Finite Group Databasebeta

← Group #258713

Character table — Group #258713

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111111112222222244444444888888888888888888888888816161616161616161616161616161616
order12222222444444444444444422444444488888888888888882244444444448888
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1
χ3111111111111111111111111111-1-111-1-111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-1-1-1111111
χ5111111111111111111111111-1-1111-1-11111111111-1-1-1-1-1-1-1-1-111-111-1-1-1-111-1-1-1-1
χ6111111111111111111111111-1-1111-1-111-1-1-1-1-1-1-1-111111111-111-1-1-1-1-1-1-1-1-11111
χ7111111111111111111111111-1-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111
χ8111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ91111111111111111-1-11-1-1-1-1111-111-1-1111111-1-1-1-11111-1-1-1-1-1-1-111111-1-1-1-111-1-1
χ101111111111111111-1-11-1-1-1-1111-111-1-111-1-1-1-11111-1-1-1-11111-1-1-11-1-111-1-111-1-111
χ111111111111111111-1-11-1-1-1-1111-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1111-1-1-1-11111-1-111
χ121111111111111111-1-11-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-111111-1-111-1-111-1-1
χ131111111111111111-1-11-1-1-1-11-1-1-11111111111-1-1-1-1-1-1-1-111111-1-1-111-1-111-1-1-1-111
χ141111111111111111-1-11-1-1-1-11-1-1-1111111-1-1-1-111111111-1-1-1-11-1-1-1-1-1-1-1111111-1-1
χ151111111111111111-1-11-1-1-1-11-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111111-1-1-111-1-11111-1-1
χ161111111111111111-1-11-1-1-1-11-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1111-11111-1-1-1-1-1-111
χ172222222222-2-222-2-222-222-2-2-222-20022000000000000000000-200-2000000000000
χ182222222222-2-222-2-222-222-2-2-2-2-2-200-2-20000000000000000002002000000000000
χ192222222222-2-222-2-2-2-2-2-2-222-222200-2-2000000000000000000200-2000000000000
χ202222222222-2-222-2-2-2-2-2-2-222-2-2-220022000000000000000000-2002000000000000
χ2122222222-2-222-2-22222-2-2-222-200-22200-2-200000000000000000-220000000000000
χ2222222222-2-222-2-22222-2-2-222-200-2-2-20022000000000000000002-20000000000000
χ2322222222-2-222-2-222-2-2-222-2-2-20022200-2-2000000000000000002-20000000000000
χ2422222222-2-222-2-222-2-2-222-2-2-2002-2-2002200000000000000000-220000000000000
χ2522222222-2-2-2-2-2-2-2-2222-2-2-2-2200200000000000000000000000000002-22-2000000
χ2622222222-2-2-2-2-2-2-2-2222-2-2-2-220020000000000000000000000000000-22-22000000
χ2722222222-2-2-2-2-2-2-2-2-2-222222200-200000000000000000000000000002-2-22000000
χ2822222222-2-2-2-2-2-2-2-2-2-222222200-20000000000000000000000000000-222-2000000
χ29222-2-2-2-222-2002-2002i−2i02i−2i0002-20002i−2i0022−2−2i2i2−i2−i222−2−2i2i2−i2−i20000000000000000
χ30222-2-2-2-222-2002-2002i−2i02i−2i0002-20002i−2i00−2−222−i2−i2i2i2−2−222−i2−i2i2i20000000000000000
χ31222-2-2-2-222-2002-2002i−2i02i−2i000-22000−2i2i0022−2−2i2i2−i2−i2−2−222−i2−i2i2i20000000000000000
χ32222-2-2-2-222-2002-2002i−2i02i−2i000-22000−2i2i00−2−222−i2−i2i2i222−2−2i2i2−i2−i20000000000000000
χ33222-2-2-2-222-2002-200−2i2i0−2i2i0002-2000−2i2i0022−2−2−i2−i2i2i222−2−2−i2−i2i2i20000000000000000
χ34222-2-2-2-222-2002-200−2i2i0−2i2i0002-2000−2i2i00−2−222i2i2−i2−i2−2−222i2i2−i2−i20000000000000000
χ35222-2-2-2-222-2002-200−2i2i0−2i2i000-220002i−2i0022−2−2−i2−i2i2i2−2−222i2i2−i2−i20000000000000000
χ36222-2-2-2-222-2002-200−2i2i0−2i2i000-220002i−2i00−2−222i2i2−i2−i222−2−2−i2−i2i2i20000000000000000
χ372-22-222-2-2222-2-2-22-200-2000020002i−2i002i−2i00002-22-20000000000000000002i−2i0000
χ382-22-222-2-2222-2-2-22-200-2000020002i−2i002i−2i0000-22-22000000000000000000−2i2i0000
χ392-22-222-2-2222-2-2-22-200-200002000−2i2i00−2i2i00002-22-2000000000000000000−2i2i0000
χ402-22-222-2-2222-2-2-22-200-200002000−2i2i00−2i2i0000-22-220000000000000000002i−2i0000
χ412-22-222-2-2-2-22-2222-20020000-20002i−2i00−2i2i2i−2i2i−2i00000000000000002-20000000000
χ422-22-222-2-2-2-22-2222-20020000-20002i−2i00−2i2i−2i2i−2i2i0000000000000000-220000000000
χ432-22-222-2-2-2-22-2222-20020000-2000−2i2i002i−2i2i−2i2i−2i0000000000000000-220000000000
χ442-22-222-2-2-2-22-2222-20020000-2000−2i2i002i−2i−2i2i−2i2i00000000000000002-20000000000
χ45444-4-4-4-44-4400-44004i−4i0−4i4i00000000000000000000000000000000000000000000
χ46444-4-4-4-44-4400-4400−4i4i04i−4i00000000000000000000000000000000000000000000
χ4744-4-44-44-4004-400-44000000000000000000000000000000000000000000000002i2−2i2
χ4844-4-44-44-4004-400-4400000000000000000000000000000000000000000000000−2i22i2
χ4944-4-44-44-400-44004-40000000000000000000000000000000000000000000002i2−2i200
χ5044-4-44-44-400-44004-4000000000000000000000000000000000000000000000−2i22i200
χ514-444-4-44-44-400-44000000000000000000000002i2−2i2−2i22i2000000000000000000000000
χ524-444-4-44-44-400-4400000000000000000000000−2i22i22i2−2i2000000000000000000000000
χ534-444-4-44-4-44004-400000000000000000002i2−2i2−2i22i20000000000000000000000000000
χ544-444-4-44-4-44004-40000000000000000000−2i22i22i2−2i20000000000000000000000000000
χ554-44-444-4-444-44-4-4-440040000-400000000000000000000000000000000000000000
χ564-44-444-4-4-4-4-4444-4400-40000400000000000000000000000000000000000000000
χ574-4-444-4-44004400-4-4000000000000000000000000000002i2−2i22i2−2i20000000000000000
χ584-4-444-4-44004400-4-400000000000000000000000000000−2i22i2−2i22i20000000000000000
χ594-4-444-4-4400-4-40044000000000000000000000000022−2222−2200000000000000000000
χ604-4-444-4-4400-4-400440000000000000000000000000−2222−222200000000000000000000
χ614-4-4-4-444400000000000004-40000000000000000002-2-222-2-220000000000000000
χ624-4-4-4-444400000000000004-4000000000000000000-222-2-222-20000000000000000
χ634-4-4-4-44440000000000000-440000000000000000002-2-22-222-20000000000000000
χ644-4-4-4-44440000000000000-44000000000000000000-222-22-2-220000000000000000
χ6588-88-88-8-8000000000000000000000000000000000000000000000000000000000

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