Finite Group Databasebeta

← Group #144146

Character table — Group #144146

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size1111222222222244444444448888888888888888888888883232323232323232
order122222444444444488888888888888881616161616161616161616161616161624444444
χ111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1111-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111-1-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-11-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-111-111-1-1
χ92222222222222222-2-2-2-2-2-2-2-22222-2-2-2-2000000000000000000000000
χ102222222222222222-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000000000000
χ1122222222-2-2-2-222-2-222-2-222-2-200000000000000002222-2-2-2-200000000
χ1222222222-2-2-2-222-2-222-2-222-2-20000000000000000-2-2-2-2222200000000
χ1322222222-2-2-2-222-2-2-2-222-2-222000000002222-2-2-2-20000000000000000
χ1422222222-2-2-2-222-2-2-2-222-2-22200000000-2-2-2-222220000000000000000
χ15222222-2-222-2-2-2-22-200000000000022-2-222−2−222−2−222−2−222−2−200000000
χ16222222-2-222-2-2-2-22-200000000000022-2-2−2−222−2−222−2−222−2−22200000000
χ17222222-2-222-2-2-2-22-2000000000000-2-22222−2−222−2−2−2−222−2−22200000000
χ18222222-2-222-2-2-2-22-2000000000000-2-222−2−222−2−22222−2−222−2−200000000
χ19222222-2-2-2-222-2-2-220000000022-2-2000022−2−2−2−22222−2−2−2−22200000000
χ20222222-2-2-2-222-2-2-220000000022-2-20000−2−22222−2−2−2−22222−2−200000000
χ21222222-2-2-2-222-2-2-2200000000-2-222000022−2−2−2−222−2−22222−2−200000000
χ22222222-2-2-2-222-2-2-2200000000-2-2220000−2−22222−2−222−2−2−2−22200000000
χ232222-2-2-2-2222222-2-222-2-2-2-222000000000000000000000000200-20000
χ242222-2-2-2-2222222-2-222-2-2-2-222000000000000000000000000-20020000
χ252222-2-2-2-2222222-2-2-2-22222-2-200000000000000000000000002-200000
χ262222-2-2-2-2222222-2-2-2-22222-2-20000000000000000000000000-2200000
χ272222-2-2-2-2-2-2-2-222222222-2-2-2-20000000000000000000000000000002i−2i
χ282222-2-2-2-2-2-2-2-222222222-2-2-2-2000000000000000000000000000000−2i2i
χ292222-2-2-2-2-2-2-2-22222-2-2-2-2222200000000000000000000000000002-200
χ302222-2-2-2-2-2-2-2-22222-2-2-2-222220000000000000000000000000000-2200
χ312-2-222-22-200002-200002-2002-2i2−i2i2−i2i2−i2i2−i200002-22-2i2−i2i2−i2i2−i2i2−i200000000
χ322-2-222-22-200002-200002-2002-2i2−i2i2−i2i2−i2i2−i20000-22-22−i2i2−i2i2−i2i2−i2i200000000
χ332-2-222-22-200002-200002-2002-2−i2i2−i2i2−i2i2−i2i200002-22-2−i2i2−i2i2−i2i2−i2i200000000
χ342-2-222-22-200002-200002-2002-2−i2i2−i2i2−i2i2−i2i20000-22-22i2−i2i2−i2i2−i2i2−i200000000
χ352-2-222-22-200002-20000-2200-22i2−i2i2−i2−i2i2−i2i22-22-20000i2−i2i2−i2−i2i2−i2i200000000
χ362-2-222-22-200002-20000-2200-22i2−i2i2−i2−i2i2−i2i2-22-220000−i2i2−i2i2i2−i2i2−i200000000
χ372-2-222-22-200002-20000-2200-22−i2i2−i2i2i2−i2i2−i22-22-20000−i2i2−i2i2i2−i2i2−i200000000
χ382-2-222-22-200002-20000-2200-22−i2i2−i2i2i2−i2i2−i2-22-220000i2−i2i2−i2−i2i2−i2i200000000
χ392-2-222-2-220000-22002-2002-200i2−i2−i2i2i2−i2−i2i22−2−222−2−2200002i−2i−2i2i00000000
χ402-2-222-2-220000-22002-2002-200i2−i2−i2i2i2−i2−i2i2−222−2−222−20000−2i2i2i−2i00000000
χ412-2-222-2-220000-22002-2002-200−i2i2i2−i2−i2i2i2−i22−2−222−2−220000−2i2i2i−2i00000000
χ422-2-222-2-220000-22002-2002-200−i2i2i2−i2−i2i2i2−i2−222−2−222−200002i−2i−2i2i00000000
χ432-2-222-2-220000-2200-2200-2200i2−i2−i2i2−i2i2i2−i22−2−22−222−22i−2i−2i2i000000000000
χ442-2-222-2-220000-2200-2200-2200i2−i2−i2i2−i2i2i2−i2−222−22−2−22−2i2i2i−2i000000000000
χ452-2-222-2-220000-2200-2200-2200−i2i2i2−i2i2−i2−i2i22−2−22−222−2−2i2i2i−2i000000000000
χ462-2-222-2-220000-2200-2200-2200−i2i2i2−i2i2−i2−i2i2−222−22−2−222i−2i−2i2i000000000000
χ474444-4-44444-4-4-4-4-440000000000000000000000000000000000000000
χ484444-4-444-4-444-4-44-40000000000000000000000000000000000000000
χ494-4-44-444-40000-44004-400-440000000000000000000000000000000000
χ504-4-44-444-40000-4400-44004-40000000000000000000000000000000000
χ514-4-44-44-4400004-400004-400-4400000000000000000000000000000000
χ524-4-44-44-4400004-40000-44004-400000000000000000000000000000000
χ5388-8-80000008-800000000000000000000000000000000000000000000
χ5488-8-8000000-8800000000000000000000000000000000000000000000
χ558-88-800008-80000000000000000000000000000000000000000000000
χ568-88-80000-880000000000000000000000000000000000000000000000

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