Finite Group Databasebeta

← Group #325398

Character table — Group #325398

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111111122222222444444444444448888888888888888888888888888881616161632323232
order12222222444444444444448888888844444444448888888888888888888888884444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-11-1
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
χ71111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11-1-1-1-11111111111111111-1-1-1-1-11-11
χ81111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111111111111-11-1
χ9111111111111111111-1-1-1-111111111-11111-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11-1-11
χ10111111111111111111-1-1-1-111111111-11111-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-111-1
χ11111111111111111111-1-1-1-111111111-1-1-1-1-11111-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-111-1
χ12111111111111111111-1-1-1-111111111-1-1-1-1-11111-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1111-1-11
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-111
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111111111-1-1-1-11111-1-1-1-1-1-111-1-111
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11111-1-1-1-111111111-1-1-1-111-1-111-1-1
χ172222222222-2-2-2-222-2-222-2-22222-2-2-2-2200000000-222-2-2000000000000000000000000
χ182222222222-2-2-2-222-2-222-2-2-2-2-2-22222200000000-2-2-222000000000000000000000000
χ192222222222-2-2-2-222-2-2-2-2222222-2-2-2-2-2000000002-2-222000000000000000000000000
χ202222222222-2-2-2-222-2-2-2-222-2-2-2-22222-200000000222-2-2000000000000000000000000
χ2122222222-2-22222-2-2-2-2222200000000-222-2-222-2-2-20000000000000000000000000000
χ2222222222-2-22222-2-2-2-2222200000000-2-2-222-2-222-20000000000000000000000000000
χ2322222222-2-22222-2-2-2-2-2-2-2-200000000222-2-2-2-22220000000000000000000000000000
χ2422222222-2-22222-2-2-2-2-2-2-2-2000000002-2-22222-2-220000000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-22222-2-200000000-20000000020000000000002i2i−2i−2i2i2i−2i−2i00000000
χ2622222222-2-2-2-2-2-2-2-22222-2-200000000-2000000002000000000000−2i−2i2i2i−2i−2i2i2i00000000
χ2722222222-2-2-2-2-2-2-2-222-2-22200000000200000000-20000000000002i2i−2i−2i−2i−2i2i2i00000000
χ2822222222-2-2-2-2-2-2-2-222-2-22200000000200000000-2000000000000−2i−2i2i2i2i2i−2i−2i00000000
χ2922-222-2-2-2-2-222-2-2222-2000022-2-222-2-20000000000000000002i2i−2i−2i00000000002i−2i0000
χ3022-222-2-2-2-2-222-2-2222-2000022-2-222-2-2000000000000000000−2i−2i2i2i0000000000−2i2i0000
χ3122-222-2-2-2-2-222-2-2222-20000-2-222-2-2220000000000000000002i2i−2i−2i0000000000−2i2i0000
χ3222-222-2-2-2-2-222-2-2222-20000-2-222-2-222000000000000000000−2i−2i2i2i00000000002i−2i0000
χ3322-222-2-2-2-2-2-2-22222-22000022-2-2-2-222000000000000002i2i−2i−2i0000000000002i−2i000000
χ3422-222-2-2-2-2-2-2-22222-22000022-2-2-2-22200000000000000−2i−2i2i2i000000000000−2i2i000000
χ3522-222-2-2-2-2-2-2-22222-220000-2-22222-2-2000000000000002i2i−2i−2i000000000000−2i2i000000
χ3622-222-2-2-2-2-2-2-22222-220000-2-22222-2-200000000000000−2i−2i2i2i0000000000002i−2i000000
χ372-222-2-2-22002-22-200002i−2i2i−2ii2−i2i2−i2i2−i2i2−i20002i−2i002-202−22−2000000002−22−2i2−i2i2−i200000000
χ382-222-2-2-22002-22-200002i−2i2i−2ii2−i2i2−i2i2−i2i2−i2000−2i2i00-2202−22−200000000−22−22−i2i2−i2i200000000
χ392-222-2-2-22002-22-200002i−2i2i−2i−i2i2−i2i2−i2i2−i2i20002i−2i002-20−22−2200000000−22−22−i2i2−i2i200000000
χ402-222-2-2-22002-22-200002i−2i2i−2i−i2i2−i2i2−i2i2−i2i2000−2i2i00-220−22−22000000002−22−2i2−i2i2−i200000000
χ412-222-2-2-22002-22-20000−2i2i−2i2ii2−i2i2−i2i2−i2i2−i20002i−2i00-220−22−22000000002−22−2−i2i2−i2i200000000
χ422-222-2-2-22002-22-20000−2i2i−2i2ii2−i2i2−i2i2−i2i2−i2000−2i2i002-20−22−2200000000−22−22i2−i2i2−i200000000
χ432-222-2-2-22002-22-20000−2i2i−2i2i−i2i2−i2i2−i2i2−i2i20002i−2i00-2202−22−200000000−22−22i2−i2i2−i200000000
χ442-222-2-2-22002-22-20000−2i2i−2i2i−i2i2−i2i2−i2i2−i2i2000−2i2i002-202−22−2000000002−22−2−i2i2−i2i200000000
χ452-222-2-2-2200-22-2200002i−2i−2i2ii2−i2i2−i2−i2i2−i2i202-2002i−2i0002−2−2200000000i2−i2−i2i2−222−200000000
χ462-222-2-2-2200-22-2200002i−2i−2i2ii2−i2i2−i2−i2i2−i2i20-2200−2i2i0002−2−2200000000−i2i2i2−i22−2−2200000000
χ472-222-2-2-2200-22-2200002i−2i−2i2i−i2i2−i2i2i2−i2i2−i202-2002i−2i000−222−200000000−i2i2i2−i22−2−2200000000
χ482-222-2-2-2200-22-2200002i−2i−2i2i−i2i2−i2i2i2−i2i2−i20-2200−2i2i000−222−200000000i2−i2−i2i2−222−200000000
χ492-222-2-2-2200-22-220000−2i2i2i−2ii2−i2i2−i2−i2i2−i2i202-200−2i2i000−222−200000000i2−i2−i2i22−2−2200000000
χ502-222-2-2-2200-22-220000−2i2i2i−2ii2−i2i2−i2−i2i2−i2i20-22002i−2i000−222−200000000−i2i2i2−i2−222−200000000
χ512-222-2-2-2200-22-220000−2i2i2i−2i−i2i2−i2i2i2−i2i2−i202-200−2i2i0002−2−2200000000−i2i2i2−i2−222−200000000
χ522-222-2-2-2200-22-220000−2i2i2i−2i−i2i2−i2i2i2−i2i2−i20-22002i−2i0002−2−2200000000i2−i2−i2i22−2−2200000000
χ53444-4-44-4-44-400004-40000000000000000000000000000000022−2222−220000000000000000
χ54444-4-44-4-44-400004-400000000000000000000000000000000−2222−22220000000000000000
χ55444-4-44-4-4-440000-44000000000000000000000000000022−2222−2200000000000000000000
χ56444-4-44-4-4-440000-440000000000000000000000000000−2222−222200000000000000000000
χ5744-444-4-4-44444-4-4-4-4-4400000000000000000000000000000000000000000000000000
χ5844-444-4-4-444-4-444-4-44-400000000000000000000000000000000000000000000000000
χ5944-4-4-4-4444-40000-4400000000000000000000000000002i2−2i2−2i22i200000000000000000000
χ6044-4-4-4-4444-40000-440000000000000000000000000000−2i22i22i2−2i200000000000000000000
χ6144-4-4-4-444-4400004-4000000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ6244-4-4-4-444-4400004-400000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ634-4-44-444-4004-4-44000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000000
χ644-4-44-444-4004-4-4400000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000000
χ654-4-44-444-400-444-4000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000000000
χ664-4-44-444-400-444-400000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000000000
χ678-88-88-88-8000000000000000000000000000000000000000000000000000000000000
χ688-8-8-888-88000000000000000000000000000000000000000000000000000000000000

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