Finite Group Databasebeta

← Group #124841

Character table — Group #124841

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122224444444444444444888888888888881616161616161616161616161616161616161616
order12222222222222224444444444444444444444444444448888888888888888
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
χ511111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ611111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii
χ711111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii
χ811111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i
χ9111111111111-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-1-1-111-1-111-1-111-1-111-1-111-1-1
χ10111111111111-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-1-1-111-1-1-1-111-1-111-1-111-1-111
χ11111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-11111-1-11111-1-111-1-1-1-111-1-111
χ12111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-11111-1-111-1-111-1-11111-1-111-1-1
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1−i−iiiii−i−iii−i−i−i−iii
χ172222222222222222-2-2-2-22222-2-2-2-222-2-2-2-20000000000000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-22222-2-2-2-2220000000000000000000000000000
χ19222222222222-2-2-2-222222222-2-2-2-2-2-2-2-2220000000000000000000000000000
χ20222222222222-2-2-2-22222-2-2-2-2222222-2-2-2-20000000000000000000000000000
χ21222-2-22-2-22-2-22000000002i2i−2i−2i2i2i−2i−2i002-200000022-2-2002i−2i0000000000000000
χ22222-2-22-2-22-2-22000000002i2i−2i−2i2i2i−2i−2i002-2000000-2-22200−2i2i0000000000000000
χ23222-2-22-2-22-2-22000000002i2i−2i−2i−2i−2i2i2i00-220022-2-200002i−2i000000000000000000
χ24222-2-22-2-22-2-22000000002i2i−2i−2i−2i−2i2i2i00-2200-2-2220000−2i2i000000000000000000
χ25222-2-22-2-22-2-2200000000−2i−2i2i2i2i2i−2i−2i00-220022-2-20000−2i2i000000000000000000
χ26222-2-22-2-22-2-2200000000−2i−2i2i2i2i2i−2i−2i00-2200-2-22200002i−2i000000000000000000
χ27222-2-22-2-22-2-2200000000−2i−2i2i2i−2i−2i2i2i002-200000022-2-200−2i2i0000000000000000
χ28222-2-22-2-22-2-2200000000−2i−2i2i2i−2i−2i2i2i002-2000000-2-222002i−2i0000000000000000
χ2922-222-2-2-2-22-2222-2-2000000002i−2i2i−2i00002i−2i0000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000
χ3022-222-2-2-2-22-2222-2-2000000002i−2i2i−2i00002i−2i000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000
χ3122-222-2-2-2-22-2222-2-200000000−2i2i−2i2i0000−2i2i0000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000
χ3222-222-2-2-2-22-2222-2-200000000−2i2i−2i2i0000−2i2i000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000
χ3322-222-2-2-2-22-22-2-222000000002i−2i2i−2i0000−2i2i0000000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i00000000
χ3422-222-2-2-2-22-22-2-222000000002i−2i2i−2i0000−2i2i000000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i00000000
χ3522-222-2-2-2-22-22-2-22200000000−2i2i−2i2i00002i−2i0000000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i00000000
χ3622-222-2-2-2-22-22-2-22200000000−2i2i−2i2i00002i−2i000000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i00000000
χ3722-2-2-2-22222-2-22-22-200002i−2i2i−2i00002i−2i0000000000000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i
χ3822-2-2-2-22222-2-22-22-200002i−2i2i−2i00002i−2i000000000000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i
χ3922-2-2-2-22222-2-22-22-20000−2i2i−2i2i0000−2i2i0000000000000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i
χ4022-2-2-2-22222-2-22-22-20000−2i2i−2i2i0000−2i2i000000000000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i
χ4122-2-2-2-22222-2-2-22-2200002i−2i2i−2i0000−2i2i0000000000000000000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i
χ4222-2-2-2-22222-2-2-22-2200002i−2i2i−2i0000−2i2i000000000000000000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i
χ4322-2-2-2-22222-2-2-22-220000−2i2i−2i2i00002i−2i0000000000000000000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i
χ4422-2-2-2-22222-2-2-22-220000−2i2i−2i2i00002i−2i000000000000000000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i
χ4544444444-4-4-4-4000044-4-4000000000000000000000000000000000000000000
χ4644444444-4-4-4-40000-4-444000000000000000000000000000000000000000000
χ47444-4-44-4-4-444-44-4-440000000000000000000000000000000000000000000000
χ48444-4-44-4-4-444-4-444-40000000000000000000000000000000000000000000000
χ4944-444-4-4-44-44-4000000004-4-4400000000000000000000000000000000000000
χ5044-444-4-4-44-44-400000000-444-400000000000000000000000000000000000000
χ5144-4-4-4-444-4-4440000000000004-4-440000000000000000000000000000000000
χ5244-4-4-4-444-4-444000000000000-444-40000000000000000000000000000000000
χ534-444-4-44-400000000004i−4i000000000000002-22-22i−2i2i−2i00000000000000000000
χ544-444-4-44-400000000004i−4i00000000000000-22-22−2i2i−2i2i00000000000000000000
χ554-444-4-44-40000000000−4i4i000000000000002-22-2−2i2i−2i2i00000000000000000000
χ564-444-4-44-40000000000−4i4i00000000000000-22-222i−2i2i−2i00000000000000000000
χ574-44-44-4-44000000004i−4i00000000000000002-2-222i−2i−2i2i00000000000000000000
χ584-44-44-4-44000000004i−4i0000000000000000-222-2−2i2i2i−2i00000000000000000000
χ594-44-44-4-4400000000−4i4i00000000000000002-2-22−2i2i2i−2i00000000000000000000
χ604-44-44-4-4400000000−4i4i0000000000000000-222-22i−2i−2i2i00000000000000000000
χ618-8-88-88-88000000000000000000000000000000000000000000000000000000
χ628-8-8-8888-8000000000000000000000000000000000000000000000000000000

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