Finite Group Databasebeta

← Group #72320973

Character table — Group #72320973

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67
size1122222444444444448888888888888161616161616161616161616161616161616161616163232323232323232323232326464
order1224488222444816161616244488816161616161688161616163232323232323232323232323232323222244444888844
χ11111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ41111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111-1-1-1-1111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1
χ6111111111111111111-1-1-1-1111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111
χ7111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-111
χ8111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1
χ91111111-1-111-1-11-1-1-1-111-1-11-1-1-1-111111-1-1-1111111-1-1-1-11111-1-1-1-11-11-11-11-111-1-11-1
χ101111111-1-111-1-11-1-1-1-111-1-11-1-1-1-111111-1-1-1111111-1-1-1-11111-1-1-1-1-11-11-11-11-1-111-11
χ111111111-1-111-1-11-1-1-1-111-1-11-1-1-1-111111-1-1-111-1-1-1-11111-1-1-1-111111-11-11-11-1-1-111-11
χ121111111-1-111-1-11-1-1-1-111-1-11-1-1-1-111111-1-1-111-1-1-1-11111-1-1-1-11111-11-11-11-1111-1-11-1
χ131111111-1-111-1-11-1-1-1-1-1-1111-1-1-1-11111-1111-1-11111-1-1-1-1-1-1-1-111111-1-111-1-1111-1-1-11
χ141111111-1-111-1-11-1-1-1-1-1-1111-1-1-1-11111-1111-1-11111-1-1-1-1-1-1-1-11111-111-1-111-1-1-1111-1
χ151111111-1-111-1-11-1-1-1-1-1-1111-1-1-1-11111-1111-1-1-1-1-1-111111111-1-1-1-11-1-111-1-11-1-1111-1
χ161111111-1-111-1-11-1-1-1-1-1-1111-1-1-1-11111-1111-1-1-1-1-1-111111111-1-1-1-1-111-1-111-111-1-1-11
χ1722222222222222-2-2-2-22222222-2-2-2-2-2-222-2-2-2-2000000000000000000000000000000
χ1822222222222222-2-2-2-2-2-2-2-2222-2-2-2-2-2-2-2-22222000000000000000000000000000000
χ1922222222-2-2-22-2222220000-22-2-2-222-2-200000000000000000000002200-2-200000000
χ2022222222-2-2-22-2222220000-22-2-2-222-2-20000000000000000000000-2-2002200000000
χ2122222222-2-2-22-22-2-2-2-20000-22-222-2-2220000000000000000000000002-200-22000000
χ2222222222-2-2-22-22-2-2-2-20000-22-222-2-222000000000000000000000000-22002-2000000
χ232222222-22-2-2-22222220000-2-22-2-2-2-2220000000000000000000000002200-2-2000000
χ242222222-22-2-2-22222220000-2-22-2-2-2-222000000000000000000000000-2-20022000000
χ252222222-22-2-2-222-2-2-2-20000-2-222222-2-200000000000000000000002-200-2200000000
χ262222222-22-2-2-222-2-2-2-20000-2-222222-2-20000000000000000000000-22002-200000000
χ272222222-2-222-2-22222222-2-22-2-222-2-2-2-22-222-2-2000000000000000000000000000000
χ282222222-2-222-2-222222-2-2222-2-222-2-2-2-2-22-2-222000000000000000000000000000000
χ2922222-2-2222222-200002222-2-2-2000000-2-2000022−2−222−2−222−2−222−2−200000000000000
χ3022222-2-2222222-200002222-2-2-2000000-2-20000−2−222−2−222−2−222−2−22200000000000000
χ3122222-2-2222222-20000-2-2-2-2-2-2-200000022000022−2−222−2−2−2−222−2−22200000000000000
χ3222222-2-2222222-20000-2-2-2-2-2-2-2000000220000−2−222−2−22222−2−222−2−200000000000000
χ3322222-2-2-2-222-2-2-2000022-2-2-222000000-22000022−2−2−2−22222−2−2−2−22200000000000000
χ3422222-2-2-2-222-2-2-2000022-2-2-222000000-220000−2−22222−2−2−2−22222−2−200000000000000
χ3522222-2-2-2-222-2-2-20000-2-222-2220000002-2000022−2−2−2−222−2−22222−2−200000000000000
χ3622222-2-2-2-222-2-2-20000-2-222-2220000002-20000−2−22222−2−222−2−2−2−22200000000000000
χ37222-2-20022-22-2-2022−2−22-22-20002−22−22−2002−22−2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ500000000000000
χ38222-2-20022-22-2-2022−2−22-22-20002−22−22−2002−22−2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ500000000000000
χ39222-2-20022-22-2-2022−2−2-22-220002−22−22−200−22−22ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ500000000000000
χ40222-2-20022-22-2-2022−2−2-22-220002−22−22−200−22−22−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ500000000000000
χ41222-2-20022-22-2-20−2−2222-22-2000−22−22−2200−22−22ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ700000000000000
χ42222-2-20022-22-2-20−2−2222-22-2000−22−22−2200−22−22−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ700000000000000
χ43222-2-20022-22-2-20−2−222-22-22000−22−22−22002−22−2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ700000000000000
χ44222-2-20022-22-2-20−2−222-22-22000−22−22−22002−22−2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ700000000000000
χ45222-2-200-2-2-2222022−2−22-2-220002−2−22−22002−2−22ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ700000000000000
χ46222-2-200-2-2-2222022−2−22-2-220002−2−22−22002−2−22−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ700000000000000
χ47222-2-200-2-2-2222022−2−2-222-20002−2−22−2200−222−2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ700000000000000
χ48222-2-200-2-2-2222022−2−2-222-20002−2−22−2200−222−2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ700000000000000
χ49222-2-200-2-2-22220−2−2222-2-22000−222−22−200−222−2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ500000000000000
χ50222-2-200-2-2-22220−2−2222-2-22000−222−22−200−222−2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ500000000000000
χ51222-2-200-2-2-22220−2−222-222-2000−222−22−2002−2−22ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ500000000000000
χ52222-2-200-2-2-22220−2−222-222-2000−222−22−2002−2−22−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ500000000000000
χ5344444-4-44-4-4-44-4-4000000004-44000000000000000000000000000000000000000000
χ5444444-4-4-44-4-4-44-40000000044-4000000000000000000000000000000000000000000
χ55444-4-4004-44-4-4402222−22−220000000−222222−22−2222000000000000000000000000000000000000
χ56444-4-4004-44-4-440−22−222222000000022−22−222222−22000000000000000000000000000000000000
χ57444-4-400-444-44-402222−22−220000000−2222−222222−22000000000000000000000000000000000000
χ58444-4-400-444-44-40−22−222222000000022−2222−22−2222000000000000000000000000000000000000
χ5944-44-444000000-44-44-400000000000000000000000000000000000000000002i−2i2i−2i00
χ6044-44-444000000-44-44-40000000000000000000000000000000000000000000−2i2i−2i2i00
χ6144-44-444000000-4-44-4400000000000000000000000000000000000000000002i−2i−2i2i00
χ6244-44-444000000-4-44-440000000000000000000000000000000000000000000−2i2i2i−2i00
χ6388-88-8-8-8000000800000000000000000000000000000000000000000000000000000
χ6488-8-8800000000042−42−42420000000000000000000000000000000000000000000000000
χ6588-8-88000000000−424242−420000000000000000000000000000000000000000000000000
χ6616-1600082−82000000000000000000000000000000000000000000000000000000000000
χ6716-16000−8282000000000000000000000000000000000000000000000000000000000000

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