Finite Group Databasebeta

← Group #501262

Character table — Group #501262

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111222222222222444444488888888888888888888888881616161616161616161616163232
order122222224444888824488882222244481616161616161616161616161616161622244488888824
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ3111111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1
χ4111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111
χ511111111111111111111111-1-1-1-1111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1
χ611111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ811111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-11111-1-11111-1-1
χ9111111-1-111111111-1-1-1-1-11111111-11-1-11111-1-1-1-11111-1-1-1-1-1-11-11-1-1111-1-11-1
χ10111111-1-111111111-1-1-1-1-11111111-11-1-1-1-1-1-11111-1-1-1-11111-1-11-11-1-11-1-111-11
χ11111111-1-111111111-1-1-1-1-1111111-11-11-11111-1-1-1-1-1-1-1-11111-1-1-11-111-111-1-1-11
χ12111111-1-111111111-1-1-1-1-1111111-11-11-1-1-1-1-111111111-1-1-1-1-1-1-11-111-1-1-1111-1
χ13111111-1-111111111-1-1-1-1-111-1-1-1-11-11-1-11111-1-1-1-11111-1-1-1-111-11-11-11-1-111-11
χ14111111-1-111111111-1-1-1-1-111-1-1-1-11-11-1-1-1-1-1-11111-1-1-1-1111111-11-11-1111-1-11-1
χ15111111-1-111111111-1-1-1-1-111-1-1-1-1-11-11-11111-1-1-1-1-1-1-1-11111111-11-11-1-1-1111-1
χ16111111-1-111111111-1-1-1-1-111-1-1-1-1-11-11-1-1-1-1-111111111-1-1-1-1111-11-11-111-1-1-11
χ17222222222222-2-2-2-2222-2-2-2-200002222-20000000000000000000000-2-2000000
χ18222222222222-2-2-2-2222-2-2-2-20000-2-2-2-2-2000000000000000000000022000000
χ19222222-2-22222-2-2-2-2-2-2-222-2-200002-22-2200000000000000000000002-2000000
χ20222222-2-22222-2-2-2-2-2-2-222-2-20000-22-2220000000000000000000000-22000000
χ212222-2-2222-2-220000-22-2000000002-2-22022−2−222−2−222−2−222−2−200000000000000
χ222222-2-2222-2-220000-22-2000000002-2-220−2−222−2−222−2−222−2−22200000000000000
χ232222-2-2222-2-220000-22-200000000-222-2022−2−222−2−2−2−222−2−22200000000000000
χ242222-2-2222-2-220000-22-200000000-222-20−2−222−2−22222−2−222−2−200000000000000
χ252222-2-222-222-22222-2-2222-2-200000000-20000000000000000002-2-2200000000
χ262222-2-222-222-22222-2-2222-2-200000000-2000000000000000000-222-200000000
χ272222-2-222-222-2-2-2-2-2-2-22-2-22222-2-20000200000000000000002-2000000000000
χ282222-2-222-222-2-2-2-2-2-2-22-2-222-2-222000020000000000000000-22000000000000
χ292222-2-2-2-22-2-2200002-220000000022-2-2022−2−2−2−22222−2−2−2−22200000000000000
χ302222-2-2-2-22-2-2200002-220000000022-2-20−2−22222−2−2−2−22222−2−200000000000000
χ312222-2-2-2-22-2-2200002-2200000000-2-222022−2−2−2−222−2−22222−2−200000000000000
χ322222-2-2-2-22-2-2200002-2200000000-2-2220−2−22222−2−222−2−2−2−22200000000000000
χ332222-2-2-2-2-222-2222222-2-2-2-2-200000000200000000000000000022-2-200000000
χ342222-2-2-2-2-222-2222222-2-2-2-2-2000000002000000000000000000-2-22200000000
χ352222-2-2-2-2-222-2-2-2-2-222-2222222-2-20000-20000000000000000-22000000000000
χ362222-2-2-2-2-222-2-2-2-2-222-22222-2-2220000-200000000000000002-2000000000000
χ372-22-22-2002-22-222-2-2000002-22-22-20000000002i−2i2i−2i0000000000000000002i−2i00
χ382-22-22-2002-22-222-2-2000002-22-22-2000000000−2i2i−2i2i000000000000000000−2i2i00
χ392-22-22-2002-22-222-2-2000002-2-22-220000000002i−2i2i−2i000000000000000000−2i2i00
χ402-22-22-2002-22-222-2-2000002-2-22-22000000000−2i2i−2i2i0000000000000000002i−2i00
χ412-22-2-2200-2-222-2-222000002-22-2-22000002-22-2000000000000000000002-20000
χ422-22-2-2200-2-222-2-222000002-22-2-2200000-22-2200000000000000000000-220000
χ432-22-2-2200-2-222-2-222000002-2-222-2000002-22-200000000000000000000-220000
χ442-22-2-2200-2-222-2-222000002-2-222-200000-22-22000000000000000000002-20000
χ4544444444-4-4-4-400004-4-40000000000000000000000000000000000000000000
χ46444444-4-4-4-4-4-40000-4440000000000000000000000000000000000000000000
χ474-44-44-4004-44-4-4-44400000-44000000000000000000000000000000000000000
χ484-44-44-400-44-440000000000000000000022−22−222200000000000000000000000000
χ494-44-44-400-44-4400000000000000000000−222222−2200000000000000000000000000
χ504-44-4-440044-4-40000000000000000000000002i2−2i2−2i22i20000000000000000000000
χ514-44-4-440044-4-4000000000000000000000000−2i22i22i2−2i20000000000000000000000
χ524-44-4-4400-4-44444-4-400000-44000000000000000000000000000000000000000
χ534-4-44004-4000022−2222−2200022−220000000000000000000ζ+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+ζ700000000000000
χ544-4-44004-4000022−2222−2200022−220000000000000000000−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−ζ700000000000000
χ554-4-44004-40000−2222−2222000−22220000000000000000000ζ−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−ζ700000000000000
χ564-4-44004-40000−2222−2222000−22220000000000000000000−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+ζ700000000000000
χ574-4-4400-44000022−2222−22000−22220000000000000000000ζ+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−ζ700000000000000
χ584-4-4400-44000022−2222−22000−22220000000000000000000−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+ζ700000000000000
χ594-4-4400-440000−2222−222200022−220000000000000000000ζ−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+ζ700000000000000
χ604-4-4400-440000−2222−222200022−220000000000000000000−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−ζ700000000000000
χ6188-8-80000000042−42−42420000000000000000000000000000000000000000000000
χ6288-8-800000000−424242−420000000000000000000000000000000000000000000000

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