Finite Group Databasebeta

← Group #300715

Character table — Group #300715

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111111112222222244444444448888888888888888888816161616161616161616161616163232
order12222222444444444444448888444444888888888888882222224488888844
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1111-1-1-111-1-111-1-11-1
χ61111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-111-1-111-11
χ71111111111111111111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-111-11
χ81111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1111-1-11111-1-11-1
χ911111111111111111-1-1-1-111111-1-11111111111-1-1-1-111111-1-11-1-1-1-1-1-11111-1-1
χ1011111111111111111-1-1-1-111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-11-1-11-1-11111-1-1-1-111
χ1111111111111111111-1-1-1-111111-1-1-1-1-1-1111111-1-1-1-11111-111-111-1-1-1-1-1-1-1-111
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-111-11111111111-1-1
χ1311111111111111111-1-1-1-11-1-1-1-1-1-111-1-11111-1-11111-1-1-1-11-1-1-111-1-11111-1-1-11
χ1411111111111111111-1-1-1-11-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111-1-1-11111-1-1-1-1111-1
χ1511111111111111111-1-1-1-11-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1111-1-1-1-111-1-1111-1
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1111-1-111-1-111-1-1-11
χ172222222222-2-22-2-22-20000-222220022220000-2-200000000-200-2000000000000
χ182222222222-2-22-2-22-20000-2222200-2-2-2-20000-2-2000000002002000000000000
χ192222222222-2-22-2-22-20000-2-2-2-2-20022-2-200002200000000-2002000000000000
χ202222222222-2-22-2-22-20000-2-2-2-2-200-2-22200002200000000200-2000000000000
χ2122222222-2-222-222-2-22222-20000-2-2000022-2-200000000000000002-200000000
χ2222222222-2-222-222-2-22222-20000-2-20000-2-2220000000000000000-2200000000
χ2322222222-2-222-222-2-2-2-2-2-2-2000022000022-2-20000000000000000-2200000000
χ2422222222-2-222-222-2-2-2-2-2-2-20000220000-2-22200000000000000002-200000000
χ252-2-2222-2-2-2200200-200000022-2-2002i−2i2i−2ii2−i2i2−i2000000i2i2−i2−i200000000002−22−200
χ262-2-2222-2-2-2200200-200000022-2-2002i−2i2i−2i−i2i2−i2i2000000−i2−i2i2i20000000000−22−2200
χ272-2-2222-2-2-2200200-200000022-2-200−2i2i−2i2ii2−i2i2−i2000000i2i2−i2−i20000000000−22−2200
χ282-2-2222-2-2-2200200-200000022-2-200−2i2i−2i2i−i2i2−i2i2000000−i2−i2i2i200000000002−22−200
χ292-2-2222-2-2-2200200-2000000-2-222002i−2i−2i2ii2−i2i2−i2000000−i2−i2i2i200000000002−2−2200
χ302-2-2222-2-2-2200200-2000000-2-222002i−2i−2i2i−i2i2−i2i2000000i2i2−i2−i20000000000−222−200
χ312-2-2222-2-2-2200200-2000000-2-22200−2i2i2i−2ii2−i2i2−i2000000−i2−i2i2i20000000000−222−200
χ322-2-2222-2-2-2200200-2000000-2-22200−2i2i2i−2i−i2i2−i2i2000000i2i2−i2−i200000000002−2−2200
χ332-2-22-2-2222-2-2-2222-2-222-2-2200002-2000000000000002-22-2000000002-2000000
χ342-2-22-2-2222-2-2-2222-2-222-2-2200002-200000000000000-22-2200000000-22000000
χ352-2-22-2-2222-2-2-2222-2-2-2-22220000-22000000000000002-22-200000000-22000000
χ362-2-22-2-2222-2-2-2222-2-2-2-22220000-2200000000000000-22-22000000002-2000000
χ372-2-22-2-222-2222-2-2-22-2000022-22-200000000002-20000000002-202-20000000000
χ382-2-22-2-222-2222-2-2-22-2000022-22-200000000002-2000000000-220-220000000000
χ392-2-22-2-222-2222-2-2-22-200002-22-220000000000-220000000002-20-220000000000
χ402-2-22-2-222-2222-2-2-22-200002-22-220000000000-22000000000-2202-20000000000
χ412-2-22-2-222-22-2-2-2222222-2-2-22-22-2-2200000000-2222-2-200000000000000000000
χ422-2-22-2-222-22-2-2-2222222-2-2-2-22-22-22000000002-2-2-22200000000000000000000
χ432-2-22-2-222-22-2-2-22222-2-222-22-22-22-200000000-22-2-22200000000000000000000
χ442-2-22-2-222-22-2-2-22222-2-222-2-22-222-2000000002-222-2-200000000000000000000
χ4544444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000
χ464444-4-4-4-44400-400-40000004-4-44000000000000000000000000000000000000
χ474444-4-4-4-44400-400-4000000-444-4000000000000000000000000000000000000
χ484444-4-4-4-4-4-4004004000000000000000000000000002i2−2i2−2i22i20000000000000000
χ494444-4-4-4-4-4-400400400000000000000000000000000−2i22i22i2−2i20000000000000000
χ5044-4-44-4-44004-404-40000000000000000000000022−2222−2200000000000000000000
χ5144-4-44-4-44004-404-400000000000000000000000−2222−222200000000000000000000
χ5244-4-44-4-4400-440-44004-44-400000000000000000000000000000000000000000
χ5344-4-44-4-4400-440-4400-44-4400000000000000000000000000000000000000000
χ544-44-4-44-44004-40-44004-4-4400000000000000000000000000000000000000000
χ554-44-4-44-44004-40-4400-444-400000000000000000000000000000000000000000
χ564-44-4-44-4400-4404-40000000000000000000000022−22−222200000000000000000000
χ574-44-4-44-4400-4404-400000000000000000000000−222222−2200000000000000000000
χ584-4-4444-4-44-400-400400000000000000002i2−2i2−2i22i200000000000000000000000000
χ594-4-4444-4-44-400-40040000000000000000−2i22i22i2−2i200000000000000000000000000
χ604-4-44-4-4444-4444-4-4-440000-40000000000000000000000000000000000000000
χ6188-8-8-888-8000000000000000000000000000000000000000000000000000000
χ628-88-88-88-8000000000000000000000000000000000000000000000000000000

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