Finite Group Databasebeta

← Group #351612

Character table — Group #351612

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222222224444444444888888888888888888888888161616161616161632323232
order12222222444444444488888888244444444444888888888888888888882444
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111-1-1-11111-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ611111111111111111111111111-1-1-11111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ9111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11-11-1
χ10111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-11-11
χ11111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-11-1-1-1-1-1-1-1-11111111111-1-111-1-1-11-11
χ12111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-111-1-1111-11-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111-1-1-1-1111111-1-1-1-1111-1-11
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111-1-1-1-11111-1-11111-1-1-111-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-111-111-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-11-1-11
χ1722222222222-2-2-2-22-2-22222-2-2-2-222-20000-2000022-2-200000000000000000000
χ1822222222222-2-2-2-22-2-22222-2-2-2-2-2-22000020000-2-22200000000000000000000
χ1922222222222-2-2-2-22-2-2-2-2-2-2222222-20000-20000-2-22200000000000000000000
χ2022222222222-2-2-2-22-2-2-2-2-2-22222-2-2200002000022-2-200000000000000000000
χ2122222222-2-2-22222-2-2-2000000002-2222-2-2-222-2-2000000000000000000000000
χ2222222222-2-2-22222-2-2-2000000002-22-2-222-2-2-222000000000000000000000000
χ2322222222-2-2-22222-2-2-200000000-22-222-2-22-2-222000000000000000000000000
χ2422222222-2-2-22222-2-2-200000000-22-2-2-222222-2-2000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-222000000002-2-200002000000002i2i−2i−2i2i2i−2i−2i000000000000
χ2622222222-2-2-2-2-2-2-2-222000000002-2-20000200000000−2i−2i2i2i−2i−2i2i2i000000000000
χ2722222222-2-2-2-2-2-2-2-22200000000-2220000-2000000002i2i−2i−2i−2i−2i2i2i000000000000
χ2822222222-2-2-2-2-2-2-2-22200000000-2220000-200000000−2i−2i2i2i2i2i−2i−2i000000000000
χ29222-2-22-2-22-2-222-2-222-200000000000000002i−2i2i−2i2i−2i2i−2i2-22-20000000000000000
χ30222-2-22-2-22-2-222-2-222-200000000000000002i−2i2i−2i−2i2i−2i2i-22-220000000000000000
χ31222-2-22-2-22-2-222-2-222-20000000000000000−2i2i−2i2i2i−2i2i−2i-22-220000000000000000
χ32222-2-22-2-22-2-222-2-222-20000000000000000−2i2i−2i2i−2i2i−2i2i2-22-20000000000000000
χ33222-2-22-2-22-2-2-2-2222-22000000000002i−2i2i−2i000002i−2i−2i2i00002-22-2000000000000
χ34222-2-22-2-22-2-2-2-2222-22000000000002i−2i2i−2i00000−2i2i2i−2i0000-22-22000000000000
χ35222-2-22-2-22-2-2-2-2222-2200000000000−2i2i−2i2i000002i−2i−2i2i0000-22-22000000000000
χ36222-2-22-2-22-2-2-2-2222-2200000000000−2i2i−2i2i00000−2i2i2i−2i00002-22-2000000000000
χ37222-2-22-2-2-22222-2-2-2-2222-2-222-2-2000000002i−2i−2i2i000000002i−2i−2i2i000000000000
χ38222-2-22-2-2-22222-2-2-2-2222-2-222-2-200000000−2i2i2i−2i00000000−2i2i2i−2i000000000000
χ39222-2-22-2-2-22222-2-2-2-22-2-222-2-222000000002i−2i−2i2i00000000−2i2i2i−2i000000000000
χ40222-2-22-2-2-22222-2-2-2-22-2-222-2-22200000000−2i2i2i−2i000000002i−2i−2i2i000000000000
χ41222-2-22-2-2-222-2-222-22-222-2-2-2-2220002i−2i−2i2i0000000002i−2i−2i2i0000000000000000
χ42222-2-22-2-2-222-2-222-22-222-2-2-2-222000−2i2i2i−2i000000000−2i2i2i−2i0000000000000000
χ43222-2-22-2-2-222-2-222-22-2-2-22222-2-20002i−2i−2i2i000000000−2i2i2i−2i0000000000000000
χ44222-2-22-2-2-222-2-222-22-2-2-22222-2-2000−2i2i2i−2i0000000002i−2i−2i2i0000000000000000
χ4544-444-4-4-444-40000-4000000000000000000000000000000000022−220000000000
χ4644-444-4-4-444-40000-40000000000000000000000000000000000−22220000000000
χ4744-444-4-4-4-4-4400004000000000000000000000000000000000000002i2−2i2000000
χ4844-444-4-4-4-4-440000400000000000000000000000000000000000000−2i22i2000000
χ4944-4-4-4-4444-440000-400000000000000000000000000000000000000002i2−2i20000
χ5044-4-4-4-4444-440000-40000000000000000000000000000000000000000−2i22i20000
χ5144-4-4-4-444-44-40000400000000000000000000000000000000000022−2200000000
χ5244-4-4-4-444-44-400004000000000000000000000000000000000000−222200000000
χ534-444-4-44-40004-44-40002i2−2i22i2−2i22i2−2i22i2−2i2000000000000000000000000000000000000
χ544-444-4-44-40004-44-4000−2i22i2−2i22i2−2i22i2−2i22i2000000000000000000000000000000000000
χ554-444-4-44-4000-44-440002i2−2i22i2−2i2−2i22i2−2i22i2000000000000000000000000000000000000
χ564-444-4-44-4000-44-44000−2i22i2−2i22i22i2−2i22i2−2i2000000000000000000000000000000000000
χ574-44-44-4-440004-4-440002i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000000000000000000000
χ584-44-44-4-440004-4-44000−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000000000000000000000
χ594-44-44-4-44000-444-40002i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000000000000000000000
χ604-44-44-4-44000-444-4000−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000000000000000000000
χ618-8-88-88-88000000000000000000000000000000000000000000000000000000
χ628-8-8-8888-8000000000000000000000000000000000000000000000000000000

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