Finite Group Databasebeta

← Group #336641

Character table — Group #336641

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111111122222222444444444488888888888888888888888888881616161616161616323232
order12222222444444444488888888224444444444888888888888888824448888244
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-111111111-11-1-1-1-111-1-1-1
χ311111111111111111111111111-1-1-1-111-1-1111111111111-1-1-1-111111-1-1-111-1-1-1-1-1
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
χ51111111111111111111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11
χ61111111111111111111111-1-1-1-11111-1-111111111-1-11111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-111-1
χ71111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11-1-1-1111111-1
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111111111-1-1-1-1-1-111-1-111-1-11
χ9111111111111111111-1-1-1-11111111111-1-11111-1-111-1-1-1-11111-1-1-1-11-1-1-1-1-1-1-11-11
χ10111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-11-1
χ11111111111111111111-1-1-1-11111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-11-1
χ12111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-11-1-111111-11
χ13111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1-1-1-111-111
χ14111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111111-1-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-11-1-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-11-1-111-1-1-111
χ172222222222-22-2-2-22-2-2000022220000220022-2-200-2-2000000000000-20000000000
χ182222222222-22-2-2-22-2-2000022220000-2-200-2-22200-2-200000000000020000000000
χ192222222222-22-2-2-22-2-20000-2-2-2-200002200-2-2220022000000000000-20000000000
χ202222222222-22-2-2-22-2-20000-2-2-2-20000-2-20022-2-2002200000000000020000000000
χ2122222222-2-22-2222-2-2-22222000022-2-200220000-2-2000000000000000-2000000000
χ2222222222-2-22-2222-2-2-222220000-2-22200-2-20000-2-20000000000000002000000000
χ2322222222-2-22-2222-2-2-2-2-2-2-2000022-2-200-2-20000220000000000000002000000000
χ2422222222-2-22-2222-2-2-2-2-2-2-20000-2-2220022000022000000000000000-2000000000
χ252-22-222-2-2-2-2-2222-222-20000000000000000000000002i2i−2i−2i22-2-20000002i−2i0000000
χ262-22-222-2-2-2-2-2222-222-20000000000000000000000002i2i−2i−2i-2-222000000−2i2i0000000
χ272-22-222-2-2-2-2-2222-222-2000000000000000000000000−2i−2i2i2i22-2-2000000−2i2i0000000
χ282-22-222-2-2-2-2-2222-222-2000000000000000000000000−2i−2i2i2i-2-2220000002i−2i0000000
χ292-2-222-22-22-202000-20022−2−22i2i−2i−2i00002i−2i002-2002−2002−22−20000i2i2−i2−i20000i2−i200000
χ302-2-222-22-22-202000-20022−2−22i2i−2i−2i0000−2i2i00-22002−200−22−220000i2i2−i2−i20000−i2i200000
χ312-2-222-22-22-202000-20022−2−2−2i−2i2i2i00002i−2i00-22002−200−22−220000−i2−i2i2i20000i2−i200000
χ322-2-222-22-22-202000-20022−2−2−2i−2i2i2i0000−2i2i002-2002−2002−22−20000−i2−i2i2i20000−i2i200000
χ332-2-222-22-22-202000-200−2−2222i2i−2i−2i00002i−2i002-200−2200−22−220000−i2−i2i2i20000−i2i200000
χ342-2-222-22-22-202000-200−2−2222i2i−2i−2i0000−2i2i00-2200−22002−22−20000−i2−i2i2i20000i2−i200000
χ352-2-222-22-22-202000-200−2−222−2i−2i2i2i00002i−2i00-2200−22002−22−20000i2i2−i2−i20000−i2i200000
χ362-2-222-22-22-202000-200−2−222−2i−2i2i2i0000−2i2i002-200−2200−22−220000i2i2−i2−i20000i2−i200000
χ372-2-2-2-222200-202-220002-22-22−22−22-200002-20000002−200002−22−22−22−20000002−2000
χ382-2-2-2-222200-202-220002-22-22−22−2-220000-220000002−20000−22−222−22−2000000−22000
χ392-2-2-2-222200-202-220002-22-2−22−222-200002-2000000−220000−22−22−22−22000000−22000
χ402-2-2-2-222200-202-220002-22-2−22−22-220000-22000000−2200002−22−2−22−220000002−2000
χ412-2-2-2-222200-202-22000-22-222−22−22-20000-220000002−200002−22−2−22−22000000−22000
χ422-2-2-2-222200-202-22000-22-222−22−2-2200002-20000002−20000−22−22−22−220000002−2000
χ432-2-2-2-222200-202-22000-22-22−22−222-20000-22000000−220000−22−222−22−20000002−2000
χ442-2-2-2-222200-202-22000-22-22−22−22-2200002-2000000−2200002−22−22−22−2000000−22000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000
χ46444-4-4-44-4000000000022−22−22222i2−2i2−2i22i20000000000000000000000002i−2i−2i2i00000000000
χ47444-4-4-44-4000000000022−22−2222−2i22i22i2−2i2000000000000000000000000−2i2i2i−2i00000000000
χ48444-4-4-44-40000000000−222222−222i2−2i2−2i22i2000000000000000000000000−2i2i2i−2i00000000000
χ49444-4-4-44-40000000000−222222−22−2i22i22i2−2i20000000000000000000000002i−2i−2i2i00000000000
χ5044-44-44-4-400404-4-4000000000000000000000000000000022−22−2222000000000000000
χ5144-44-44-4-400404-4-40000000000000000000000000000000−222222−22000000000000000
χ5244-44-44-4-400-40-44400000000000004i−4i00000000000000000000000000000000000
χ5344-44-44-4-400-40-4440000000000000−4i4i00000000000000000000000000000000000
χ5444-4-44-4-444-40-40004000000000000000000004-4000000000000000000000000000
χ5544-4-44-4-444-40-4000400000000000000000000-44000000000000000000000000000
χ5644-4-44-4-44-4404000-4000000000000000000000000002i2−2i2−2i22i20000000000000000000
χ5744-4-44-4-44-4404000-400000000000000000000000000−2i22i22i2−2i20000000000000000000
χ584-44-444-4-4444-4-4-44-44-400000000000000000000000000000000000000000000000
χ594-44-444-4-444-4-444-4-4-4400000000000000000000000000000000000000000000000
χ604-44-444-4-4-4-444-4-444-4400000000000000000000000000000000000000000000000
χ614-4-444-44-4-440-40004002222−22−220000000000000000−22220000000000000000000000000
χ624-4-444-44-4-440-4000400−22−222222000000000000000022−220000000000000000000000000
χ634-4-4-4-44440040-44-4000000022−2222−2200000000000000−222200000000000000000000000
χ644-4-4-4-44440040-44-40000000−2222−22220000000000000022−2200000000000000000000000
χ658-888-8-8-88000000000000000000000000000000000000000000000000000000000

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