Finite Group Databasebeta

← Group #100142

Character table — Group #100142

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122222222444444444488888888888888881616161616161616161616161616161616161616
order12222222222244444444444444444444444444444444448888888888888888
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111
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
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ9111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1ii−i−iii−i−iii−i−iii−i−i
χ10111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1−i−iii−i−iii−i−iii−i−iii
χ11111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111ii−i−iii−i−i−i−iii−i−iii
χ12111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111−i−iii−i−iiiii−i−iii−i−i
χ13111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ14111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ15111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ16111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1−i−iiiii−i−iii−i−i−i−iii
χ17222222222222222222-2-2-2-2-2-2-2-222-2-222-2-20000000000000000000000000000
χ18222222222222222222-2-2-2-2-2-2-2-2-2-222-2-2220000000000000000000000000000
χ19222222222222-2-2-2-2-2-2-2-2-2-2222222-2-2-2-2220000000000000000000000000000
χ20222222222222-2-2-2-2-2-2-2-2-2-22222-2-22222-2-20000000000000000000000000000
χ2122222222-2-2-2-22222-2-222-2-222-2-20000000000000000000000002-22-200000000
χ2222222222-2-2-2-22222-2-222-2-222-2-2000000000000000000000000-22-2200000000
χ2322222222-2-2-2-22222-2-2-2-222-2-222000000000000000000002-22-2000000000000
χ2422222222-2-2-2-22222-2-2-2-222-2-22200000000000000000000-22-22000000000000
χ2522222222-2-2-2-2-2-2-2-22222-2-2-2-2220000000000000000000000002i−2i−2i2i00000000
χ2622222222-2-2-2-2-2-2-2-22222-2-2-2-222000000000000000000000000−2i2i2i−2i00000000
χ2722222222-2-2-2-2-2-2-2-222-2-22222-2-2000000000000000000002i−2i−2i2i000000000000
χ2822222222-2-2-2-2-2-2-2-222-2-22222-2-200000000000000000000−2i2i2i−2i000000000000
χ29222-2-2-2-222-22-22i2i−2i−2i2i−2i2-22-22i−2i2i−2i00000000000000002i−2i2-20000000000000000
χ30222-2-2-2-222-22-22i2i−2i−2i2i−2i2-22-22i−2i2i−2i0000000000000000−2i2i-220000000000000000
χ31222-2-2-2-222-22-22i2i−2i−2i2i−2i-22-22−2i2i−2i2i0000000022-2-22i2i−2i−2i00000000000000000000
χ32222-2-2-2-222-22-22i2i−2i−2i2i−2i-22-22−2i2i−2i2i00000000-2-222−2i−2i2i2i00000000000000000000
χ33222-2-2-2-222-22-2−2i−2i2i2i−2i2i2-22-2−2i2i−2i2i00000000000000002i−2i-220000000000000000
χ34222-2-2-2-222-22-2−2i−2i2i2i−2i2i2-22-2−2i2i−2i2i0000000000000000−2i2i2-20000000000000000
χ35222-2-2-2-222-22-2−2i−2i2i2i−2i2i-22-222i−2i2i−2i0000000022-2-2−2i−2i2i2i00000000000000000000
χ36222-2-2-2-222-22-2−2i−2i2i2i−2i2i-22-222i−2i2i−2i00000000-2-2222i2i−2i−2i00000000000000000000
χ37222-2-2-2-22-22-222i2i−2i−2i−2i2i2-2-222i−2i−2i2i00000000000000000000000000002ζ3−2ζ32ζ−2ζ0000
χ38222-2-2-2-22-22-222i2i−2i−2i−2i2i2-2-222i−2i−2i2i0000000000000000000000000000−2ζ32ζ3−2ζ2ζ0000
χ39222-2-2-2-22-22-222i2i−2i−2i−2i2i-222-2−2i2i2i−2i000000000000000000000000000000002ζ3−2ζ32ζ−2ζ
χ40222-2-2-2-22-22-222i2i−2i−2i−2i2i-222-2−2i2i2i−2i00000000000000000000000000000000−2ζ32ζ3−2ζ2ζ
χ41222-2-2-2-22-22-22−2i−2i2i2i2i−2i2-2-22−2i2i2i−2i00000000000000000000000000002ζ−2ζ2ζ3−2ζ30000
χ42222-2-2-2-22-22-22−2i−2i2i2i2i−2i2-2-22−2i2i2i−2i0000000000000000000000000000−2ζ2ζ−2ζ32ζ30000
χ43222-2-2-2-22-22-22−2i−2i2i2i2i−2i-222-22i−2i−2i2i000000000000000000000000000000002ζ−2ζ2ζ3−2ζ3
χ44222-2-2-2-22-22-22−2i−2i2i2i2i−2i-222-22i−2i−2i2i00000000000000000000000000000000−2ζ2ζ−2ζ32ζ3
χ4544-444-4-4-400004-44-40000000000000000002-22-22-22-200000000000000000000
χ4644-444-4-4-400004-44-4000000000000000000-22-22-22-2200000000000000000000
χ4744-444-4-4-40000-44-440000000000000000002-22-2-22-2200000000000000000000
χ4844-444-4-4-40000-44-44000000000000000000-22-222-22-200000000000000000000
χ4944-4-4-444-400004i−4i−4i4i0000000000000000002-2-222i−2i−2i2i00000000000000000000
χ5044-4-4-444-400004i−4i−4i4i000000000000000000-222-2−2i2i2i−2i00000000000000000000
χ5144-4-4-444-40000−4i4i4i−4i0000000000000000002-2-22−2i2i2i−2i00000000000000000000
χ5244-4-4-444-40000−4i4i4i−4i000000000000000000-222-22i−2i−2i2i00000000000000000000
χ534-4-44-44-4444-4-400000000000000004i−4i00000000000000000000000000000000
χ544-4-44-44-4444-4-40000000000000000−4i4i00000000000000000000000000000000
χ554-4-44-44-44-4-444000000000000000000004-40000000000000000000000000000
χ564-4-44-44-44-4-44400000000000000000000-440000000000000000000000000000
χ574-4-4-44-4444-4-44000000000000004-40000000000000000000000000000000000
χ584-4-4-44-4444-4-4400000000000000-440000000000000000000000000000000000
χ594-4-4-44-444-444-40000000000000000004-4000000000000000000000000000000
χ604-4-4-44-444-444-4000000000000000000-44000000000000000000000000000000
χ618-888-8-88-8000000000000000000000000000000000000000000000000000000
χ628-88-888-8-8000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.