Finite Group Databasebeta

← Group #72321288

Character table — Group #72321288

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73
size1122222222244444444444888888888888888888161616161616161616161616161616161616161616161632323232323264646464
order12244881616161622244444816162448888816161616161616161616224481616323232323232323232323232323232322222444444
χ11111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111-1-1111-1-1-1-1-111111-1-1-1-111111111-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1
χ611111111111111111-1-1111-1-1-1-1-111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111
χ711111111111111111-1-1111-1-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-111
χ811111111111111111-1-1111-1-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-1
χ9111111111111-1-11-1-111111-1-11111-1-1111111-1-1-1-11111-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-111i−ii−i
χ10111111111111-1-11-1-111111-1-11111-1-1111111-1-1-1-11111-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-111−ii−ii
χ11111111111111-1-11-1-111111-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1−ii−ii
χ12111111111111-1-11-1-111111-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1i−ii−i
χ13111111111111-1-11-1-1-1-111111-1-1-11-1-111-1-1-1-1-1-1-1-11111111iiii−i−i−i−i−i−i−i−iiiii-1-111-1-1i−i−ii
χ14111111111111-1-11-1-1-1-111111-1-1-11-1-111-1-1-1-1-1-1-1-11111111−i−i−i−iiiiiiiii−i−i−i−i-1-111-1-1−iii−i
χ15111111111111-1-11-1-1-1-111111-1-1-11-1-111-1-1-1-1-1-1-1-1-1-1-1-1111iiii−i−i−i−i−i−i−i−iiiii11-1-111−iii−i
χ16111111111111-1-11-1-1-1-111111-1-1-11-1-111-1-1-1-1-1-1-1-1-1-1-1-1111−i−i−i−iiiiiiiii−i−i−i−i11-1-111i−i−ii
χ1722222222222-22-2-22-20022200000-22-2-2-2000022-2-222-2-200000000000000000002-200000000
χ1822222222222-22-2-22-20022200000-22-2-2-2000022-2-2-2-2220000000000000000000-2200000000
χ1922222222222-2-22-2-220022200000-2-22-2-20000-2-22222-2-20000000000000000000-2200000000
χ2022222222222-2-22-2-220022200000-2-22-2-20000-2-222-2-22200000000000000000002-200000000
χ212222222-2-2-2-2222222222-2-222222222-2-2-2-2-2-2-2-2-2-200002-2-200000000000000000000000000
χ222222222-2-2-2-2222222-2-22-2-2-2-2-2-2-2222-2-22222-2-2-2-20000-22200000000000000000000000000
χ232222222-2-2-2-22-2-22-2-2222-2-2-2-22222-2-2-2-2-2-2-2-222220000-22200000000000000000000000000
χ242222222-2-2-2-22-2-22-2-2-2-22-2-222-2-2-22-2-2-2-22222222200002-2-200000000000000000000000000
χ252222222-2-2-2-2-22-2-22-2002-2-200000-22-2220000-2-22200000000000000000000000002-22-20000
χ262222222-2-2-2-2-22-2-22-2002-2-200000-22-2220000-2-2220000000000000000000000000-22-220000
χ272222222-2-2-2-2-2-22-2-22002-2-200000-2-2222000022-2-200000000000000000000000002-2-220000
χ282222222-2-2-2-2-2-22-2-22002-2-200000-2-2222000022-2-20000000000000000000000000-222-20000
χ2922222-2-2000022222222-200222-2-2-2-2-200000000000000-20022−2−222−2−222−2−222−2−20000000000
χ3022222-2-2000022222222-200222-2-2-2-2-200000000000000-200−2−222−2−222−2−222−2−2220000000000
χ3122222-2-20000222222-2-2-200-2-2-222-2-2-20000000000000020022−2−222−2−2−2−222−2−2220000000000
χ3222222-2-20000222222-2-2-200-2-2-222-2-2-200000000000000200−2−222−2−22222−2−222−2−20000000000
χ3322222-2-200002-2-22-2-222-200-2-22-2-2-22200000000000000200i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000000000
χ3422222-2-200002-2-22-2-222-200-2-22-2-2-22200000000000000200−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000000000
χ3522222-2-200002-2-22-2-2-2-2-20022-222-22200000000000000-200i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i20000000000
χ3622222-2-200002-2-22-2-2-2-2-20022-222-22200000000000000-200−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i20000000000
χ37222-2-20022−2−2-2222-2-22202−22-2-2000002−222−2−22−22−2000002−2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ50000000000
χ38222-2-20022−2−2-2222-2-22202−22-2-2000002−222−2−22−22−2000002−2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ50000000000
χ39222-2-20022−2−2-2222-2-2-2-202−2-222000002−2−2−2222−22−200000−22ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ50000000000
χ40222-2-20022−2−2-2222-2-2-2-202−2-222000002−2−2−2222−22−200000−22−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ50000000000
χ41222-2-20022−2−2-2-2-22222202−2-22-2000002−222−2−2−22−2200000−22ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ70000000000
χ42222-2-20022−2−2-2-2-22222202−2-22-2000002−222−2−2−22−2200000−22−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ70000000000
χ43222-2-20022−2−2-2-2-2222-2-202−22-22000002−2−2−222−22−22000002−2ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ70000000000
χ44222-2-20022−2−2-2-2-2222-2-202−22-22000002−2−2−222−22−22000002−2−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ70000000000
χ45222-2-200−2−222-2222-2-2220−222-2-200000−22−2−222−22−2200000−22ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ70000000000
χ46222-2-200−2−222-2222-2-2220−222-2-200000−22−2−222−22−2200000−22−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ70000000000
χ47222-2-200−2−222-2222-2-2-2-20−22-22200000−2222−2−2−22−22000002−2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ70000000000
χ48222-2-200−2−222-2222-2-2-2-20−22-22200000−2222−2−2−22−22000002−2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ70000000000
χ49222-2-200−2−222-2-2-2222220−22-22-200000−22−2−2222−22−2000002−2ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ50000000000
χ50222-2-200−2−222-2-2-2222220−22-22-200000−22−2−2222−22−2000002−2−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ50000000000
χ51222-2-200−2−222-2-2-2222-2-20−222-2200000−2222−2−22−22−200000−22ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ50000000000
χ52222-2-200−2−222-2-2-2222-2-20−222-2200000−2222−2−22−22−200000−22−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ50000000000
χ5344444-4-40000-44-4-44-400-400000004-440000000000000000000000000000000000000000000
χ5444444-4-40000-4-44-4-4400-4000000044-40000000000000000000000000000000000000000000
χ55444-4-4002222−22−2244-4-4-4400022−2200000000−2222000022−22−2222000000000000000000000000000000000
χ56444-4-4002222−22−224-44-44-400022−2200000000−22220000−222222−22000000000000000000000000000000000
χ57444-4-400−22−22222244-4-4-44000−22220000000022−220000−222222−22000000000000000000000000000000000
χ58444-4-400−22−2222224-44-44-4000−22220000000022−22000022−22−2222000000000000000000000000000000000
χ5944-4-4444444400000000-4-4-40000000000000000004-40000000000000000000000000000000
χ6044-4-4444444400000000-4-4-4000000000000000000-440000000000000000000000000000000
χ6144-4-4444-4-4-4-400000000-444000000000000000000004-400000000000000000000000000000
χ6244-4-4444-4-4-4-400000000-44400000000000000000000-4400000000000000000000000000000
χ6388-88-8004242−42−42000000000−4242000000000000000000000000000000000000000000000000000
χ6488-88-800−42−42424200000000042−42000000000000000000000000000000000000000000000000000
χ6588-8-88-8-8000000000000800000000000000000000000000000000000000000000000000000
χ668-800042−424ζ−4ζ7−4ζ+4ζ74ζ3−4ζ5−4ζ3+4ζ50000004-400000022−22000002ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ50000000000000000000000000000000000000
χ678-800042−424ζ−4ζ7−4ζ+4ζ74ζ3−4ζ5−4ζ3+4ζ5000000-44000000−222200000−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ50000000000000000000000000000000000000
χ688-800042−42−4ζ+4ζ74ζ−4ζ7−4ζ3+4ζ54ζ3−4ζ50000004-400000022−2200000−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ50000000000000000000000000000000000000
χ698-800042−42−4ζ+4ζ74ζ−4ζ7−4ζ3+4ζ54ζ3−4ζ5000000-44000000−2222000002ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ50000000000000000000000000000000000000
χ708-8000−42424ζ3−4ζ5−4ζ3+4ζ5−4ζ+4ζ74ζ−4ζ70000004-4000000−2222000002ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ70000000000000000000000000000000000000
χ718-8000−42424ζ3−4ζ5−4ζ3+4ζ5−4ζ+4ζ74ζ−4ζ7000000-4400000022−2200000−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ70000000000000000000000000000000000000
χ728-8000−4242−4ζ3+4ζ54ζ3−4ζ54ζ−4ζ7−4ζ+4ζ70000004-4000000−222200000−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ70000000000000000000000000000000000000
χ738-8000−4242−4ζ3+4ζ54ζ3−4ζ54ζ−4ζ7−4ζ+4ζ7000000-4400000022−22000002ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ70000000000000000000000000000000000000

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