Finite Group Databasebeta

← Group #504665

Character table — Group #504665

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11112222222222222244444444444444444444444488888888161616161616161616161616161616163232
order1222224444888888884444888816161616161616161616161616161616244444444444448888881616161644
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1
χ3111111111111111111111111111111111111111111-1-111-1-1111-1-11-1-1-1-11111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-111-111-1-1-1-1-1-1-1-1-1-111
χ511111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-111-1111111-1-1-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11-1-11-1-111-1-111-1-1-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-111-1-1111111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1
χ91111111111-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-1111-1111-1-1111-11-1-1-1-111-1-11-1
χ101111111111-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-1-11-1-1-1-111-1-1-1-11111111-1-1-11
χ111111111111-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1111-11111111-1-11-1-1-1-1-1-1-111-11
χ121111111111-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-11-1-1-11-1-1-1-1-1-1111-11111-1-1111-1
χ131111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111-1111-111-1-1-1-111-11-1-111-1-111-11
χ141111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111-1-1-11-1-1-11111-1-1-1111-1-1-1-1111-1
χ151111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1111-1111-111-1-1-11-1-1-11111-1-11-1
χ161111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-11-1-1-11-1-11-1-11111-111-1-111-1-1-11
χ1722222222222222-2-2-2-2-2-2-2-222-2-2000000000000000022002200000000-2-20000000000
χ1822222222222222-2-2-2-2-2-2-2-222-2-20000000000000000-2-200-2-200000000220000000000
χ192222222222-2-2-2-2-2-2-2-22222-2-2-2-200000000000000002-2002-2000000002-20000000000
χ202222222222-2-2-2-2-2-2-2-22222-2-2-2-20000000000000000-2200-2200000000-220000000000
χ212222-2-22-22-200002222000000-2-22222-2-2-2-200000000002200-2-2200-200000000000000
χ222222-2-22-22-200002222000000-2-22222-2-2-2-20000000000-2-20022-200200000000000000
χ232222-2-22-22-200002222000000-2-2-2-2-2-2222200000000002200-2-2-200200000000000000
χ242222-2-22-22-200002222000000-2-2-2-2-2-222220000000000-2-20022200-200000000000000
χ252222-2-2-22-22222200000000-2-20022−2−222−2−22222−2−2−2−22200-2-2000000000000002−22−200
χ262222-2-2-22-22222200000000-2-20022−2−222−2−22222−2−2−2−2-2-2002200000000000000−22−2200
χ272222-2-2-22-22222200000000-2-200−2−222−2−222−2−2−2−222222200-2-200000000000000−22−2200
χ282222-2-2-22-22222200000000-2-200−2−222−2−222−2−2−2−22222-2-20022000000000000002−22−200
χ292222-2-2-22-22-2-2-2-200000000220022−2−222−2−2−2−2−2−222222-200-22000000000000002−2−2200
χ302222-2-2-22-22-2-2-2-200000000220022−2−222−2−2−2−2−2−22222-22002-200000000000000−222−200
χ312222-2-2-22-22-2-2-2-2000000002200−2−222−2−2222222−2−2−2−22-200-2200000000000000−222−200
χ322222-2-2-22-22-2-2-2-2000000002200−2−222−2−2222222−2−2−2−2-22002-2000000000000002−2−2200
χ332-22-22-2-2-2222i2i−2i−2i22-2-22i2i−2i−2i2i−2i-2200000000000000000000000002-202i−2i000000000000
χ342-22-22-2-2-2222i2i−2i−2i22-2-22i2i−2i−2i2i−2i-220000000000000000000000000-220−2i2i000000000000
χ352-22-22-2-2-2222i2i−2i−2i-2-222−2i−2i2i2i2i−2i2-20000000000000000002i−2i002i−2i000000002-200000000
χ362-22-22-2-2-2222i2i−2i−2i-2-222−2i−2i2i2i2i−2i2-2000000000000000000−2i2i00−2i2i00000000-2200000000
χ372-22-22-2-2-222−2i−2i2i2i22-2-2−2i−2i2i2i−2i2i-2200000000000000000000000002-20−2i2i000000000000
χ382-22-22-2-2-222−2i−2i2i2i22-2-2−2i−2i2i2i−2i2i-220000000000000000000000000-2202i−2i000000000000
χ392-22-22-2-2-222−2i−2i2i2i-2-2222i2i−2i−2i−2i2i2-20000000000000000002i−2i002i−2i00000000-2200000000
χ402-22-22-2-2-222−2i−2i2i2i-2-2222i2i−2i−2i−2i2i2-2000000000000000000−2i2i00−2i2i000000002-200000000
χ412-22-2-22-222-20000-2-222000000-220000000022-2-222-2-2002i−2i00−2i2i00000000002i−2i000000
χ422-22-2-22-222-20000-2-222000000-220000000022-2-222-2-200−2i2i002i−2i0000000000−2i2i000000
χ432-22-2-22-222-20000-2-222000000-2200000000-2-222-2-222002i−2i00−2i2i0000000000−2i2i000000
χ442-22-2-22-222-20000-2-222000000-2200000000-2-222-2-22200−2i2i002i−2i00000000002i−2i000000
χ45444444-4-4-4-400000000000000002222−22−22−22−2222220000000000000000000000000000000000
χ46444444-4-4-4-40000000000000000−22−2222222222−22−220000000000000000000000000000000000
χ474444-4-44-44-40000-4-4-4-400000044000000000000000000000000000000000000000000
χ4844-4-400000022−2222−2222−2222−222-22-200002ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ50000ζ+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
χ4944-4-400000022−2222−2222−2222−222-22-20000−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ50000−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
χ5044-4-400000022−2222−22−2222−2222-22-2200002ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ70000ζ−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
χ5144-4-400000022−2222−22−2222−2222-22-220000−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ70000−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
χ5244-4-4000000−2222−222222−2222−22-22-2200002ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ50000−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
χ5344-4-4000000−2222−222222−2222−22-22-220000−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ50000ζ+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
χ5444-4-4000000−2222−2222−2222−22222-22-200002ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ70000−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
χ5544-4-4000000−2222−2222−2222−22222-22-20000−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ70000ζ−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
χ564-44-44-444-4-40000000000000000000000002222−22−22−22−22222200000000000000000000000000
χ574-44-44-444-4-4000000000000000000000000−22−2222222222−22−2200000000000000000000000000
χ584-44-4-444-4-444i4i−4i−4i00000000−4i4i00000000000000000000000000000000000000000000
χ594-44-4-444-4-44−4i−4i4i4i000000004i−4i00000000000000000000000000000000000000000000
χ604-44-4-44-444-4000044-4-40000004-4000000000000000000000000000000000000000000
χ614-4-440000002i2−2i2−2i22i222−22−22222i−2i−2i2i000000002ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ5ζ−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+ζ700000000000000000000000000
χ624-4-440000002i2−2i2−2i22i222−22−22222i−2i−2i2i00000000−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ5−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−ζ700000000000000000000000000
χ634-4-440000002i2−2i2−2i22i2−222222−22−2i2i2i−2i000000002ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ7ζ+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−ζ700000000000000000000000000
χ644-4-440000002i2−2i2−2i22i2−222222−22−2i2i2i−2i00000000−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ7−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+ζ700000000000000000000000000
χ654-4-44000000−2i22i22i2−2i222−22−2222−2i2i2i−2i000000002ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ5−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−ζ700000000000000000000000000
χ664-4-44000000−2i22i22i2−2i222−22−2222−2i2i2i−2i00000000−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ5ζ−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+ζ700000000000000000000000000
χ674-4-44000000−2i22i22i2−2i2−222222−222i−2i−2i2i000000002ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ7−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+ζ700000000000000000000000000
χ684-4-44000000−2i22i22i2−2i2−222222−222i−2i−2i2i00000000−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ7ζ+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−ζ700000000000000000000000000

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