Finite Group Databasebeta

← Group #115751

Character table — Group #115751

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122222222444444444488888888888888881616161616161616161616161616161616161616
order12222222222244442222444444222222228888888844444444888888888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ511111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-111-1-1111-11-11111-1-1-1-1iiii−i−i−i−i11-1-1ii−i−iii−i−i11-1-1ii−i−i
χ1011111111-1-1-1-1-1-1-1-111-1-1111-11-11111-1-1-1-1iiii−i−i−i−i-1-111ii−i−i−i−iii-1-111−i−iii
χ1111111111-1-1-1-1-1-1-1-111-1-1111-11-11111-1-1-1-1−i−i−i−iiiii11-1-1−i−iii−i−iii11-1-1−i−iii
χ1211111111-1-1-1-1-1-1-1-111-1-1111-11-11111-1-1-1-1−i−i−i−iiiii-1-111−i−iiiii−i−i-1-111ii−i−i
χ1311111111-1-1-1-1-1-1-1-111-1-1111-11-1-1-1-1-11111iiii−i−i−i−i11-1-1−i−iiiii−i−i-1-111−i−iii
χ1411111111-1-1-1-1-1-1-1-111-1-1111-11-1-1-1-1-11111iiii−i−i−i−i-1-111−i−iii−i−iii11-1-1ii−i−i
χ1511111111-1-1-1-1-1-1-1-111-1-1111-11-1-1-1-1-11111−i−i−i−iiiii11-1-1ii−i−i−i−iii-1-111ii−i−i
χ1611111111-1-1-1-1-1-1-1-111-1-1111-11-1-1-1-1-11111−i−i−i−iiiii-1-111ii−i−iii−i−i11-1-1−i−iii
χ172222222222222222-2-2-2-222-2-2-2-20000000022-2-222-2-200000000000000000000
χ182222222222222222-2-2-2-222-2-2-2-200000000-2-222-2-22200000000000000000000
χ19222222222222-2-2-2-22222-2-2-2-2-2-20000000000000000000000002i−2i2i−2i00000000
χ20222222222222-2-2-2-22222-2-2-2-2-2-2000000000000000000000000−2i2i−2i2i00000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2222200000000000000002-22-20000000000000000
χ22222222222222-2-2-2-2-2-2-2-2-2-222220000000000000000-22-220000000000000000
χ2322222222-2-2-2-2222222-2-2-2-2-22-220000000000000000000000002-2-2200000000
χ2422222222-2-2-2-2222222-2-2-2-2-22-22000000000000000000000000-222-200000000
χ2522222222-2-2-2-22222-2-222-2-22-22-200000000000000002-2-220000000000000000
χ2622222222-2-2-2-22222-2-222-2-22-22-20000000000000000-222-20000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-22222-22-22000000002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-22222-22-2200000000−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ29222-2-2-2-2222-2-222-2-22-22-22-222-2-222-2-222-2-20000000000000000000000000000
χ30222-2-2-2-2222-2-222-2-22-22-22-222-2-2-2-222-2-2220000000000000000000000000000
χ31222-2-2-2-2222-2-222-2-2-22-222-2-2-222000000000000000000002i−2i2i−2i000000000000
χ32222-2-2-2-2222-2-222-2-2-22-222-2-2-22200000000000000000000−2i2i−2i2i000000000000
χ33222-2-2-2-2222-2-2-2-2222-22-2-22-2-222000000000000000000000000000000002-22-2
χ34222-2-2-2-2222-2-2-2-2222-22-2-22-2-22200000000000000000000000000000000-22-22
χ35222-2-2-2-2222-2-2-2-222-22-22-2222-2-200000000000000000000000000002i−2i2i−2i0000
χ36222-2-2-2-2222-2-2-2-222-22-22-2222-2-20000000000000000000000000000−2i2i−2i2i0000
χ37222-2-2-2-22-2-22222-2-22-2-22-22-222-2000000000000000000000000000000002i−2i−2i2i
χ38222-2-2-2-22-2-22222-2-22-2-22-22-222-200000000000000000000000000000000−2i2i2i−2i
χ39222-2-2-2-22-2-22222-2-2-222-2-222-2-2200000000000000000000000000002i−2i−2i2i0000
χ40222-2-2-2-22-2-22222-2-2-222-2-222-2-220000000000000000000000000000−2i2i2i−2i0000
χ41222-2-2-2-22-2-222-2-2222-2-222-22-2-2222-2-2-2-2220000000000000000000000000000
χ42222-2-2-2-22-2-222-2-2222-2-222-22-2-22-2-22222-2-20000000000000000000000000000
χ43222-2-2-2-22-2-222-2-222-222-22-2-222-2000000000000000000002-2-22000000000000
χ44222-2-2-2-22-2-222-2-222-222-22-2-222-200000000000000000000-222-2000000000000
χ4544-444-4-4-44-44-40000000000000000000000002i2−2i2002i2−2i200000000000000000000
χ4644-444-4-4-44-44-4000000000000000000000000−2i22i200−2i22i200000000000000000000
χ4744-444-4-4-4-44-4400000000000000000000000022−2200−222200000000000000000000
χ4844-444-4-4-4-44-44000000000000000000000000−22220022−2200000000000000000000
χ4944-4-4-444-44-4-44000000000000000000000022−220022−220000000000000000000000
χ5044-4-4-444-44-4-440000000000000000000000−222200−22220000000000000000000000
χ5144-4-4-444-4-444-400000000000000000000002i2−2i200−2i22i20000000000000000000000
χ5244-4-4-444-4-444-40000000000000000000000−2i22i2002i2−2i20000000000000000000000
χ534-4-44-44-4400004-44-400000000002-22-22-22-20000000000000000000000000000
χ544-4-44-44-4400004-44-40000000000-22-22-22-220000000000000000000000000000
χ554-4-44-44-440000-44-4400000000002-22-2-22-220000000000000000000000000000
χ564-4-44-44-440000-44-440000000000-22-222-22-20000000000000000000000000000
χ574-4-4-44-44400004-4-4400000000002-2-222-2-220000000000000000000000000000
χ584-4-4-44-44400004-4-440000000000-222-2-222-20000000000000000000000000000
χ594-4-4-44-4440000-444-400000000002-2-22-222-20000000000000000000000000000
χ604-4-4-44-4440000-444-40000000000-222-22-2-220000000000000000000000000000
χ618-888-8-88-8000000000000000000000000000000000000000000000000000000
χ628-88-888-8-8000000000000000000000000000000000000000000000000000000

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