Finite Group Databasebeta

← Group #336839

Character table — Group #336839

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111111122222222444444444488888888888888888888888888881616161616161616323232
order12222222444444444488888888222244444444888888888888888844448888444
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-11111-1-1-1-11111-1-1-1-111111111-1-1-11-1-111-1-1-1
χ311111111111111111111111111-1-111-1-1-1-1111111111111-1-1-1-11111-1-11-111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111
χ51111111111111111111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11
χ61111111111111111111111-1-1-1-111-1-11111111111-1-11111-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111-1
χ71111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-11-1111111-1
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111111111-1-1-1-111-1-1-1-111-1-11
χ9111111111111111111-1-1-1-11111111111-1-11111-1-111-1-1-1-11111-1-1-1-1-1-11-1-1-1-1-1-111
χ10111111111111111111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-111-1-11-1-1
χ11111111111111111111-1-1-1-11111-1-111-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111-1-1
χ12111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-111111-111
χ13111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11-1-1-1111-11
χ14111111111111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-11-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-11-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1111-1-11-11
χ1722222222222-2-2-2-22-2-2000022220022000022-2-200-2-200000000000000-200000000
χ1822222222222-2-2-2-22-2-20000222200-2-20000-2-22200-2-200000000000000200000000
χ1922222222222-2-2-2-22-2-20000-2-2-2-200220000-2-222002200000000000000-200000000
χ2022222222222-2-2-2-22-2-20000-2-2-2-200-2-2000022-2-2002200000000000000200000000
χ2122222222-2-2-22222-2-2-2222200002200-2-2-2-20000-2-20000000000000000020000000
χ2222222222-2-2-22222-2-2-222220000-2-20022220000-2-200000000000000000-20000000
χ2322222222-2-2-22222-2-2-2-2-2-2-200002200-2-22200002200000000000000000-20000000
χ2422222222-2-2-22222-2-2-2-2-2-2-20000-2-20022-2-20000220000000000000000020000000
χ2522-2-22-22-20002-22-20002i2i−2i−2ii2i2−i2−i200002i−2i2-2000000i2−i2000022−2−222−2−2000000i2−i2000
χ2622-2-22-22-20002-22-20002i2i−2i−2ii2i2−i2−i20000−2i2i-22000000i2−i20000−2−22222−2−2000000−i2i2000
χ2722-2-22-22-20002-22-20002i2i−2i−2i−i2−i2i2i200002i−2i2-2000000−i2i20000−2−222−2−222000000−i2i2000
χ2822-2-22-22-20002-22-20002i2i−2i−2i−i2−i2i2i20000−2i2i-22000000−i2i2000022−2−2−2−222000000i2−i2000
χ2922-2-22-22-20002-22-2000−2i−2i2i2ii2i2−i2−i200002i−2i-22000000i2−i2000022−2−2−2−222000000−i2i2000
χ3022-2-22-22-20002-22-2000−2i−2i2i2ii2i2−i2−i20000−2i2i2-2000000i2−i20000−2−222−2−222000000i2−i2000
χ3122-2-22-22-20002-22-2000−2i−2i2i2i−i2−i2i2i200002i−2i-22000000−i2i20000−2−22222−2−2000000i2−i2000
χ3222-2-22-22-20002-22-2000−2i−2i2i2i−i2−i2i2i20000−2i2i2-2000000−i2i2000022−2−222−2−2000000−i2i2000
χ332-222-2-22-2-2-2222-2-222-20000000000000000000000002i2i−2i−2i2-22-200002i−2i000000000
χ342-222-2-22-2-2-2222-2-222-20000000000000000000000002i2i−2i−2i-22-220000−2i2i000000000
χ352-222-2-22-2-2-2222-2-222-2000000000000000000000000−2i−2i2i2i2-22-20000−2i2i000000000
χ362-222-2-22-2-2-2222-2-222-2000000000000000000000000−2i−2i2i2i-22-2200002i−2i000000000
χ372-2-222-2-222-220000-2002−22−22i−2i2i−2i002-200002i−2i002−200i2−i2i2−i20000i2−i2i2−i200002−200000
χ382-2-222-2-222-220000-2002−22−22i−2i2i−2i00-220000−2i2i002−200−i2i2−i2i20000i2−i2i2−i20000−2200000
χ392-2-222-2-222-220000-2002−22−2−2i2i−2i2i002-20000−2i2i002−200−i2i2−i2i20000−i2i2−i2i200002−200000
χ402-2-222-2-222-220000-2002−22−2−2i2i−2i2i00-2200002i−2i002−200i2−i2i2−i20000−i2i2−i2i20000−2200000
χ412-2-222-2-222-220000-200−22−222i−2i2i−2i002-200002i−2i00−2200−i2i2−i2i20000−i2i2−i2i20000−2200000
χ422-2-222-2-222-220000-200−22−222i−2i2i−2i00-220000−2i2i00−2200i2−i2i2−i20000−i2i2−i2i200002−200000
χ432-2-222-2-222-220000-200−22−22−2i2i−2i2i002-20000−2i2i00−2200i2−i2i2−i20000i2−i2i2−i20000−2200000
χ442-2-222-2-222-220000-200−22−22−2i2i−2i2i00-2200002i−2i00−2200−i2i2−i2i20000i2−i2i2−i200002−200000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000
χ4644-44-44-4-44-4-400004000000000000000000004i−4i000000000000000000000000000
χ4744-44-44-4-44-4-40000400000000000000000000−4i4i000000000000000000000000000
χ4844-44-44-4-4-4440000-40000000000000000000000000022−22−22220000000000000000000
χ4944-44-44-4-4-4440000-400000000000000000000000000−222222−220000000000000000000
χ5044-4-44-44-4000-44-4400000002i22i2−2i2−2i200000000000000−2i22i200000000000000000000000
χ5144-4-44-44-4000-44-440000000−2i2−2i22i22i2000000000000002i2−2i200000000000000000000000
χ524-444-4-44-444-444-4-4-4-4400000000000000000000000000000000000000000000000
χ534-444-4-44-444-4-4-444-44-400000000000000000000000000000000000000000000000
χ544-444-4-44-4-4-44-4-4444-4400000000000000000000000000000000000000000000000
χ554-44-444-4-400000000002i2−2i2−2i22i222−22−2222000000000000000000000000−2i2i2i−2i00000000000
χ564-44-444-4-400000000002i2−2i2−2i22i2−222222−220000000000000000000000002i−2i−2i2i00000000000
χ574-44-444-4-40000000000−2i22i22i2−2i222−22−22220000000000000000000000002i−2i−2i2i00000000000
χ584-44-444-4-40000000000−2i22i22i2−2i2−222222−22000000000000000000000000−2i2i2i−2i00000000000
χ594-4-444-4-44-44-4000040022−2222−220000000000000000−22220000000000000000000000000
χ604-4-444-4-44-44-40000400−2222−2222000000000000000022−220000000000000000000000000
χ614-4-4-4-44440004-4-44000000000000000000000000000000022−22−2222000000000000000
χ624-4-4-4-44440004-4-440000000000000000000000000000000−222222−22000000000000000
χ634-4-4-4-4444000-444-4000000000004-40000000000000000000000000000000000000
χ644-4-4-4-4444000-444-400000000000-440000000000000000000000000000000000000
χ65888-8-8-8-88000000000000000000000000000000000000000000000000000000000

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