Finite Group Databasebeta

← Group #259352

Character table — Group #259352

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222222224444448888888888888888888888161616161616161616161616161616161616
order12222222444444444444444444444444444488888888224444444488888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-11111-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111
χ5111111111111111111111111-1-1-1-11111-1-1-1-11111111111-1-111-1-111-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111
χ7111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1
χ91111111111111111-1-1-1-111-1-111-1-1111111-1-11111-1-1-1-1-1-11-1111-1-1-111-1-111-1-1
χ101111111111111111-1-1-1-111-1-111-1-1111111-1-1-1-1-1-11111-1-11-1-1-11-111-1-111-1-111
χ111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-111-11-1-11-11111-1-1-1-111
χ121111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-111-1-1-1-1111111-11111-1-1-1-1-11111-1-1
χ131111111111111111-1-1-1-111-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1111-11-1-1-1-111-1-111
χ141111111111111111-1-1-1-111-1-1-1-1111111-1-111-1-1-1-11111-1-1-11-1-1-111111-1-111-1-1
χ151111111111111111-1-1-1-111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1111-1-1-1-1111-1-11111-1-1
χ161111111111111111-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-1-1-11111111-111-11-1-111-1-1-1-111
χ1722222222222-2-2-2-222222-2-2-2-222220000000000000000000000-2-20000000000
χ1822222222222-2-2-2-222222-2-2-2-2-2-2-2-20000000000000000000000220000000000
χ1922222222222-2-2-2-22-2-2-2-2-2-22222-2-20000000000000000000000-220000000000
χ2022222222222-2-2-2-22-2-2-2-2-2-222-2-22200000000000000000000002-20000000000
χ2122222222-2-2-22222-222-2-2-2-22-20000000022-2-20000000000-2200000000000000
χ2222222222-2-2-22222-222-2-2-2-22-200000000-2-22200000000002-200000000000000
χ2322222222-2-2-22222-2-2-222-2-2-220000000022220000000000-2-200000000000000
χ2422222222-2-2-22222-2-2-222-2-2-2200000000-2-2-2-200000000002200000000000000
χ2522222222-2-2-2-2-2-2-2-222-2-222-22000022-2-20000000000002-20000000000000000
χ2622222222-2-2-2-2-2-2-2-222-2-222-220000-2-222000000000000-220000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-222222-2000022-2-2000000000000-220000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-222222-20000-2-2220000000000002-20000000000000000
χ29222-2-2-22-22-2-2000022-22-200002i−2i2i−2i00000000i2i2−i2−i2i2i2−i2−i200000000002−22−20000
χ30222-2-2-22-22-2-2000022-22-200002i−2i2i−2i00000000−i2−i2i2i2−i2−i2i2i20000000000−22−220000
χ31222-2-2-22-22-2-2000022-22-20000−2i2i−2i2i00000000i2i2−i2−i2i2i2−i2−i20000000000−22−220000
χ32222-2-2-22-22-2-2000022-22-20000−2i2i−2i2i00000000−i2−i2i2i2−i2−i2i2i200000000002−22−20000
χ33222-2-2-22-22-2-200002-22-2200002i−2i−2i2i00000000i2i2−i2−i2−i2−i2i2i200000000002−2−220000
χ34222-2-2-22-22-2-200002-22-2200002i−2i−2i2i00000000−i2−i2i2i2i2i2−i2−i20000000000−222−20000
χ35222-2-2-22-22-2-200002-22-220000−2i2i2i−2i00000000i2i2−i2−i2−i2−i2i2i20000000000−222−20000
χ36222-2-2-22-22-2-200002-22-220000−2i2i2i−2i00000000−i2−i2i2i2i2i2−i2−i200000000002−2−220000
χ3722-22-2-2-2222-2-2-222-200002-20000002i−2i2i−2i000000002i−2i2i−2i000000002-200000000
χ3822-22-2-2-2222-2-2-222-200002-20000002i−2i2i−2i00000000−2i2i−2i2i00000000-2200000000
χ3922-22-2-2-2222-2-2-222-200002-2000000−2i2i−2i2i000000002i−2i2i−2i00000000-2200000000
χ4022-22-2-2-2222-2-2-222-200002-2000000−2i2i−2i2i00000000−2i2i−2i2i000000002-200000000
χ4122-22-2-2-22-2-2222-2-2200002-20000002i−2i−2i2i00002-22-2000000002i−2i000000000000
χ4222-22-2-2-22-2-2222-2-2200002-20000002i−2i−2i2i0000-22-2200000000−2i2i000000000000
χ4322-22-2-2-22-2-2222-2-2200002-2000000−2i2i2i−2i00002-22-200000000−2i2i000000000000
χ4422-22-2-2-22-2-2222-2-2200002-2000000−2i2i2i−2i0000-22-22000000002i−2i000000000000
χ45444-4-4-44-4-4440000-44-4-44000000000000000000000000000000000000000000
χ46444-4-4-44-4-4440000-4-444-4000000000000000000000000000000000000000000
χ4744-44-4-4-4444-444-4-4-40000-440000000000000000000000000000000000000000
χ4844-44-4-4-44-4-44-4-44440000-440000000000000000000000000000000000000000
χ4944-4-444-4-44-440000-400000000000000000000000022−22−2222000000000000000000
χ5044-4-444-4-44-440000-4000000000000000000000000−222222−22000000000000000000
χ5144-4-444-4-4-44-400004000000000000000000002i2−2i2−2i22i20000000000000000000000
χ5244-4-444-4-4-44-40000400000000000000000000−2i22i22i2−2i20000000000000000000000
χ534-44-44-4-440004-44-400000000000000000000000000000000000000000002i2−2i200
χ544-44-44-4-440004-44-40000000000000000000000000000000000000000000−2i22i200
χ554-44-44-4-44000-44-440000000000000000000000000000000000000000000002i2−2i2
χ564-44-44-4-44000-44-44000000000000000000000000000000000000000000000−2i22i2
χ574-4-4-4-44440004-4-44000000000000000004-40000000000000000000000000000
χ584-4-4-4-44440004-4-4400000000000000000-440000000000000000000000000000
χ594-4-4-4-4444000-444-400000000000000000004-400000000000000000000000000
χ604-4-4-4-4444000-444-40000000000000000000-4400000000000000000000000000
χ618-888-88-8-8000000000000000000000000000000000000000000000000000000
χ628-8-888-88-8000000000000000000000000000000000000000000000000000000

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