Finite Group Databasebeta

← Group #173920

Character table — Group #173920

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222222244444488888888888888888888888888888888888881616161616163232
order12222222444444444444444444222244444444488888888888888888888888844444422
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ31111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1
χ41111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ511111111111111111111111111-1-1-1-111111-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111
χ711111111111111111111111111-1-1-1-11-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ811111111111111111111111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11-11-11-11-1
χ1011111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111-11-11-1-11
χ1111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-11-111-1-11
χ1211111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-11-111-11-1
χ1311111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-11-11-11
χ1411111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-11-111-1
χ1511111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-111-1-111-1
χ1611111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-11111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-111-1-11-11
χ172222222222222222-2-2-2-22-2-22-2-22222-2000000000000000000000000000000000000-2-200
χ182222222222222222-2-2-2-22-2-22-2-2-2-2-2-2-20000000000000000000000000000000000002200
χ19222222222222-2-2-2-22222-22-2-22-20000-20000222200000000000000000000000000-2-20000
χ20222222222222-2-2-2-22222-22-2-22-20000-20000-2-2-2-200000000000000000000000000220000
χ21222222222222-2-2-2-2-2-2-2-2-2-22-2-220000222-2-20000000000000000000000000000-22000000
χ22222222222222-2-2-2-2-2-2-2-2-2-22-2-2200002-2-22200000000000000000000000000002-2000000
χ2322222222-2-2-2-222222222-2-22-2-220000-222220000000000000000000000000000-2-2000000
χ2422222222-2-2-2-222222222-2-22-2-220000-2-2-2-2-2000000000000000000000000000022000000
χ2522222222-2-2-2-22222-2-2-2-2-22-2-22-200002000022-2-200000000000000000000000000-220000
χ2622222222-2-2-2-22222-2-2-2-2-22-2-22-2000020000-2-222000000000000000000000000002-20000
χ2722222222-2-2-2-2-2-2-2-222222-2-22-2-222-2-22000000000000000000000000000000000000-2200
χ2822222222-2-2-2-2-2-2-2-222222-2-22-2-2-2-22220000000000000000000000000000000000002-200
χ292222-2-2-2-222-2-222-2-20000-2002002-22-2000000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ302222-2-2-2-222-2-222-2-20000-2002002-22-2000000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ312222-2-2-2-222-2-222-2-20000-200200-22-22000000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ322222-2-2-2-222-2-222-2-20000-200200-22-22000000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ332222-2-2-2-2-2-222-2-2220000-2002002-2-22000000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ342222-2-2-2-2-2-222-2-2220000-2002002-2-22000000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ352222-2-2-2-2-2-222-2-2220000-200200-222-2000000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ362222-2-2-2-2-2-222-2-2220000-200200-222-2000000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ3722-2-2-22-2200002-22-222-2-200-2002000002-22-200002−22−22−22−20000000022−2−222−2−200000000
χ3822-2-2-22-2200002-22-222-2-200-2002000002-22-20000−22−22−22−2200000000−2−222−2−22200000000
χ3922-2-2-22-2200002-22-222-2-200-200200000-22-2200002−22−22−22−200000000−2−222−2−22200000000
χ4022-2-2-22-2200002-22-222-2-200-200200000-22-220000−22−22−22−220000000022−2−222−2−200000000
χ4122-2-2-22-220000-22-22-2-22200-2002000002-2-2200002−22−2−22−220000000022−2−2−2−22200000000
χ4222-2-2-22-220000-22-22-2-22200-2002000002-2-220000−22−222−22−200000000−2−22222−2−200000000
χ4322-2-2-22-220000-22-22-2-22200-200200000-222-200002−22−2−22−2200000000−2−22222−2−200000000
χ4422-2-2-22-220000-22-22-2-22200-200200000-222-20000−22−222−22−20000000022−2−2−2−22200000000
χ452-22-2-2-2222-22-200002-22-20-200200000000002-22-2000000002−22−22−22−22−22−22−22−200000000
χ462-22-2-2-2222-22-200002-22-20-200200000000002-22-200000000−22−22−22−22−22−22−22−2200000000
χ472-22-2-2-2222-22-200002-22-20-20020000000000-22-22000000002−22−22−22−2−22−22−22−2200000000
χ482-22-2-2-2222-22-200002-22-20-20020000000000-22-2200000000−22−22−22−222−22−22−22−200000000
χ492-22-2-2-222-22-220000-22-220-200200000000002-2-22000000002−22−2−22−222−22−2−22−2200000000
χ502-22-2-2-222-22-220000-22-220-200200000000002-2-2200000000−22−222−22−2−22−222−22−200000000
χ512-22-2-2-222-22-220000-22-220-20020000000000-222-2000000002−22−2−22−22−22−222−22−200000000
χ522-22-2-2-222-22-220000-22-220-20020000000000-222-200000000−22−222−22−22−22−2−22−2200000000
χ534444-4-4-4-444-4-4-4-4440000400-400000000000000000000000000000000000000000000000
χ544444-4-4-4-4-4-44444-4-40000400-400000000000000000000000000000000000000000000000
χ5544-4-44-44-400004-4-44000000000000000000000002i−2i−2i2i2i−2i−2i2i000000000000000000000000
χ5644-4-44-44-400004-4-4400000000000000000000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000
χ5744-4-44-44-40000-444-4000000000000000000000002i−2i−2i2i−2i2i2i−2i000000000000000000000000
χ5844-4-44-44-40000-444-400000000000000000000000−2i2i2i−2i2i−2i−2i2i000000000000000000000000
χ5944-4-4-44-4400004-44-4-4-44400400-4000000000000000000000000000000000000000000000
χ6044-4-4-44-440000-44-4444-4-400400-4000000000000000000000000000000000000000000000
χ614-44-444-4-44-4-44000000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ624-44-444-4-44-4-4400000000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ634-44-444-4-4-444-4000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ644-44-444-4-4-444-400000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ654-44-4-4-4444-44-40000-44-440400-40000000000000000000000000000000000000000000000
χ664-44-4-4-444-44-4400004-44-40400-40000000000000000000000000000000000000000000000
χ674-4-444-4-44000000004-4-44000000000000000000000000000000000002-2-222-2-2200000000
χ684-4-444-4-44000000004-4-4400000000000000000000000000000000000-222-2-222-200000000
χ694-4-444-4-4400000000-444-4000000000000000000000000000000000002-2-22-222-200000000
χ704-4-444-4-4400000000-444-400000000000000000000000000000000000-222-22-2-2200000000
χ718-8-88-888-8000000000000000000000000000000000000000000000000000000000000000

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