Finite Group Databasebeta

← Group #267237

Character table — Group #267237

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111111122222222222244444488888888888888888888888881616161616161616161616163232
order12222222222244444444444444222244444888888888888888844448888888844
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ311111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ511111111111111111111111111-1-1-1-1-1-1-1-111111111111111111-1-1-1-11111-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111
χ811111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
χ911111111-1-1-1-111111111-1-1-1-11111-1-111-1-1-111-1-111-1-11111-1-1-1-111-1-111-1-111-1-11-1
χ1011111111-1-1-1-111111111-1-1-1-11111-1-111-1-1-111-1-111-1-1-1-1-1-11111-1-111-1-11111-1-1-11
χ1111111111-1-1-1-111111111-1-1-1-11111-1-111-1-1-1-1-111-1-1111111-1-1-1-111-1-1-1-111-1-111-11
χ1211111111-1-1-1-111111111-1-1-1-11111-1-111-1-1-1-1-111-1-111-1-1-1-11111-1-11111-1-1-1-1111-1
χ1311111111-1-1-1-111111111-1-1-1-111-1-111-1-111-111-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111-11
χ1411111111-1-1-1-111111111-1-1-1-111-1-111-1-111-111-1-111-1-1-1-1-1-1111111-1-1-1-111-1-1111-1
χ1511111111-1-1-1-111111111-1-1-1-111-1-111-1-111-1-1-111-1-1111111-1-1-1-1-1-111-1-11111-1-11-1
χ1611111111-1-1-1-111111111-1-1-1-111-1-111-1-111-1-1-111-1-111-1-1-1-1111111-1-111-1-111-1-1-11
χ172222222222222-2-222-2-2222-2-2-2-22222-2-2-2-2-2000000000000000000000000000000
χ182222222222222-2-222-2-2222-2-2-2-2-2-2-2-22222-2000000000000000000000000000000
χ19222222222222-222-2-222-2-2-222-2-200000000-22222-2-2-2-20000000000000000000000
χ20222222222222-222-2-222-2-2-222-2-200000000-2-2-2-2-222220000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-2220000000020000000000000000000000002i−2i2i−2i00
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-222000000002000000000000000000000000−2i2i−2i2i00
χ2322222222-2-2-2-22-2-222-2-22-2-222-2-222-2-2-2-2222000000000000000000000000000000
χ2422222222-2-2-2-22-2-222-2-22-2-222-2-2-2-22222-2-22000000000000000000000000000000
χ2522222222-2-2-2-2-222-2-222-222-2-2-2-200000000222-2-2-2-2220000000000000000000000
χ2622222222-2-2-2-2-222-2-222-222-2-2-2-2000000002-2-22222-2-20000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-222222200000000-20000000000000000000000002i−2i−2i2i00
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-222222200000000-2000000000000000000000000−2i2i2i−2i00
χ29222-2-2-22-222-2-20-2-200220002-20000000000000002-22-2i2i2−i2−i2i2i2−i2−i20000i2−i2i2−i2000000
χ30222-2-2-22-222-2-20-2-200220002-20000000000000002-22-2−i2−i2i2i2−i2−i2i2i20000−i2i2−i2i2000000
χ31222-2-2-22-222-2-20-2-200220002-2000000000000000-22-22i2i2−i2−i2i2i2−i2−i20000−i2i2−i2i2000000
χ32222-2-2-22-222-2-20-2-200220002-2000000000000000-22-22−i2−i2i2i2−i2−i2i2i20000i2−i2i2−i2000000
χ33222-2-2-22-2-2-2220-2-20022000-220000000000000002-2-22i2i2−i2−i2−i2−i2i2i20000i2−i2−i2i2000000
χ34222-2-2-22-2-2-2220-2-20022000-220000000000000002-2-22−i2−i2i2i2i2i2−i2−i20000−i2i2i2−i2000000
χ35222-2-2-22-2-2-2220-2-20022000-22000000000000000-222-2i2i2−i2−i2−i2−i2i2i20000−i2i2i2−i2000000
χ36222-2-2-22-2-2-2220-2-20022000-22000000000000000-222-2−i2−i2i2i2i2i2−i2−i20000i2−i2−i2i2000000
χ372-2-2-22-2220000-22-22-22-2200002-2002-2002-20000000002-22-20000002-20000000000
χ382-2-2-22-2220000-22-22-22-2200002-2002-2002-2000000000-22-22000000-220000000000
χ392-2-2-22-2220000-22-22-22-2200002-200-2200-220000000002-22-2000000-220000000000
χ402-2-2-22-2220000-22-22-22-2200002-200-2200-22000000000-22-220000002-20000000000
χ412-2-2-22-2220000-2-222-2-2220000-22002-200-2200000000000002-22-22-2000000000000
χ422-2-2-22-2220000-2-222-2-2220000-22002-200-220000000000000-22-22-22000000000000
χ432-2-2-22-2220000-2-222-2-2220000-2200-22002-200000000000002-22-2-22000000000000
χ442-2-2-22-2220000-2-222-2-2220000-2200-22002-20000000000000-22-222-2000000000000
χ45444-4-4-44-444-4-404400-4-4000-4400000000000000000000000000000000000000000
χ46444-4-4-44-4-4-44404400-4-40004-400000000000000000000000000000000000000000
χ4744-444-4-4-44-44-4400-4-40044-40000000000000000000000000000000000000000000
χ4844-444-4-4-44-44-4-4004400-4-440000000000000000000000000000000000000000000
χ4944-444-4-4-4-44-44400-4-4004-440000000000000000000000000000000000000000000
χ5044-444-4-4-4-44-44-4004400-44-40000000000000000000000000000000000000000000
χ5144-4-4-44-444-4-440000000000000000000000022−2222−2200000000000000000000000000
χ5244-4-4-44-444-4-4400000000000000000000000−2222−222200000000000000000000000000
χ5344-4-4-44-44-444-40000000000000000000000022−22−222200000000000000000000000000
χ5444-4-4-44-44-444-400000000000000000000000−222222−2200000000000000000000000000
χ554-44-444-4-400004004-400-40000004-40000000000000000000000000000000000000
χ564-44-444-4-400004004-400-4000000-440000000000000000000000000000000000000
χ574-44-444-4-40000-400-4400400000000004i−4i000000000000000000000000000000000
χ584-44-444-4-40000-400-440040000000000−4i4i000000000000000000000000000000000
χ594-4-44-444-4000004-400-4400000000000000000000000000002i2−2i2−2i22i200000000000000
χ604-4-44-444-4000004-400-440000000000000000000000000000−2i22i22i2−2i200000000000000
χ614-4-44-444-400000-44004-40000000000000000000000002i2−2i2−2i22i2000000000000000000
χ624-4-44-444-400000-44004-4000000000000000000000000−2i22i22i2−2i2000000000000000000
χ634-4-4-44-444000044-4-444-4-40000-44000000000000000000000000000000000000000
χ644-4-4-44-44400004-44-44-44-400004-4000000000000000000000000000000000000000
χ658-888-8-8-88000000000000000000000000000000000000000000000000000000000

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