Finite Group Databasebeta

← Group #72315280

Character table — Group #72315280

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82
size111122222244444444444444448888888888888888881616161616161616161616161616161616161616161616161616323232323232323232323232
order1222224444222222444444444422222222444444444422222244444444444444448888444444888888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-11111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1111111-1-111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1-1-1
χ411111111111111111111111111111111-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-11111
χ51111111111111111111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ81111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1
χ91111111111111111111-1-1-1-1111-1-111-1-111-1-111-1-111-1-111-1-11111-1-11111-1-111-1-1-1-1111111-1-1-1-1-1-111-1-1
χ101111111111111111111-1-1-1-1111-1-111-1-111-1-111-1-111-1-111-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1111111-1-111
χ111111111111111111111-1-1-1-1111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111-1-11111-1-111-1-1-1-111-1-111-1-1-1-111
χ121111111111111111111-1-1-1-1111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1111111-1-111-1-11111-1-1
χ131111111111111111111-1-1-1-1111-1-1-1-11111-1-1-1-11111-1-111-1-111-1-11111-1-111-1-111-1-11111-1-111-1-1-1-1-1-111
χ141111111111111111111-1-1-1-1111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-111-1-1111111-1-1
χ151111111111111111111-1-1-1-1111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1111111-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1
χ161111111111111111111-1-1-1-1111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-111-1-111-1-1-1-111-1-1-1-11111111111-1-1-1-111-1-111
χ1722222222222-2-22-2-22-2-200002-2-200002222000022-2-2002-2000000220000-2-200-2-2000000000000000000
χ1822222222222-2-22-2-22-2-200002-2-2000022-2-20000222200-22000000-2-200002200-2-2000000000000000000
χ1922222222222-2-22-2-22-2-200002-2-20000-2-2220000-2-2-2-2002-2000000-2-20000220022000000000000000000
χ2022222222222-2-22-2-22-2-200002-2-20000-2-2-2-20000-2-22200-22000000220000-2-20022000000000000000000
χ212222222222-22-2-22-2-22-20000-22-200220022002200-2-200-220000220000-2-200-2-200000000000000000000
χ222222222222-22-2-22-2-22-20000-22-2002200-2-200220022002-20000-2-200002200-2-200000000000000000000
χ232222222222-22-2-22-2-22-20000-22-200-2-2002200-2-200-2-200-220000-2-2000022002200000000000000000000
χ242222222222-22-2-22-2-22-20000-22-200-2-200-2-200-2-20022002-20000220000-2-2002200000000000000000000
χ252222222222-2-22-2-22-2-222222-2-22-2-2000022-2-200002222-2-2-2-20000000000000000220000000000000000
χ262222222222-2-22-2-22-2-222222-2-22-2-20000-2-2-2-20000-2-22222220000000000000000-2-20000000000000000
χ272222222222-2-22-2-22-2-22-2-2-2-2-2-222200002222000022-2-2-2-2220000000000000000-2-20000000000000000
χ282222222222-2-22-2-22-2-22-2-2-2-2-2-22220000-2-2220000-2-2-2-222-2-20000000000000000220000000000000000
χ29222222-2-2-2-222-222-2-2-222222-2-2222222200-2-2-2-2-2-200-2-200000000000000002-22-2000000000000000000
χ30222222-2-2-2-222-222-2-2-222222-2-2222-2-2-2-200-2-2222200-2-20000000000000000-22-22000000000000000000
χ31222222-2-2-2-222-222-2-2-22-2-2-2-2-2-22-2-222-2-20022-2-222002200000000000000002-2-22000000000000000000
χ32222222-2-2-2-222-222-2-2-22-2-2-2-2-2-22-2-2-2-222002222-2-200220000000000000000-222-2000000000000000000
χ33222222-2-2-2-22-222-22-22-20000-22-2000022000000-2-20000002-2002-200002-20000-222-20000000000000000
χ34222222-2-2-2-22-222-22-22-20000-22-2000022000000-2-2000000-2200-220000-220000-22-220000000000000000
χ35222222-2-2-2-22-222-22-22-20000-22-20000-2-2000000220000002-200-220000-2200002-22-20000000000000000
χ36222222-2-2-2-22-222-22-22-20000-22-20000-2-200000022000000-22002-200002-200002-2-220000000000000000
χ37222222-2-2-2-2-222-2222-2-200002-2-20022000000-2-2000000002-200002-200002-2-2200-220000000000000000
χ38222222-2-2-2-2-222-2222-2-200002-2-20022000000-2-200000000-220000-220000-22-22002-20000000000000000
χ39222222-2-2-2-2-222-2222-2-200002-2-200-2-200000022000000002-20000-220000-222-200-220000000000000000
χ40222222-2-2-2-2-222-2222-2-200002-2-200-2-20000002200000000-2200002-200002-22-2002-20000000000000000
χ41222222-2-2-2-2-2-2-2-2-2-22222222222-2-200000022000000-2-20000002-2-2200-222-20000000000000000000000
χ42222222-2-2-2-2-2-2-2-2-2-22222222222-2-200000022000000-2-2000000-222-2002-2-220000000000000000000000
χ43222222-2-2-2-2-2-2-2-2-2-2222-2-2-2-222222000000-2-2000000220000002-22-200-22-220000000000000000000000
χ44222222-2-2-2-2-2-2-2-2-2-2222-2-2-2-222222000000-2-200000022000000-22-22002-22-20000000000000000000000
χ452-2-22-2222-2-2222-2-2-222-222-2-2-2-222-20000002-20000002-200000000000000000000000000000000002i−2i2i−2i
χ462-2-22-2222-2-2222-2-2-222-222-2-2-2-222-20000002-20000002-20000000000000000000000000000000000−2i2i−2i2i
χ472-2-22-2222-2-2222-2-2-222-2-2-222-2-22-22000000-22000000-2200000000000000000000000000000000002i−2i−2i2i
χ482-2-22-2222-2-2222-2-2-222-2-2-222-2-22-22000000-22000000-220000000000000000000000000000000000−2i2i2i−2i
χ492-2-22-2222-2-2-2-2222-2-2-2-222-2-2222-22000000-220000002-2000000000000000000000000002-22-200000000
χ502-2-22-2222-2-2-2-2222-2-2-2-222-2-2222-22000000-220000002-200000000000000000000000000-22-2200000000
χ512-2-22-2222-2-2-2-2222-2-2-2-2-2-2222222-20000002-2000000-22000000000000000000000000002-2-2200000000
χ522-2-22-2222-2-2-2-2222-2-2-2-2-2-2222222-20000002-2000000-2200000000000000000000000000-222-200000000
χ532-2-22-22-2-22222-2-2-22-2-2-222-2-22222-2000000-22000000-22000000000000000000000022-2-200002-2000000
χ542-2-22-22-2-22222-2-2-22-2-2-222-2-22222-2000000-22000000-220000000000000000000000-2-2220000-22000000
χ552-2-22-22-2-22222-2-2-22-2-2-2-2-222222-220000002-20000002-2000000000000000000000022-2-20000-22000000
χ562-2-22-22-2-22222-2-2-22-2-2-2-2-222222-220000002-20000002-20000000000000000000000-2-22200002-2000000
χ572-2-22-22-2-222-2-2-222222-222-2-2-2-22-220000002-2000000-2200002-200002-2000000000000000000002-20000
χ582-2-22-22-2-222-2-2-222222-222-2-2-2-22-220000002-2000000-220000-220000-2200000000000000000000-220000
χ592-2-22-22-2-222-2-2-222222-2-2-222-2-222-2000000-220000002-200002-200002-200000000000000000000-220000
χ602-2-22-22-2-222-2-2-222222-2-2-222-2-222-2000000-220000002-20000-220000-22000000000000000000002-20000
χ614444-4-44-4-4400000000000000000000004-400000000000000220000-2-200000000002-22-2000000000000
χ624444-4-44-4-4400000000000000000000004-400000000000000-2-20000220000000000-22-22000000000000
χ634444-4-44-4-440000000000000000000000-4400000000000000220000-2-20000000000-22-22000000000000
χ644444-4-44-4-440000000000000000000000-4400000000000000-2-200002200000000002-22-2000000000000
χ654-4-444-4-44-440000000000000000000000000000004-40000002-20000-2200000000002-2-22000000000000
χ664-4-444-4-44-440000000000000000000000000000004-4000000-2200002-20000000000-222-2000000000000
χ674-4-444-4-44-44000000000000000000000000000000-440000002-20000-220000000000-222-2000000000000
χ684-4-444-4-44-44000000000000000000000000000000-44000000-2200002-200000000002-2-22000000000000
χ694-4-44-4444-4-44-4-4-4444-440000-44-400000000000000000000000000000000000000000000000000000000
χ704-4-44-4444-4-4-44-44-44-44400004-4-400000000000000000000000000000000000000000000000000000000
χ714-4-44-44-4-4444-44-44-4-44400004-4-400000000000000000000000000000000000000000000000000000000
χ724-4-44-44-4-444-4444-4-44-440000-44-400000000000000000000000000000000000000000000000000000000
χ738888-8-8-888-8000000000000000000000000000000000000000000000000000000000000000000000000
χ7488-8-80000000000000004-44-400000000000004i−4i4i−4i000000000000000000000000000000000000000000
χ7588-8-80000000000000004-44-40000000000000−4i4i−4i4i000000000000000000000000000000000000000000
χ7688-8-8000000000000000-44-4400000000000004i−4i−4i4i000000000000000000000000000000000000000000
χ7788-8-8000000000000000-44-440000000000000−4i4i4i−4i000000000000000000000000000000000000000000
χ788-88-80000000000000004-4-44000004-44-400000000000000000000000000000000000000000000000000
χ798-88-80000000000000004-4-4400000-44-4400000000000000000000000000000000000000000000000000
χ808-88-8000000000000000-444-4000004-4-4400000000000000000000000000000000000000000000000000
χ818-88-8000000000000000-444-400000-444-400000000000000000000000000000000000000000000000000
χ828-8-888-88-88-8000000000000000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).