Finite Group Databasebeta

← Group #256333

Character table — Group #256333

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122224444444444444444888888888888881616161616161616161616161616161616161616
order12222222222222224444444444444444444444444444444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-1-1-11111-1-1-1-1-1-1111111111-111-1-11-1-1-1-1-11111-1-1-1-1
χ611111111111111111111-1-1-1-11111-1-1-1-1-1-111111111-11-1-111-11-1-1-1-1-1-1-1-11111
χ711111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-11-11111-1-1-1-11111
χ811111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1111111111-1-1-1-1
χ9111111111111-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-1-1-11-1-1-1111-111-1-111-1-111-1-1
χ10111111111111-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-1-1-1-1111-1-1-1111-1-1-1-111-1-111
χ11111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-111111-1-1-1111-1-1-111-1-111-1-111
χ12111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-11111-1111-1-1-11-1-11111-1-111-1-1
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-111
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-11111-1-11111-1-111-1-111-1-1-1-111
χ172222222222222222-2-2-2-22222-2-2-2-222-2-2-2-20000000000000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000
χ19222222222222-2-2-2-222222222-2-2-2-2-2-2-2-2220000000000000000000000000000
χ20222222222222-2-2-2-22222-2-2-2-2-2-2-2-22222-2-20000000000000000000000000000
χ2122222222-2-2-2-222-2-222-2-2000022-2-20000000000000002002-20-2000000000000
χ2222222222-2-2-2-222-2-222-2-2000022-2-2000000000000000-200-2202000000000000
χ2322222222-2-2-2-222-2-2-2-2220000-2-22200000000000000202-200-20000000000000
χ2422222222-2-2-2-222-2-2-2-2220000-2-22200000000000000-20-220020000000000000
χ2522222222-2-2-2-2-2-22222-2-20000-2-2220000000000000020-2200-20000000000000
χ2622222222-2-2-2-2-2-22222-2-20000-2-22200000000000000-202-20020000000000000
χ2722222222-2-2-2-2-2-222-2-222000022-2-2000000000000000200-220-2000000000000
χ2822222222-2-2-2-2-2-222-2-222000022-2-2000000000000000-2002-202000000000000
χ29222-2-2-2-222-2-222-22-2000022-2-200002-2000000000000000000000000i2−i2i2−i2i2−i2i2−i2
χ30222-2-2-2-222-2-222-22-2000022-2-200002-2000000000000000000000000−i2i2−i2i2−i2i2−i2i2
χ31222-2-2-2-222-2-222-22-20000-2-2220000-22000000000000000000000000i2−i2i2−i2−i2i2−i2i2
χ32222-2-2-2-222-2-222-22-20000-2-2220000-22000000000000000000000000−i2i2−i2i2i2−i2i2−i2
χ33222-2-2-2-222-2-22-22-22000022-2-20000-22000000000000000000000000i2−i2−i2i2i2−i2−i2i2
χ34222-2-2-2-222-2-22-22-22000022-2-20000-22000000000000000000000000−i2i2i2−i2−i2i2i2−i2
χ35222-2-2-2-222-2-22-22-220000-2-22200002-2000000000000000000000000i2−i2−i2i2−i2i2i2−i2
χ36222-2-2-2-222-2-22-22-220000-2-22200002-2000000000000000000000000−i2i2i2−i2i2−i2−i2i2
χ3722-22-2-22-2-22-22000000002i−2i2i−2i2-22-2002i−2i0000002i2i−2i−2i00000000002-200000000
χ3822-22-2-22-2-22-22000000002i−2i2i−2i2-22-2002i−2i000000−2i−2i2i2i0000000000-2200000000
χ3922-22-2-22-2-22-22000000002i−2i2i−2i-22-2200−2i2i002i2i−2i−2i0000000000002-20000000000
χ4022-22-2-22-2-22-22000000002i−2i2i−2i-22-2200−2i2i00−2i−2i2i2i000000000000-220000000000
χ4122-22-2-22-2-22-2200000000−2i2i−2i2i2-22-200−2i2i0000002i2i−2i−2i0000000000-2200000000
χ4222-22-2-22-2-22-2200000000−2i2i−2i2i2-22-200−2i2i000000−2i−2i2i2i00000000002-200000000
χ4322-22-2-22-2-22-2200000000−2i2i−2i2i-22-22002i−2i002i2i−2i−2i000000000000-220000000000
χ4422-22-2-22-2-22-2200000000−2i2i−2i2i-22-22002i−2i00−2i−2i2i2i0000000000002-20000000000
χ45444-4-4-4-44-444-44-4-440000000000000000000000000000000000000000000000
χ46444-4-4-4-44-444-4-444-40000000000000000000000000000000000000000000000
χ4744-44-4-44-44-44-40000000000004-4-440000000000000000000000000000000000
χ4844-44-4-44-44-44-4000000000000-444-40000000000000000000000000000000000
χ4944-4-444-4-444-4-4000000000000000000004-40000000000000000000000000000
χ5044-4-444-4-444-4-400000000000000000000-440000000000000000000000000000
χ5144-4-444-4-4-4-444000000004i−4i−4i4i00000000000000000000000000000000000000
χ5244-4-444-4-4-4-44400000000−4i4i4i−4i00000000000000000000000000000000000000
χ534-44-44-44-400000000004-4000000000000002i−2i2i−2i2i−2i2i−2i00000000000000000000
χ544-44-44-44-400000000004-400000000000000−2i2i−2i2i−2i2i−2i2i00000000000000000000
χ554-44-44-44-40000000000-44000000000000002i−2i2i−2i−2i2i−2i2i00000000000000000000
χ564-44-44-44-40000000000-4400000000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000
χ574-4-4-4-4444000000004-400000000000000002-2-222-2-2200000000000000000000
χ584-4-4-4-4444000000004-40000000000000000-222-2-222-200000000000000000000
χ594-4-4-4-444400000000-4400000000000000002-2-22-222-200000000000000000000
χ604-4-4-4-444400000000-440000000000000000-222-22-2-2200000000000000000000
χ618-888-88-8-8000000000000000000000000000000000000000000000000000000
χ628-8-888-8-88000000000000000000000000000000000000000000000000000000

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