Finite Group Databasebeta

← Group #351568

Character table — Group #351568

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222222224444444444888888888888888888888888161616161616161632323232
order12222222444444444488888888244444444444888888888888888888884444
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111-1-1-111-1-111-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11-11-1
χ611111111111111111111111111-1-1-111-1-111-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-11-11
χ711111111111111111111111111-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-111111111-1-1-1-1-11-11
χ811111111111111111111111111-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-11111-1-1-1-111111-11-1
χ9111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11-1-11
χ10111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-111-1
χ11111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-11-1-1-1-11111111111-1-111-1-1-111-1
χ12111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-11-1-1-1-111111111-1-111-1-1111-1-11
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-11111-1-1-1-11111-1-11111-1-1-1-111
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-111111111-1-1-1-111-1-1-1-111-1-111
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-111111111-1-1-1-1-1-11111-1-111-1-1
χ1722222222222-2-2-2-22-2-22222-2-2-2-222-200000000-222-2-200000000000000000000
χ1822222222222-2-2-2-22-2-22222-2-2-2-2-2-22000000002-2-22200000000000000000000
χ1922222222222-2-2-2-22-2-2-2-2-2-2222222-200000000-2-2-22200000000000000000000
χ2022222222222-2-2-2-22-2-2-2-2-2-22222-2-2200000000222-2-200000000000000000000
χ2122222222-2-2-22222-2-2-2000000002-2-222-2-2-2-2222000000000000000000000000
χ2222222222-2-2-22222-2-2-2000000002-2-2-2-22222-2-22000000000000000000000000
χ2322222222-2-2-22222-2-2-200000000-2222222-2-2-2-2-2000000000000000000000000
χ2422222222-2-2-22222-2-2-200000000-222-2-2-2-22222-2000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-222000000002-2200000000-200002i2i−2i−2i2i2i−2i−2i000000000000
χ2622222222-2-2-2-2-2-2-2-222000000002-2200000000-20000−2i−2i2i2i−2i−2i2i2i000000000000
χ2722222222-2-2-2-2-2-2-2-22200000000-22-200000000200002i2i−2i−2i−2i−2i2i2i000000000000
χ2822222222-2-2-2-2-2-2-2-22200000000-22-20000000020000−2i−2i2i2i2i2i−2i−2i000000000000
χ29222-2-2-2-222-2-222-2-222-22i2i−2i−2i2i2i−2i−2i000002i−2i002i−2i0000000002-22-2000000000000
χ30222-2-2-2-222-2-222-2-222-22i2i−2i−2i2i2i−2i−2i00000−2i2i00−2i2i000000000-22-22000000000000
χ31222-2-2-2-222-2-222-2-222-2−2i−2i2i2i−2i−2i2i2i000002i−2i002i−2i000000000-22-22000000000000
χ32222-2-2-2-222-2-222-2-222-2−2i−2i2i2i−2i−2i2i2i00000−2i2i00−2i2i0000000002-22-2000000000000
χ33222-2-2-2-222-2-2-2-2222-222i2i−2i−2i−2i−2i2i2i0002i−2i002i−2i00000002-22-20000000000000000
χ34222-2-2-2-222-2-2-2-2222-222i2i−2i−2i−2i−2i2i2i000−2i2i00−2i2i0000000-22-220000000000000000
χ35222-2-2-2-222-2-2-2-2222-22−2i−2i2i2i2i2i−2i−2i0002i−2i002i−2i0000000-22-220000000000000000
χ36222-2-2-2-222-2-2-2-2222-22−2i−2i2i2i2i2i−2i−2i000−2i2i00−2i2i00000002-22-20000000000000000
χ37222-2-2-2-22-22222-2-2-2-2200000000000002i−2i00−2i2i02-22-22i−2i−2i2i0000000000000000
χ38222-2-2-2-22-22222-2-2-2-2200000000000002i−2i00−2i2i0-22-22−2i2i2i−2i0000000000000000
χ39222-2-2-2-22-22222-2-2-2-220000000000000−2i2i002i−2i02-22-2−2i2i2i−2i0000000000000000
χ40222-2-2-2-22-22222-2-2-2-220000000000000−2i2i002i−2i0-22-222i−2i−2i2i0000000000000000
χ41222-2-2-2-22-222-2-222-22-2000000000002i−2i00−2i2i0002-2-220000−2i2i2i−2i000000000000
χ42222-2-2-2-22-222-2-222-22-2000000000002i−2i00−2i2i000-222-200002i−2i−2i2i000000000000
χ43222-2-2-2-22-222-2-222-22-200000000000−2i2i002i−2i0002-2-2200002i−2i−2i2i000000000000
χ44222-2-2-2-22-222-2-222-22-200000000000−2i2i002i−2i000-222-20000−2i2i2i−2i000000000000
χ4544-44-44-4-444-40000-4000000000000000000000000000000000000000022−220000
χ4644-44-44-4-444-40000-40000000000000000000000000000000000000000−22220000
χ4744-44-44-4-4-4-44000040000000000000000000000000000000000002i2−2i200000000
χ4844-44-44-4-4-4-4400004000000000000000000000000000000000000−2i22i200000000
χ4944-4-44-44-44-440000-40000000000000000000000000000000000000022−22000000
χ5044-4-44-44-44-440000-400000000000000000000000000000000000000−2222000000
χ5144-4-44-44-4-44-40000400000000000000000000000000000000002i2−2i20000000000
χ5244-4-44-44-4-44-4000040000000000000000000000000000000000−2i22i20000000000
χ534-4-444-4-440004-44-40002i2−2i22i2−2i22i2−2i22i2−2i2000000000000000000000000000000000000
χ544-4-444-4-440004-44-4000−2i22i2−2i22i2−2i22i2−2i22i2000000000000000000000000000000000000
χ554-4-444-4-44000-44-440002i2−2i22i2−2i2−2i22i2−2i22i2000000000000000000000000000000000000
χ564-4-444-4-44000-44-44000−2i22i2−2i22i22i2−2i22i2−2i2000000000000000000000000000000000000
χ574-4-4-4-44440004-4-4400022−22−222222−22−2222000000000000000000000000000000000000
χ584-4-4-4-44440004-4-44000−222222−22−222222−22000000000000000000000000000000000000
χ594-4-4-4-4444000-444-400022−22−2222−222222−22000000000000000000000000000000000000
χ604-4-4-4-4444000-444-4000−222222−2222−22−2222000000000000000000000000000000000000
χ618-888-8-88-8000000000000000000000000000000000000000000000000000000
χ628-88-888-8-8000000000000000000000000000000000000000000000000000000

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