111-1-1-111-1-1-1-111-1-1-1-1-1-1111111-1-111-111-1-11111-1-1-1-111-1-1-11-11
χ121111111-1-11111111-1-111-1-1-111-1-1-1-111-1-1-1-1-1-1111111-1-111-111-1-1-1-1-1-11111-1-1111-11-1
χ131111111-1-11111111-1-1-1-111-1-1-111-1-1111111-1-111-1-1-1-1-1-111-1-1-1111111-1-1-1-1-1-1111-1-11
χ141111111-1-11111111-1-1-1-111-1-1-111-1-1111111-1-111-1-1-1-1-1-111-1-1-111-1-1-1-1111111-1-1-111-1
χ151111111-1-11111111-1-1-1-111-1-1-111-1-111-1-1-1-111-1-1111111-1-1-1-1-1111111-1-1-1-1-1-111-111-1
χ161111111-1-11111111-1-1-1-111-1-1-111-1-111-1-1-1-111-1-1111111-1-1-1-1-111-1-1-1-1111111-1-11-1-11
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
χ192222222-2-2222-2-2-2-2-2-222-2-2-222-2-222-2-200000000000000002-2-2220000000000000000
χ202222222-2-2222-2-2-2-2-2-2-2-222-2-2-22222-2-20000000000000000222-2-20000000000000000
χ212222-2-2222-2-2222222-20000-2000022-2-2000022-2-20000-2-222-200000000000000000000
χ222222-2-2222-2-2222222-20000-2000022-2-20000-2-222000022-2-2-200000000000000000000
χ232222-2-2222-2-22-2-2-2-22-20000-20000-2-22222-2-2000022-2-20000200000000000000000000
χ242222-2-2222-2-22-2-2-2-22-20000-20000-2-222-2-2220000-2-2220000200000000000000000000
χ252222-2-22-2-2-2-222222-22000020000-2-2-2-2000022220000-2-2-2-2200000000000000000000
χ262222-2-22-2-2-2-222222-22000020000-2-2-2-20000-2-2-2-200002222200000000000000000000
χ272222-2-22-2-2-2-22-2-2-2-2-22000020000222222-2-20000-2-2220000-200000000000000000000
χ282222-2-22-2-2-2-22-2-2-2-2-220000200002222-2-222000022-2-20000-200000000000000000000
χ292222-2-2-22222-20000-2222-2-2-2-2-222000000000000000000000000022−2−222−2−22−22−20000
χ302222-2-2-22222-20000-2222-2-2-2-2-2220000000000000000000000000−2−222−2−222−22−220000
χ312222-2-2-22222-20000-22-2-222-222-2-2000000000000000000000000022−2−222−2−2−22−220000
χ322222-2-2-22222-20000-22-2-222-222-2-20000000000000000000000000−2−222−2−2222−22−20000
χ332222-2-2-2-2-222-200002-222222-2-2-2-2000000000000000000000000022−2−2−2−2222−2−220000
χ342222-2-2-2-2-222-200002-222222-2-2-2-20000000000000000000000000−2−22222−2−2−222−20000
χ352222-2-2-2-2-222-200002-2-2-2-2-222222000000000000000000000000022−2−2−2−222−222−20000
χ362222-2-2-2-2-222-200002-2-2-2-2-2222220000000000000000000000000−2−22222−2−22−2−220000
χ372-2-222-2-2002-2222-2-200002-20002-2002-200002-2002-22-22-2000002-20000000000000000
χ382-2-222-2-2002-2222-2-200002-20002-2002-20000-2200-22-22-22000002-20000000000000000
χ392-2-222-2-2002-2222-2-20000-22000-22002-200002-200-22-222-200000-220000000000000000
χ402-2-222-2-2002-2222-2-20000-22000-22002-20000-22002-22-2-2200000-220000000000000000
χ412-2-222-2-2002-22-2-22200002-20002-200-222-22-2002-20000002-2000-220000000000000000
χ422-2-222-2-2002-22-2-22200002-20002-200-22-22-2200-22000000-22000-220000000000000000
χ432-2-222-2-2002-22-2-2220000-22000-2200-222-22-200-22000000-220002-20000000000000000
χ442-2-222-2-2002-22-2-2220000-22000-2200-22-22-22002-20000002-20002-20000000000000000
χ452-2-22-22-200-22222-2-2002-20002-20000-222-2-222-2000000-220002-2000000000000000000
χ462-2-22-22-200-22222-2-2002-20002-20000-22-222-2-220000002-20002-2000000000000000000
χ472-2-22-22-200-22222-2-200-22000-220000-222-2-22-220000002-2000-22000000000000000000
χ482-2-22-22-200-22222-2-200-22000-220000-22-222-22-2000000-22000-22000000000000000000
χ492-2-22-22-200-222-2-222002-20002-200002-20000002-2-222-200-220-22000000000000000000
χ502-2-22-22-200-222-2-222002-20002-200002-2000000-222-2-22002-20-22000000000000000000
χ512-2-22-22-200-222-2-22200-22000-2200002-20000002-22-2-2200-2202-2000000000000000000
χ522-2-22-22-200-222-2-22200-22000-2200002-2000000-22-222-2002-202-2000000000000000000
χ53444444-444-4-4-40000-4-400004000000000000000000000000000000000000000000000
χ54444444-4-4-4-4-4-40000440000-4000000000000000000000000000000000000000000000
χ5544-4-40004i−4i00022−2222−22000000000002i2−2i200000000000000000000000ζ+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
χ5644-4-40004i−4i00022−2222−22000000000002i2−2i200000000000000000000000−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
χ5744-4-40004i−4i000−2222−222200000000000−2i22i200000000000000000000000ζ−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
χ5844-4-40004i−4i000−2222−222200000000000−2i22i200000000000000000000000−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
χ5944-4-4000−4i4i00022−2222−2200000000000−2i22i200000000000000000000000ζ+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
χ6044-4-4000−4i4i00022−2222−2200000000000−2i22i200000000000000000000000−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
χ6144-4-4000−4i4i000−2222−2222000000000002i2−2i200000000000000000000000ζ−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
χ6244-4-4000−4i4i000−2222−2222000000000002i2−2i200000000000000000000000−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
χ634-4-444-4400-44-40000004-4000-440000000000000000000000000000000000000000000
χ644-4-444-4400-44-4000000-440004-40000000000000000000000000000000000000000000
χ654-4-44-444004-4-4000000004-4000-4400000000000000000000000000000000000000000
χ664-4-44-444004-4-400000000-440004-400000000000000000000000000000000000000000
χ678-88-80000000042−42−42420000000000000000000000000000000000000000000000000000
χ688-88-800000000−424242−420000000000000000000000000000000000000000000000000000

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