Finite Group Databasebeta

← Group #98620

Character table — Group #98620

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222244444444444488888888888888888888161616161616161616161616161616161616
order12222222222244444444444422224444444488888888224444444488888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-1-1-111-1-111-1-111111111-1-11-11-1-1-1-1-11111-1-1-1-1
χ6111111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11-11-11111-1-1-1-11111
χ7111111111111111111111111-1-1-1-1-1-111-1-11111111111-1-1-11-11-1-1-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-11-1111111111-1-1-1-1
χ911111111-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-1iiii−i−i−i−i-1-111-1-1ii−i−iii−i−iii−i−i
χ1011111111-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-1−i−i−i−iiiii-1-111-1-1−i−iii−i−iii−i−iii
χ1111111111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-11111iiii−i−i−i−i-1-1-1-111ii−i−i−i−iii−i−iii
χ1211111111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-11111−i−i−i−iiiii-1-1-1-111−i−iiiii−i−iii−i−i
χ1311111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-111-1-1-1-111iiii−i−i−i−i111-1-11−i−iiiii−i−i−i−iii
χ1411111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-111-1-1-1-111−i−i−i−iiiii111-1-11ii−i−i−i−iiiii−i−i
χ1511111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1iiii−i−i−i−i11-111-1−i−iii−i−iiiii−i−i
χ1611111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1−i−i−i−iiiii11-111-1ii−i−iii−i−i−i−iii
χ1722222222222222-2-22-2-2-2-22-2-200000022002200000000000-20-2000000000000
χ1822222222222222-2-22-2-2-2-22-2-2000000-2-200-2-200000000000202000000000000
χ19222222222222-2-222-22-2-2-2-22-20000220022000000000000-20-20000000000000
χ20222222222222-2-222-22-2-2-2-22-20000-2-200-2-20000000000002020000000000000
χ21222222222222-2-2-2-2-2-2222-2-2222-2-200000000000000002-20000000000000000
χ22222222222222-2-2-2-2-2-2222-2-22-2-2220000000000000000-220000000000000000
χ2322222222-2-2-2-222-2-2-22-2-22-2220000002200-2-200000000000-202000000000000
χ2422222222-2-2-2-222-2-2-22-2-22-222000000-2-200220000000000020-2000000000000
χ2522222222-2-2-2-2-2-2222-2-2-222-2200002200-2-2000000000000-2020000000000000
χ2622222222-2-2-2-2-2-2222-2-2-222-220000-2-2002200000000000020-20000000000000
χ2722222222-2-2-2-2-2-2-2-22222-222-222-2-20000000000000000-220000000000000000
χ2822222222-2-2-2-2-2-2-2-22222-222-2-2-22200000000000000002-20000000000000000
χ29222-22-2-2-222-2-2002-20-200002000002i−2i002i−2i00i2i2−i2−i2i2i2−i2−i200000000002−22−20000
χ30222-22-2-2-222-2-2002-20-200002000002i−2i002i−2i00−i2−i2i2i2−i2−i2i2i20000000000−22−220000
χ31222-22-2-2-222-2-2002-20-20000200000−2i2i00−2i2i00i2i2−i2−i2i2i2−i2−i20000000000−22−220000
χ32222-22-2-2-222-2-2002-20-20000200000−2i2i00−2i2i00−i2−i2i2i2−i2−i2i2i200000000002−22−20000
χ33222-22-2-2-2-2-222002-2020000-2000002i−2i00−2i2i0022−2−2−2−2220000000000−i2i2i2−i20000
χ34222-22-2-2-2-2-222002-2020000-2000002i−2i00−2i2i00−2−22222−2−20000000000i2−i2−i2i20000
χ35222-22-2-2-2-2-222002-2020000-200000−2i2i002i−2i0022−2−2−2−2220000000000i2−i2−i2i20000
χ36222-22-2-2-2-2-222002-2020000-200000−2i2i002i−2i00−2−22222−2−20000000000−i2i2i2−i20000
χ3722-22-22-2-22-22-22-200-200002000000002i−2i002i−2ii2−i2i2−i2i2−i2i2−i2000000000000002−22−2
χ3822-22-22-2-22-22-22-200-200002000000002i−2i002i−2i−i2i2−i2i2−i2i2−i2i200000000000000−22−22
χ3922-22-22-2-22-22-22-200-20000200000000−2i2i00−2i2ii2−i2i2−i2i2−i2i2−i200000000000000−22−22
χ4022-22-22-2-22-22-22-200-20000200000000−2i2i00−2i2i−i2i2−i2i2−i2i2−i2i2000000000000002−22−2
χ4122-22-22-2-2-22-222-20020000-2000000002i−2i00−2i2i2−22−2−22−2200000000000000−i2i2i2−i2
χ4222-22-22-2-2-22-222-20020000-2000000002i−2i00−2i2i−22−222−22−200000000000000i2−i2−i2i2
χ4322-22-22-2-2-22-222-20020000-200000000−2i2i002i−2i2−22−2−22−2200000000000000i2−i2−i2i2
χ4422-22-22-2-2-22-222-20020000-200000000−2i2i002i−2i−22−222−22−200000000000000−i2i2i2−i2
χ45444-44-4-4-444-4-400-44040000-4000000000000000000000000000000000000000
χ46444-44-4-4-4-4-44400-440-400004000000000000000000000000000000000000000
χ4744-44-44-4-44-44-4-440040000-40000000000000000000000000000000000000000
χ4844-44-44-4-4-44-44-4400-4000040000000000000000000000000000000000000000
χ4944-4-4-4-4444-4-440000000000000000000000002-2-222-2-22000000000000000000
χ5044-4-4-4-4444-4-44000000000000000000000000-222-2-222-2000000000000000000
χ5144-4-4-4-444-444-40000000000000000000000002i−2i−2i2i−2i2i2i−2i000000000000000000
χ5244-4-4-4-444-444-4000000000000000000000000−2i2i2i−2i2i−2i−2i2i000000000000000000
χ534-444-4-4-44000000000000400-4000000000000000000000000002i−2i2i−2i00000000
χ544-444-4-4-44000000000000400-400000000000000000000000000−2i2i−2i2i00000000
χ554-444-4-4-44000000000000-4004000000000000000000000000002-2-2200000000
χ564-444-4-4-44000000000000-400400000000000000000000000000-222-200000000
χ574-4-4-444-4400000000004-40000004-40000000000000000000000000000000000
χ584-4-4-444-4400000000004-4000000-440000000000000000000000000000000000
χ594-4-4-444-440000000000-4400004-4000000000000000000000000000000000000
χ604-4-4-444-440000000000-440000-44000000000000000000000000000000000000
χ618-88-8-888-8000000000000000000000000000000000000000000000000000000
χ628-8-888-88-8000000000000000000000000000000000000000000000000000000

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