Finite Group Databasebeta

← Group #323952

Character table — Group #323952

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111111122222222444444444444448888888888888888888888888888881616161632323232
order12222222444444444444448888888822244444448888888888888888888888882444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-11-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111-1-11-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11-11-1
χ61111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-11
χ71111111111111111111111-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-1-1-1111111111111-1-11111-1-1-1-1-11-11
χ81111111111111111111111-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111111-11-1
χ9111111111111111111-1-1-1-111111111-111-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-111-1-1
χ10111111111111111111-1-1-1-111111111-111-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-111-1-111
χ11111111111111111111-1-1-1-111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111
χ12111111111111111111-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1111-1-11
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111111111-1-1-1-1111111-1-1-1-111-1-1-111-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1111111-1-111-111-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1111111111111-1-11-1-11
χ17222222222-2-2-2-2222-2-222-2-22222-2-2-2-2-200200000022000000000000-2-2000000000000
χ18222222222-2-2-2-2222-2-222-2-2-2-2-2-22222-2002000000-2-200000000000022000000000000
χ19222222222-2-2-2-2222-2-2-2-2222222-2-2-2-2200-2000000-2-200000000000022000000000000
χ20222222222-2-2-2-2222-2-2-2-222-2-2-2-22222200-200000022000000000000-2-2000000000000
χ2122222222-22222-2-2-2-2-2222200000000-222-2-2-222-2-20000000000000000000000000000
χ2222222222-22222-2-2-2-2-2222200000000-2-2-2-222-2-2220000000000000000000000000000
χ2322222222-22222-2-2-2-2-2-2-2-2-200000000222222-2-2-2-20000000000000000000000000000
χ2422222222-22222-2-2-2-2-2-2-2-2-2000000002-2-22-2-222220000000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-22222-2-200000000200-2000000002i2i−2i−2i00000000002i2i−2i−2i00000000
χ2622222222-2-2-2-2-2-2-2-22222-2-200000000200-200000000−2i−2i2i2i0000000000−2i−2i2i2i00000000
χ2722222222-2-2-2-2-2-2-2-222-2-22200000000-2002000000002i2i−2i−2i0000000000−2i−2i2i2i00000000
χ2822222222-2-2-2-2-2-2-2-222-2-22200000000-200200000000−2i−2i2i2i00000000002i2i−2i−2i00000000
χ292-222-22-2-2022-2-2000002i−2i2i−2i22−2−222−2−200002-2002i−2ii2−i22−22−200000000i2−i2i2−i2i2−i200000000
χ302-222-22-2-2022-2-2000002i−2i2i−2i22−2−222−2−20000-2200−2i2ii2−i2−22−2200000000i2−i2−i2i2−i2i200000000
χ312-222-22-2-2022-2-2000002i−2i2i−2i−2−222−2−22200002-2002i−2i−i2i2−22−2200000000−i2i2−i2i2−i2i200000000
χ322-222-22-2-2022-2-2000002i−2i2i−2i−2−222−2−2220000-2200−2i2i−i2i22−22−200000000−i2i2i2−i2i2−i200000000
χ332-222-22-2-2022-2-200000−2i2i−2i2i22−2−222−2−200002-200−2i2i−i2i22−22−200000000−i2i2−i2i2−i2i200000000
χ342-222-22-2-2022-2-200000−2i2i−2i2i22−2−222−2−20000-22002i−2i−i2i2−22−2200000000−i2i2i2−i2i2−i200000000
χ352-222-22-2-2022-2-200000−2i2i−2i2i−2−222−2−22200002-200−2i2ii2−i2−22−2200000000i2−i2i2−i2i2−i200000000
χ362-222-22-2-2022-2-200000−2i2i−2i2i−2−222−2−2220000-22002i−2ii2−i22−22−200000000i2−i2−i2i2−i2i200000000
χ372-222-22-2-20-2-222000002i−2i−2i2i22−2−2−2−22202-20002i−2i00i2−i2i2−i2−i2i200000000−i2i2−222−200000000
χ382-222-22-2-20-2-222000002i−2i−2i2i22−2−2−2−2220-22000−2i2i00i2−i2−i2i2i2−i200000000−i2i22−2−2200000000
χ392-222-22-2-20-2-222000002i−2i−2i2i−2−22222−2−202-20002i−2i00−i2i2−i2i2i2−i200000000i2−i22−2−2200000000
χ402-222-22-2-20-2-222000002i−2i−2i2i−2−22222−2−20-22000−2i2i00−i2i2i2−i2−i2i200000000i2−i2−222−200000000
χ412-222-22-2-20-2-22200000−2i2i2i−2i22−2−2−2−22202-2000−2i2i00−i2i2−i2i2i2−i200000000i2−i2−222−200000000
χ422-222-22-2-20-2-22200000−2i2i2i−2i22−2−2−2−2220-220002i−2i00−i2i2i2−i2−i2i200000000i2−i22−2−2200000000
χ432-222-22-2-20-2-22200000−2i2i2i−2i−2−22222−2−202-2000−2i2i00i2−i2i2−i2−i2i200000000−i2i22−2−2200000000
χ442-222-22-2-20-2-22200000−2i2i2i−2i−2−22222−2−20-220002i−2i00i2−i2−i2i2i2−i200000000−i2i2−222−200000000
χ452-22-22-2-2222-22-22-2-22-200002i−2i2i−2i2i−2i2i−2i000000000000000000002i2i−2i−2i000000002-20000
χ462-22-22-2-2222-22-22-2-22-200002i−2i2i−2i2i−2i2i−2i00000000000000000000−2i−2i2i2i00000000-220000
χ472-22-22-2-2222-22-22-2-22-20000−2i2i−2i2i−2i2i−2i2i000000000000000000002i2i−2i−2i00000000-220000
χ482-22-22-2-2222-22-22-2-22-20000−2i2i−2i2i−2i2i−2i2i00000000000000000000−2i−2i2i2i000000002-20000
χ492-22-22-2-222-22-222-2-2-2200002i−2i2i−2i−2i2i−2i2i000000000000000022-2-200000000002i−2i000000
χ502-22-22-2-222-22-222-2-2-2200002i−2i2i−2i−2i2i−2i2i0000000000000000-2-2220000000000−2i2i000000
χ512-22-22-2-222-22-222-2-2-220000−2i2i−2i2i2i−2i2i−2i000000000000000022-2-20000000000−2i2i000000
χ522-22-22-2-222-22-222-2-2-220000−2i2i−2i2i2i−2i2i−2i0000000000000000-2-22200000000002i−2i000000
χ53444-4-4-44-404-4-440000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000000
χ54444-4-4-44-404-4-44000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000000
χ55444-4-4-44-40-444-40000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000000000
χ56444-4-4-44-40-444-4000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000000000
χ5744-4-4-44-4440000-44-400000000000000000000000000000000002i2−2i22i2−2i200000000000000
χ5844-4-4-44-4440000-44-40000000000000000000000000000000000−2i22i2−2i22i200000000000000
χ5944-4-4-44-44-400004-4400000000000000000000000000000022−2222−22000000000000000000
χ6044-4-4-44-44-400004-44000000000000000000000000000000−2222−2222000000000000000000
χ614-44-44-4-44-44-44-4-444-4400000000000000000000000000000000000000000000000000
χ624-44-44-4-44-4-44-44-4444-400000000000000000000000000000000000000000000000000
χ634-4-44-4-44440000-4-44000000000000000000000000000000000022−22−222200000000000000
χ644-4-44-4-44440000-4-440000000000000000000000000000000000−222222−2200000000000000
χ654-4-44-4-444-4000044-400000000000000000000000000000022−22−2222000000000000000000
χ664-4-44-4-444-4000044-4000000000000000000000000000000−222222−22000000000000000000
χ6788-888-8-8-8000000000000000000000000000000000000000000000000000000000000
χ688-8-8-8888-8000000000000000000000000000000000000000000000000000000000000

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