Finite Group Databasebeta

← Group #72342915

Character table — Group #72342915

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73
size1122222222244444444444888888888888888888161616161616161616161616161616161616163232323232323232323232326464
order12244881616161622244444816162448888816161616161616161616816163232323232323232323232323232323222222244444488
χ11111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ41111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ51111111111111111-1-11111-1-1-1-1-111111-1-1-1-11111-1-1-111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1
χ61111111111111111-1-11111-1-1-1-1-111111-1-1-1-11111-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111
χ71111111111111111-1-11111-1-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-111
χ81111111111111111-1-11111-1-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-111-1-1
χ91111111-1-1-1-11-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1111111-1-1-1-11111-1-1-1-11-11-11-11-11-11-11-1
χ101111111-1-1-1-11-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1111111-1-1-1-11111-1-1-1-1-11-11-11-11-11-11-11
χ111111111-1-1-1-11-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-111-1-1-1-11111-1-1-1-111111-11-1-11-111-11-1-11
χ121111111-1-1-1-11-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-111-1-1-1-11111-1-1-1-11111-11-111-11-1-11-111-1
χ131111111-1-1-1-11-1-1-1-1-1-111-1-111-1-1-11-1-1-1-1111111111-1-11111-1-1-1-1-1-1-1-111111-1-111-11-11-1-11-11
χ141111111-1-1-1-11-1-1-1-1-1-111-1-111-1-1-11-1-1-1-1111111111-1-11111-1-1-1-1-1-1-1-11111-111-1-11-11-111-11-1
χ151111111-1-1-1-11-1-1-1-1-1-111-1-111-1-1-11-1-1-1-1111111111-1-1-1-1-1-111111111-1-1-1-11-1-11-11-111-1-111-1
χ161111111-1-1-1-11-1-1-1-1-1-111-1-111-1-1-11-1-1-1-1111111111-1-1-1-1-1-111111111-1-1-1-1-111-11-11-1-111-1-11
χ17222222222222-2-2-2-2222222-2-22222-2-2222222-2-2-2-2-2-2-2000000000000000000000000000000
χ18222222222222-2-2-2-2-2-2222222-2-2-22-2-222-2-2-2-2-2-2-2-2222000000000000000000000000000000
χ1922222222222-22-22-200-222200000-22-2-2-2000022-2-2000000000000000000022000000-2-20000
χ2022222222222-22-22-200-222200000-22-2-2-2000022-2-20000000000000000000-2-2000000220000
χ2122222222222-2-22-2200-222200000-2-22-2-20000-2-22200000000000000000000022000000-2-200
χ2222222222222-2-22-2200-222200000-2-22-2-20000-2-222000000000000000000000-2-20000002200
χ232222222-2-2-2-2222222222-2-222222222-2-2-2-2-2-2-2-2-2-22-2-2000000000000000000000000000000
χ242222222-2-2-2-222222-2-222-2-2-2-2-2-2-2222-2-22222-2-2-2-2-222000000000000000000000000000000
χ252222222-2-2-2-2-22-22-200-22-2-200000-22-2220000-2-2220000000000000000000002-2000000-2200
χ262222222-2-2-2-2-22-22-200-22-2-200000-22-2220000-2-222000000000000000000000-220000002-200
χ272222222-2-2-2-2-2-22-2200-22-2-200000-2-2222000022-2-200000000000000000002-2000000-220000
χ282222222-2-2-2-2-2-22-2200-22-2-200000-2-2222000022-2-20000000000000000000-220000002-20000
χ2922222-2-2000022222222-200222-2-2-2-2-20000000000-20022−2−222−2−222−2−222−2−200000000000000
χ3022222-2-2000022222222-200222-2-2-2-2-20000000000-200−2−222−2−222−2−222−2−22200000000000000
χ3122222-2-2000022222-2-22-200-2-2-222-2-2-2000000000020022−2−222−2−2−2−222−2−22200000000000000
χ3222222-2-2000022222-2-22-200-2-2-222-2-2-20000000000200−2−222−2−22222−2−222−2−200000000000000
χ3322222-2-200002-2-2-2-2222-200-2-22-2-2-222000000000020022−2−2−2−22222−2−2−2−22200000000000000
χ3422222-2-200002-2-2-2-2222-200-2-22-2-2-2220000000000200−2−22222−2−2−2−22222−2−200000000000000
χ3522222-2-200002-2-2-2-2-2-22-20022-222-2220000000000-20022−2−2−2−222−2−22222−2−200000000000000
χ3622222-2-200002-2-2-2-2-2-22-20022-222-2220000000000-200−2−22222−2−222−2−2−2−22200000000000000
χ37222-2-20022−2−2-222-2-222202−22-2-2000002−222−2−22−22−202−2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ500000000000000
χ38222-2-20022−2−2-222-2-222202−22-2-2000002−222−2−22−22−202−2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ500000000000000
χ39222-2-20022−2−2-222-2-2-2-2202−2-222000002−2−2−2222−22−20−22ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ500000000000000
χ40222-2-20022−2−2-222-2-2-2-2202−2-222000002−2−2−2222−22−20−22−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ500000000000000
χ41222-2-20022−2−2-2-2-22222202−2-22-2000002−222−2−2−22−220−22ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ700000000000000
χ42222-2-20022−2−2-2-2-22222202−2-22-2000002−222−2−2−22−220−22−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ700000000000000
χ43222-2-20022−2−2-2-2-222-2-2202−22-22000002−2−2−222−22−2202−2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ700000000000000
χ44222-2-20022−2−2-2-2-222-2-2202−22-22000002−2−2−222−22−2202−2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ700000000000000
χ45222-2-200−2−222-222-2-22220−222-2-200000−22−2−222−22−220−22ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ700000000000000
χ46222-2-200−2−222-222-2-22220−222-2-200000−22−2−222−22−220−22−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ700000000000000
χ47222-2-200−2−222-222-2-2-2-220−22-22200000−2222−2−2−22−2202−2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ700000000000000
χ48222-2-200−2−222-222-2-2-2-220−22-22200000−2222−2−2−22−2202−2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ700000000000000
χ49222-2-200−2−222-2-2-2222220−22-22-200000−22−2−2222−22−202−2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ500000000000000
χ50222-2-200−2−222-2-2-2222220−22-22-200000−22−2−2222−22−202−2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ500000000000000
χ51222-2-200−2−222-2-2-222-2-220−222-2200000−2222−2−22−22−20−22ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ500000000000000
χ52222-2-200−2−222-2-2-222-2-220−222-2200000−2222−2−22−22−20−22−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ500000000000000
χ5344444-4-40000-44-44-400-4-400000004-440000000000000000000000000000000000000000000
χ5444444-4-40000-4-44-4400-4-4000000044-40000000000000000000000000000000000000000000
χ55444-4-4002222−22−2244-4-4400-4022−2200000000−2222000022−22−2222000000000000000000000000000000000
χ56444-4-4002222−22−224-444-400-4022−2200000000−22220000−222222−22000000000000000000000000000000000
χ57444-4-400−22−22222244-4-4400-40−22220000000022−220000−222222−22000000000000000000000000000000000
χ58444-4-400−22−2222224-444-400-40−22220000000022−22000022−22−2222000000000000000000000000000000000
χ5944-4-4444444400000000-4-4-40000000000000000000000000000000000000000022-2-2000000
χ6044-4-4444444400000000-4-4-400000000000000000000000000000000000000000-2-222000000
χ6144-4-4444-4-4-4-400000000-444000000000000000000000000000000000000000002-2-22000000
χ6244-4-4444-4-4-4-400000000-44400000000000000000000000000000000000000000-222-2000000
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+4ζ5000004-4000000022−22000002ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ50000000000000000000000000000000000000
χ678-800042−424ζ−4ζ7−4ζ+4ζ74ζ3−4ζ5−4ζ3+4ζ500000-440000000−222200000−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ50000000000000000000000000000000000000
χ688-800042−42−4ζ+4ζ74ζ−4ζ7−4ζ3+4ζ54ζ3−4ζ5000004-4000000022−2200000−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ50000000000000000000000000000000000000
χ698-800042−42−4ζ+4ζ74ζ−4ζ7−4ζ3+4ζ54ζ3−4ζ500000-440000000−2222000002ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ50000000000000000000000000000000000000
χ708-8000−42424ζ3−4ζ5−4ζ3+4ζ5−4ζ+4ζ74ζ−4ζ7000004-40000000−2222000002ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ70000000000000000000000000000000000000
χ718-8000−42424ζ3−4ζ5−4ζ3+4ζ5−4ζ+4ζ74ζ−4ζ700000-44000000022−2200000−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ70000000000000000000000000000000000000
χ728-8000−4242−4ζ3+4ζ54ζ3−4ζ54ζ−4ζ7−4ζ+4ζ7000004-40000000−222200000−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ70000000000000000000000000000000000000
χ738-8000−4242−4ζ3+4ζ54ζ3−4ζ54ζ−4ζ7−4ζ+4ζ700000-44000000022−22000002ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ70000000000000000000000000000000000000

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