Finite Group Databasebeta

← Group #281321

Character table — Group #281321

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122222222444444888888888888888888888888881616161616161616161616163232
order12222222444444444488882244444444448888888888888824444488888844
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-1-1-11111-1-1-1-1111111-1-1-1-11-1-11-1-1-1-1-1-1-1-111
χ3111111111111111111111111-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ4111111111111111111111111-1-1-1-1-1-111-1-1111111-1-1-1-111111-1-11-1-1-1-11111-1-1
χ51111111111111111111111-1-1111111-1-11111111111111111-1-1-1-1-1-111-1-1-1-1-1-1
χ61111111111111111111111-1-111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-111-111-1-11111-1-1
χ71111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-111-111-1-1-1-1-1-111
χ9111111111111111111-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-111-1-1-11
χ10111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-111111-1-111-11
χ11111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-111111111-1111-1-1-1-1-1-1111-1
χ12111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-11111111-1-11-1
χ13111111111111111111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-11-1-1-111-1-1-1-1111-1
χ14111111111111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111-1-1-11111-1-11-1
χ15111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111-1-1-111-1-111-1-1-11
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1-1-1111-1-1-111-1-111-11
χ172222222222-2-22-2-22-2-222222200000022000000-2-200000000-200-20000000000
χ182222222222-2-22-2-22-2-22222-2-2000000-2-2000000-2-20000000020020000000000
χ192222222222-2-22-2-22-2-2-2-2-2-222000000-2-20000002200000000200-20000000000
χ202222222222-2-22-2-22-2-2-2-2-2-2-2-2000000220000002200000000-20020000000000
χ2122222222-2-222-222-2-2-20000002222-2-200-2-222-2-2000000000000000000000000
χ2222222222-2-222-222-2-2-200000022-2-22200-2-2-2-222000000000000000000000000
χ2322222222-2-222-222-2-2-2000000-2-222-2-20022-2-222000000000000000000000000
χ2422222222-2-222-222-2-2-2000000-2-2-2-222002222-2-2000000000000000000000000
χ252-222-2-22-22-2-2-2222-2-22000000002i−2i2i−2i00000000002i2i−2i−2i22-2-200000000000000
χ262-222-2-22-22-2-2-2222-2-22000000002i−2i2i−2i0000000000−2i−2i2i2i-2-22200000000000000
χ272-222-2-22-22-2-2-2222-2-2200000000−2i2i−2i2i00000000002i2i−2i−2i-2-22200000000000000
χ282-222-2-22-22-2-2-2222-2-2200000000−2i2i−2i2i0000000000−2i−2i2i2i22-2-200000000000000
χ292-222-2-22-2-2222-2-2-22-2222-2-200000000000000002-20000000002i−2i02i−2i00000000
χ302-222-2-22-2-2222-2-2-22-2222-2-200000000000000002-2000000000−2i2i0−2i2i00000000
χ312-222-2-22-2-2222-2-2-22-22-2-2220000000000000000-220000000002i−2i0−2i2i00000000
χ322-222-2-22-2-2222-2-2-22-22-2-2220000000000000000-22000000000−2i2i02i−2i00000000
χ332-222-2-22-2-22-2-2-22222-222-2-200002i−2i−2i2i00000000-22000000000000002i−2i000000
χ342-222-2-22-2-22-2-2-22222-222-2-20000−2i2i2i−2i00000000-2200000000000000−2i2i000000
χ352-222-2-22-2-22-2-2-22222-2-2-22200002i−2i−2i2i000000002-200000000000000−2i2i000000
χ362-222-2-22-2-22-2-2-22222-2-2-2220000−2i2i2i−2i000000002-2000000000000002i−2i000000
χ372-22-222-2-22-200-2002002i−2i2i−2i2-20000002i−2i00i2−i2i2−i20000002−22−200000000i2−i22−200
χ382-22-222-2-22-200-2002002i−2i2i−2i2-20000002i−2i00−i2i2−i2i2000000−22−2200000000−i2i2−2200
χ392-22-222-2-22-200-2002002i−2i2i−2i-22000000−2i2i00i2−i2i2−i20000002−22−200000000−i2i2−2200
χ402-22-222-2-22-200-2002002i−2i2i−2i-22000000−2i2i00−i2i2−i2i2000000−22−2200000000i2−i22−200
χ412-22-222-2-22-200-200200−2i2i−2i2i2-2000000−2i2i00i2−i2i2−i2000000−22−2200000000i2−i2−2200
χ422-22-222-2-22-200-200200−2i2i−2i2i2-2000000−2i2i00−i2i2−i2i20000002−22−200000000−i2i22−200
χ432-22-222-2-22-200-200200−2i2i−2i2i-220000002i−2i00i2−i2i2−i2000000−22−2200000000−i2i22−200
χ442-22-222-2-22-200-200200−2i2i−2i2i-220000002i−2i00−i2i2−i2i20000002−22−200000000i2−i2−2200
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000
χ46444-4-4-4-444400-400-4000000000000000000000000000022−22−222200000000000000
χ47444-4-4-4-444400-400-40000000000000000000000000000−222222−2200000000000000
χ48444-4-4-4-44-4-4004004004i−4i−4i4i0000000000000000000000000000000000000000
χ49444-4-4-4-44-4-400400400−4i4i4i−4i0000000000000000000000000000000000000000
χ5044-4-44-44-4004-404-400000000000000000000000002i2−2i22i2−2i2000000000000000000
χ5144-4-44-44-4004-404-40000000000000000000000000−2i22i2−2i22i2000000000000000000
χ5244-4-44-44-400-440-440000000004i−4i000000000000000000000000000000000000
χ5344-4-44-44-400-440-44000000000−4i4i000000000000000000000000000000000000
χ544-444-4-44-44-4444-4-4-44-400000000000000000000000000000000000000000000
χ554-44-444-4-4-4400400-40000000000000000002i2−2i2−2i22i2000000000000000000000000
χ564-44-444-4-4-4400400-4000000000000000000−2i22i22i2−2i2000000000000000000000000
χ574-4-4-4-4444004-40-44000000000000000004-40000000000000000000000000000
χ584-4-4-4-4444004-40-4400000000000000000-440000000000000000000000000000
χ594-4-4-4-444400-4404-4000000000000000000000000022−22−2222000000000000000000
χ604-4-4-4-444400-4404-40000000000000000000000000−222222−22000000000000000000
χ6188-88-88-8-8000000000000000000000000000000000000000000000000000000
χ628-8-888-8-88000000000000000000000000000000000000000000000000000000

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