Finite Group Databasebeta

← Group #336648

Character table — Group #336648

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111111122222222444444444488888888888888888888888888881616161616161616323232
order12222222444444444488888888224444444444888888888888888844448888444
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-11111-1-1-1-11111-1-1-1-111111111-11-1-1-1-111-1-1-1
χ311111111111111111111111111-1-111-1-1-1-1111111111111-1-1-1-111111-1-1-111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1111
χ51111111111111111111111-1-1-1-111111111-1-11111-1-11111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-111-1
χ61111111111111111111111-1-1-1-111-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11
χ71111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-111-1-111-1-11
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11-1-1-1111111-1
χ9111111111111111111-1-1-1-111111111-1-1111111-1-111-1-1-1-11111-1-1-1-11-1-1-1-1-1-1-1-111
χ10111111111111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-11-1-1
χ11111111111111111111-1-1-1-11111-1-11111-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111-1-1
χ12111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-11-1-11111-111
χ13111111111111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-11-1
χ14111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111111-1-1-1-1-1111-11
χ15111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111111111-11-1-111-1-11-11
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111111111111111-1-1-1-1-11-1
χ172222222222-2-22-2-22-2-20000222200220000-2-2-2-200-2-200000000000020000000000
χ182222222222-2-22-2-22-2-20000222200-2-20000222200-2-2000000000000-20000000000
χ192222222222-2-22-2-22-2-20000-2-2-2-20022000022-2-20022000000000000-20000000000
χ202222222222-2-22-2-22-2-20000-2-2-2-200-2-20000-2-222002200000000000020000000000
χ2122222222-2-222-222-2-2-2222200002200-2-2-2-20000-2-20000000000000002000000000
χ2222222222-2-222-222-2-2-222220000-2-20022220000-2-2000000000000000-2000000000
χ2322222222-2-222-222-2-2-2-2-2-2-20000220022-2-2000022000000000000000-2000000000
χ2422222222-2-222-222-2-2-2-2-2-2-20000-2-200-2-2220000220000000000000002000000000
χ252-222-2-2-22002-202-200022-2-2i2i2−i2−i200002i−2i2i−2i000000i2−i2000022−2−2i2i2−i2−i20000002−2000
χ262-222-2-2-22002-202-200022-2-2i2i2−i2−i20000−2i2i−2i2i000000i2−i20000−2−222i2i2−i2−i2000000−22000
χ272-222-2-2-22002-202-200022-2-2−i2−i2i2i200002i−2i2i−2i000000−i2i20000−2−222−i2−i2i2i2000000−22000
χ282-222-2-2-22002-202-200022-2-2−i2−i2i2i20000−2i2i−2i2i000000−i2i2000022−2−2−i2−i2i2i20000002−2000
χ292-222-2-2-22002-202-2000-2-222i2i2−i2−i200002i−2i−2i2i000000i2−i20000−2−222−i2−i2i2i20000002−2000
χ302-222-2-2-22002-202-2000-2-222i2i2−i2−i20000−2i2i2i−2i000000i2−i2000022−2−2−i2−i2i2i2000000−22000
χ312-222-2-2-22002-202-2000-2-222−i2−i2i2i200002i−2i−2i2i000000−i2i2000022−2−2i2i2−i2−i2000000−22000
χ322-222-2-2-22002-202-2000-2-222−i2−i2i2i20000−2i2i2i−2i000000−i2i20000−2−222i2i2−i2−i20000002−2000
χ332-22-22-22-2-2-2222-2-222-20000000000000000000000002i2i−2i−2i2-22-20000002i−2i0000000
χ342-22-22-22-2-2-2222-2-222-20000000000000000000000002i2i−2i−2i-22-22000000−2i2i0000000
χ352-22-22-22-2-2-2222-2-222-2000000000000000000000000−2i−2i2i2i2-22-2000000−2i2i0000000
χ362-22-22-22-2-2-2222-2-222-2000000000000000000000000−2i−2i2i2i-22-220000002i−2i0000000
χ372-2-2-2-22222-200-2002002−22−22-22-2000000002-22-22−2002−22−200002−22−200002−200000
χ382-2-2-2-22222-200-2002002−22−22-22-200000000-22-222−200−22−2200002−22−20000−2200000
χ392-2-2-2-22222-200-2002002−22−2-22-22000000002-2-222−200−22−220000−22−2200002−200000
χ402-2-2-2-22222-200-2002002−22−2-22-2200000000-222-22−2002−22−20000−22−220000−2200000
χ412-2-2-2-22222-200-200200−22−222-22-2000000002-22-2−2200−22−220000−22−220000−2200000
χ422-2-2-2-22222-200-200200−22−222-22-200000000-22-22−22002−22−20000−22−2200002−200000
χ432-2-2-2-22222-200-200200−22−22-22-22000000002-2-22−22002−22−200002−22−20000−2200000
χ442-2-2-2-22222-200-200200−22−22-22-2200000000-222-2−2200−22−2200002−22−200002−200000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000
χ46444-4-44-4-4004-40-44000000000000000000000000000000022−22−2222000000000000000
χ47444-4-44-4-4004-40-440000000000000000000000000000000−222222−22000000000000000
χ48444-4-44-4-400-4404-4000000000004-40000000000000000000000000000000000000
χ49444-4-44-4-400-4404-400000000000-440000000000000000000000000000000000000
χ5044-44-4-44-44-400400-40000000000004-400000000000000000000000000000000000
χ5144-44-4-44-44-400400-4000000000000-4400000000000000000000000000000000000
χ5244-44-4-44-4-4400-4004000000000000000000000000002i2−2i2−2i22i20000000000000000000
χ5344-44-4-44-4-4400-400400000000000000000000000000−2i22i22i2−2i20000000000000000000
χ5444-4-44-4-44000000000022−22−22222i2−2i2−2i22i20000000000000000000000002i−2i−2i2i00000000000
χ5544-4-44-4-44000000000022−22−2222−2i22i22i2−2i2000000000000000000000000−2i2i2i−2i00000000000
χ5644-4-44-4-440000000000−222222−222i2−2i2−2i22i2000000000000000000000000−2i2i2i−2i00000000000
χ5744-4-44-4-440000000000−222222−22−2i22i22i2−2i20000000000000000000000002i−2i−2i2i00000000000
χ584-444-4-4-4400-440-4400000002i22i2−2i2−2i200000000000000−2i22i200000000000000000000000
χ594-444-4-4-4400-440-440000000−2i2−2i22i22i2000000000000002i2−2i200000000000000000000000
χ604-44-44-44-44444-4-4-4-4-4400000000000000000000000000000000000000000000000
χ614-44-44-44-444-4-4-444-44-400000000000000000000000000000000000000000000000
χ624-44-44-44-4-4-4-4-44444-4400000000000000000000000000000000000000000000000
χ634-4-4-4-4444-4400400-40022−2222−220000000000000000−22220000000000000000000000000
χ644-4-4-4-4444-4400400-400−2222−2222000000000000000022−220000000000000000000000000
χ658-8-8888-8-8000000000000000000000000000000000000000000000000000000000

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