Finite Group Databasebeta

← Group #267236

Character table — Group #267236

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111111122222222222244444488888888888888888888888881616161616161616161616163232
order12222222222244444444444444222244444888888888888888844448888888844
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ511111111111111111111111111-1-1-1-11-1-1-1-11111111111111111-1-1-1-111-1-1-1-111-1-1
χ611111111111111111111111111-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ711111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-111
χ811111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
χ911111111-1-1-1-11111111111-1-1-1-111-1-1-111-1-111-1-111-1-11111-1-1-1-111-1-11111-1-1-1-11-1
χ1011111111-1-1-1-11111111111-1-1-1-111-1-1-111-1-111-1-111-1-1-1-1-1-11111-1-111-1-111-1-111-11
χ1111111111-1-1-1-11111111111-1-1-1-111-1-1-111-1-1-1-111-1-1111111-1-1-1-111-1-1-1-1-1-11111-11
χ1211111111-1-1-1-11111111111-1-1-1-111-1-1-111-1-1-1-111-1-111-1-1-1-11111-1-11111-1-111-1-11-1
χ1311111111-1-1-1-11111111111-1-1-1-1-1-111-1-1-11111-1-111-1-11111-1-1-1-1-1-11111-1-111-1-1-11
χ1411111111-1-1-1-11111111111-1-1-1-1-1-111-1-1-11111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-111111-1
χ1511111111-1-1-1-11111111111-1-1-1-1-1-111-1-1-111-1-111-1-1111111-1-1-1-1-1-111-1-111-1-1111-1
χ1611111111-1-1-1-11111111111-1-1-1-1-1-111-1-1-111-1-111-1-111-1-1-1-1111111-1-11111-1-1-1-1-11
χ1722222222222222-2-22-2-22-2-2-2-2222222-2-2-2-2-2000000000000000000000000000000
χ1822222222222222-2-22-2-22-2-2-2-222-2-2-2-2-22222000000000000000000000000000000
χ19222222222222-2-222-222-2-2-222-2-20000-200002222-2-2-2-20000000000000000000000
χ20222222222222-2-222-222-2-2-222-2-20000-20000-2-2-2-222220000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-222-2-2-2-200002000000000000000000000000002i−2i2i−2i0000
χ22222222222222-2-2-2-2-2-2-2-222-2-2-2-20000200000000000000000000000000−2i2i−2i2i0000
χ2322222222-2-2-2-222-2-22-2-22-2-222-2-222-2-22-2-222000000000000000000000000000000
χ2422222222-2-2-2-222-2-22-2-22-2-222-2-2-2-222222-2-2000000000000000000000000000000
χ2522222222-2-2-2-2-2-222-222-2-2-2-2-22200002000022-2-2-2-2220000000000000000000000
χ2622222222-2-2-2-2-2-222-222-2-2-2-2-222000020000-2-22222-2-20000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-22222220000-2000000000000000000000000002i−2i−2i2i0000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-22222220000-200000000000000000000000000−2i2i2i−2i0000
χ29222-2-22-2-222-2-200-2-20220002-20000000000000002-22-2i2i2−i2−i2i2i2−i2−i20000i2−i20000i2−i200
χ30222-2-22-2-222-2-200-2-20220002-20000000000000002-22-2−i2−i2i2i2−i2−i2i2i20000−i2i20000−i2i200
χ31222-2-22-2-222-2-200-2-20220002-2000000000000000-22-22i2i2−i2−i2i2i2−i2−i20000−i2i20000−i2i200
χ32222-2-22-2-222-2-200-2-20220002-2000000000000000-22-22−i2−i2i2i2−i2−i2i2i20000i2−i20000i2−i200
χ33222-2-22-2-2-2-22200-2-2022000-220000000000000002-2-22i2i2−i2−i2−i2−i2i2i20000i2−i20000−i2i200
χ34222-2-22-2-2-2-22200-2-2022000-220000000000000002-2-22−i2−i2i2i2i2i2−i2−i20000−i2i20000i2−i200
χ35222-2-22-2-2-2-22200-2-2022000-22000000000000000-222-2i2i2−i2−i2−i2−i2i2i20000−i2i20000i2−i200
χ36222-2-22-2-2-2-22200-2-2022000-22000000000000000-222-2−i2−i2i2i2i2i2−i2−i20000i2−i20000−i2i200
χ372-2-2-2-222200002-22-2-22-222-200002-20002-2000000000000002-22-2002-20000000000
χ382-2-2-2-222200002-22-2-22-222-200002-20002-200000000000000-22-2200-220000000000
χ392-2-2-2-222200002-22-2-22-222-20000-22000-22000000000000002-22-200-220000000000
χ402-2-2-2-222200002-22-2-22-222-20000-22000-2200000000000000-22-22002-20000000000
χ412-2-2-2-222200002-2-22-2-222-2200002-2000-2200000000002-22-200002-2000000000000
χ422-2-2-2-222200002-2-22-2-222-2200002-2000-220000000000-22-220000-22000000000000
χ432-2-2-2-222200002-2-22-2-222-220000-220002-200000000002-22-20000-22000000000000
χ442-2-2-2-222200002-2-22-2-222-220000-220002-20000000000-22-2200002-2000000000000
χ45444-4-44-4-444-4-400440-4-4000-4400000000000000000000000000000000000000000
χ46444-4-44-4-4-4-44400440-4-40004-400000000000000000000000000000000000000000
χ4744-44-4-4-444-44-44400-400-400004-4000000000000000000000000000000000000000
χ4844-44-4-4-444-44-4-4-40040040000-44000000000000000000000000000000000000000
χ4944-44-4-4-44-44-444400-400-40000-44000000000000000000000000000000000000000
χ5044-44-4-4-44-44-44-4-400400400004-4000000000000000000000000000000000000000
χ5144-4-44-44-44-4-44000000000000000000000002i2−2i22i2−2i200000000000000000000000000
χ5244-4-44-44-44-4-4400000000000000000000000−2i22i2−2i22i200000000000000000000000000
χ5344-4-44-44-4-444-4000000000000000000000002i2−2i2−2i22i200000000000000000000000000
χ5444-4-44-44-4-444-400000000000000000000000−2i22i22i2−2i200000000000000000000000000
χ554-44-44-4-4400004-400400-400000000000004i−4i000000000000000000000000000000
χ564-44-44-4-4400004-400400-40000000000000−4i4i000000000000000000000000000000
χ574-44-44-4-440000-4400-4004000000004-400000000000000000000000000000000000
χ584-44-44-4-440000-4400-400400000000-4400000000000000000000000000000000000
χ594-4-4444-4-40000004-40-440000000000000000000000002i2−2i2−2i22i2000000000000000000
χ604-4-4444-4-40000004-40-44000000000000000000000000−2i22i22i2−2i2000000000000000000
χ614-4-4444-4-4000000-4404-400000000000000000000000000002i2−2i2−2i22i200000000000000
χ624-4-4444-4-4000000-4404-40000000000000000000000000000−2i22i22i2−2i200000000000000
χ634-4-4-4-44440000-444-444-4-4-440000000000000000000000000000000000000000000
χ644-4-4-4-44440000-44-444-44-44-40000000000000000000000000000000000000000000
χ658-888-8-88-8000000000000000000000000000000000000000000000000000000000

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