Finite Group Databasebeta

← Group #72220535

Character table — Group #72220535

Order 2304.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111224488889999161618181818181818181818181818182424242432323636363636363636363636363636363636363636484848484848727272729696144144
order122244223666222212124444448888888844446622444444888888888888221212121244446644
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1
χ4111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ5111111-1-11111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ6111111-1-1111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111
χ7111111-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111
χ8111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1
χ91111-1-11-111111111-1-1-1-111111111111111-1-11-11-1-1-111-1-1-1-1-1-11111-1-1-1-11-111-1-111-1-11-11-1
χ101111-1-11-111111111-1-1-1-1111111111111-1-1111-11-1-1-111-1-1-1-1-1-11111-1-1-1-1-11-1-111-1-111-11-11
χ111111-1-11-111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11-11-1-1-111-1-11111-1-1-1-111111-111-1-1-1-1111-1-11
χ121111-1-11-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111-11-1-1-111-1-11111-1-1-1-11111-11-1-11111-1-1-111-1
χ131111-1-1-1111111111-1-1-1-111111111111111-1-1-11-11-1-1-1-111-1-1-1-1-1-1-1-11111-1111-1-111-1-1-11-11
χ141111-1-1-1111111111-1-1-1-1111111111111-1-111-11-11-1-1-1-111-1-1-1-1-1-1-1-111111-1-1-111-1-1111-11-1
χ151111-1-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-11-11-1-1-1-11111111111-1-1-1-1-1111-1-1-1-111-111-1
χ161111-1-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-11-11-1-1-1-11111111111-1-1-1-11-1-1-11111-1-11-1-11
χ1722222222222222222222-2-2-2-20000000000002222-2-2-2-2-2-200000000000000000000000000
χ18222222222222-2-2-2-222-2-20000i2i2i2i2−i2−i2−i2−i2000022-2-2000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200000000000000
χ19222222222222-2-2-2-222-2-20000−i2−i2−i2−i2i2i2i2i2000022-2-2000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200000000000000
χ20222222-2-2222222222222-2-2-2-2000000000000-2-2-2-2-2-2222200000000000000000000000000
χ21222222-2-22222-2-2-2-222-2-20000i2i2i2i2−i2−i2−i2−i20000-2-222000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i200000000000000
χ22222222-2-22222-2-2-2-222-2-20000−i2−i2−i2−i2i2i2i2i20000-2-222000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i200000000000000
χ232222-2-22-222222222-2-2-2-2-2-2-2-20000000000002-22-222-2-22200000000000000000000000000
χ242222-2-22-22222-2-2-2-2-2-2220000i2i2i2i2−i2−i2−i2−i200002-2-22000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i200000000000000
χ252222-2-22-22222-2-2-2-2-2-2220000−i2−i2−i2−i2i2i2i2i200002-2-22000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i200000000000000
χ262222-2-2-2222222222-2-2-2-2-2-2-2-2000000000000-22-222222-2-200000000000000000000000000
χ272222-2-2-222222-2-2-2-2-2-2220000i2i2i2i2−i2−i2−i2−i20000-222-2000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i200000000000000
χ282222-2-2-222222-2-2-2-2-2-2220000−i2−i2−i2−i2i2i2i2i20000-222-2000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i200000000000000
χ2922-2-22-20022-2-22-2-222-22-222-2-200000000000000002-2000000002i−2i2i−2i2i−2i2i−2i00000000000000
χ3022-2-22-20022-2-22-2-222-22-222-2-200000000000000002-200000000−2i2i−2i2i−2i2i−2i2i00000000000000
χ3122-2-22-20022-2-22-2-222-22-2-2-22222-2-222-2-200000000-2200002-22-20000000000000000000000
χ3222-2-22-20022-2-22-2-222-22-2-2-222-2-222-2-22200000000-220000-22-220000000000000000000000
χ3322-2-22-20022-2-2-222-22-2-220000i2i2−i2−i2−i2−i2i2i200000000002i−2i2i−2ii2−i2−i2i22−2−222−2−2200000000000000
χ3422-2-22-20022-2-2-222-22-2-220000i2i2−i2−i2−i2−i2i2i20000000000−2i2i−2i2ii2−i2−i2i2−222−2−222−200000000000000
χ3522-2-22-20022-2-2-222-22-2-220000−i2−i2i2i2i2i2−i2−i200000000002i−2i2i−2i−i2i2i2−i2−222−2−222−200000000000000
χ3622-2-22-20022-2-2-222-22-2-220000−i2−i2i2i2i2i2−i2−i20000000000−2i2i−2i2i−i2i2i2−i22−2−222−2−2200000000000000
χ3722-2-2-220022-2-22-2-22-22-2222-2-20000000000000000-22000000002i−2i2i−2i−2i2i−2i2i00000000000000
χ3822-2-2-220022-2-22-2-22-22-2222-2-20000000000000000-2200000000−2i2i−2i2i2i−2i2i−2i00000000000000
χ3922-2-2-220022-2-22-2-22-22-22-2-22222-2-222-2-2000000002-20000-22-220000000000000000000000
χ4022-2-2-220022-2-22-2-22-22-22-2-222-2-222-2-222000000002-200002-22-20000000000000000000000
χ4122-2-2-220022-2-2-222-2-222-20000i2i2−i2−i2−i2−i2i2i200000000002i−2i−2i2i−i2i2i2−i22−2−22−222−200000000000000
χ4222-2-2-220022-2-2-222-2-222-20000i2i2−i2−i2−i2−i2i2i20000000000−2i2i2i−2i−i2i2i2−i2−222−22−2−2200000000000000
χ4322-2-2-220022-2-2-222-2-222-20000−i2−i2i2i2i2i2−i2−i200000000002i−2i−2i2ii2−i2−i2i2−222−22−2−2200000000000000
χ4422-2-2-220022-2-2-222-2-222-20000−i2−i2i2i2i2i2−i2−i20000000000−2i2i2i−2ii2−i2−i2i22−2−22−222−200000000000000
χ452-22-200002-22-2-22-2200002-2-222-22-22-22-2002-2000000000000000000000000002-2002-20000
χ462-22-200002-22-2-22-2200002-2-222-22-22-22-200-2200000000000000000000000000-2200-220000
χ472-22-200002-22-2-22-2200002-2-22-22-22-22-22002-2000000000000000000000000002-200-220000
χ482-22-200002-22-2-22-2200002-2-22-22-22-22-2200-2200000000000000000000000000-22002-20000
χ492-2-2200002-2-22-2-2220000-22-222-2-222-2-222-2000000000000000000000000002-2002-2000000
χ502-2-2200002-2-22-2-2220000-22-222-2-222-2-22-2200000000000000000000000000-2200-22000000
χ512-2-2200002-2-22-2-2220000-22-22-222-2-222-22-2000000000000000000000000002-200-22000000
χ522-2-2200002-2-22-2-2220000-22-22-222-2-222-2-2200000000000000000000000000-22002-2000000
χ534-44-400004-44-44-44-4000000002i2−2i22i2−2i2−2i22i2−2i22i20000000000000000000000000000000000000000
χ544-44-400004-44-44-44-400000000−2i22i2−2i22i22i2−2i22i2−2i20000000000000000000000000000000000000000
χ554-44-400004-44-4-44-440000-444-4000000000000000000000000000000000000000000000000
χ564-4-4400004-4-4444-4-4000000002i2−2i2−2i22i2−2i22i22i2−2i20000000000000000000000000000000000000000
χ574-4-4400004-4-4444-4-400000000−2i22i22i2−2i22i2−2i2−2i22i20000000000000000000000000000000000000000
χ584-4-4400004-4-44-4-44400004-44-4000000000000000000000000000000000000000000000000
χ5988888888-1-1-1-10000-1-1000000000000002222-1-10000000000000000000022-1-1-1-10000-1-100
χ6088888888-1-1-1-10000-1-100000000000000-2-2-2-2-1-100000000000000000000-2-2111100001100
χ61888888-8-8-1-1-1-10000-1-10000000000000022221100000000000000000000-2-2-1-1-1-100001100
χ62888888-8-8-1-1-1-10000-1-100000000000000-2-2-2-211000000000000000000002211110000-1-100
χ638888-8-88-8-1-1-1-10000110000000000000022-2-2-11000000000000000000002-2-1-1110000-1100
χ648888-8-88-8-1-1-1-100001100000000000000-2-222-1100000000000000000000-2211-1-100001-100
χ658888-8-8-88-1-1-1-10000110000000000000022-2-21-100000000000000000000-22-1-11100001-100
χ668888-8-8-88-1-1-1-100001100000000000000-2-2221-1000000000000000000002-211-1-10000-1100
χ671616-16-1616-1600-2-2220000-22000000000000000000000000000000000000000000000000000000
χ681616-16-16-161600-2-22200002-2000000000000000000000000000000000000000000000000000000
χ6916-1616-160000-22-2200000000000000000000004-400000000000000000000000000-2200000000
χ7016-1616-160000-22-220000000000000000000000-44000000000000000000000000002-200000000
χ7116-16-16160000-222-2000000000000000000004-400000000000000000000000000-220000000000
χ7216-16-16160000-222-200000000000000000000-44000000000000000000000000002-20000000000

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