Finite Group Databasebeta

← Group #317698

Character table — Group #317698

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222222222444444444444444444444444161616161616161616161616161616161616161616161616
order12222222444444444444444444448888888888888888444444444444888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ311111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ91111111111-1-1-1-1111111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-111-1-111-1-1
χ101111111111-1-1-1-1111111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-111-1-11111-1-1
χ111111111111-1-1-1-1111111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-111-1-111
χ121111111111-1-1-1-1111111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-111-1-1-1-111
χ131111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-11111-1-1-1-111-1-111
χ141111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-11111-1-1-1-111
χ151111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-111-1-11111-1-111-1-1
χ161111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-111-1-1-1-11111-1-1
χ1722222222222222-2-2-222-222-2-2-2-2-2-200000000000000002-22-200000000000000000000
χ1822222222222222-2-2-222-222-2-2-2-2-2-20000000000000000-22-2200000000000000000000
χ192222222222-2-2-2-2-2-2-222-2-2-222-2-22200000000000000002-2-2200000000000000000000
χ202222222222-2-2-2-2-2-2-222-2-2-222-2-2220000000000000000-222-200000000000000000000
χ2122222222-2-22222222-2-22-2-222-2-2-2-22222-2-2-2-22222-2-2-2-2000000000000000000000000
χ2222222222-2-22222222-2-22-2-222-2-2-2-2-2-2-2-22222-2-2-2-22222000000000000000000000000
χ2322222222-2-22222-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000000000002i−2i2i−2i
χ2422222222-2-22222-2-2-2-2-2-2-2-2-2-22222000000000000000000000000000000000000−2i2i−2i2i
χ2522222222-2-2-2-2-2-2222-2-2222-2-2-2-2222222-2-2-2-2-2-2-2-22222000000000000000000000000
χ2622222222-2-2-2-2-2-2222-2-2222-2-2-2-222-2-2-2-222222222-2-2-2-2000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2-20000000000000000000000000000000000002i−2i−2i2i
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2-2000000000000000000000000000000000000−2i2i2i−2i
χ29222-2-2-22-22-200002-2-22-2200002-2002i2i−2i−2i2i2i−2i−2i000000000000002i−2i002-2000000000000
χ30222-2-2-22-22-200002-2-22-2200002-2002i2i−2i−2i2i2i−2i−2i00000000000000−2i2i00-22000000000000
χ31222-2-2-22-22-200002-2-22-2200002-200−2i−2i2i2i−2i−2i2i2i000000000000002i−2i00-22000000000000
χ32222-2-2-22-22-200002-2-22-2200002-200−2i−2i2i2i−2i−2i2i2i00000000000000−2i2i002-2000000000000
χ33222-2-2-22-2-2200002-2-2-2220000-22002i2i−2i−2i−2i−2i2i2i0000000000002-2002i−2i00000000000000
χ34222-2-2-22-2-2200002-2-2-2220000-22002i2i−2i−2i−2i−2i2i2i000000000000-2200−2i2i00000000000000
χ35222-2-2-22-2-2200002-2-2-2220000-2200−2i−2i2i2i2i2i−2i−2i0000000000002-200−2i2i00000000000000
χ36222-2-2-22-2-2200002-2-2-2220000-2200−2i−2i2i2i2i2i−2i−2i000000000000-22002i−2i00000000000000
χ3722-2-222-2-20022-2-2-22-2002002-2000000002-22-2000022-2-2000000000000i2−i2i2−i2i2−i2i2−i20000
χ3822-2-222-2-20022-2-2-22-2002002-2000000002-22-2000022-2-2000000000000−i2i2−i2i2−i2i2−i2i20000
χ3922-2-222-2-20022-2-2-22-2002002-200000000-22-220000-2-222000000000000i2−i2i2−i2−i2i2−i2i20000
χ4022-2-222-2-20022-2-2-22-2002002-200000000-22-220000-2-222000000000000−i2i2−i2i2i2−i2i2−i20000
χ4122-2-222-2-200-2-222-22-200200-22000000002-22-20000-2-222000000000000i2−i2−i2i2i2−i2−i2i20000
χ4222-2-222-2-200-2-222-22-200200-22000000002-22-20000-2-222000000000000−i2i2i2−i2−i2i2i2−i20000
χ4322-2-222-2-200-2-222-22-200200-2200000000-22-22000022-2-2000000000000i2−i2−i2i2−i2i2i2−i20000
χ4422-2-222-2-200-2-222-22-200200-2200000000-22-22000022-2-2000000000000−i2i2i2−i2i2−i2−i2i20000
χ45444-4-4-44-44-40000-4444-4-40000-44000000000000000000000000000000000000000000
χ46444-4-4-44-4-440000-444-44-400004-4000000000000000000000000000000000000000000
χ4744-44-4-4-4400000044-400-4000000000000000044-4-40000000000000000000000000000
χ4844-44-4-4-4400000044-400-40000000000000000-4-4440000000000000000000000000000
χ4944-44-4-4-44000000-4-440040000000000004i−4i−4i4i00000000000000000000000000000000
χ5044-44-4-4-44000000-4-44004000000000000−4i4i4i−4i00000000000000000000000000000000
χ5144-4-444-4-40044-4-44-4400-400-4400000000000000000000000000000000000000000000
χ5244-4-444-4-400-4-4444-4400-4004-400000000000000000000000000000000000000000000
χ534-4444-4-4-44-44-44-4000-4404-40000000000000000000000000000000000000000000000
χ544-4444-4-4-44-4-44-44000-440-440000000000000000000000000000000000000000000000
χ554-4444-4-4-4-444-44-40004-40-440000000000000000000000000000000000000000000000
χ564-4444-4-4-4-44-44-440004-404-40000000000000000000000000000000000000000000000
χ574-44-4-44-44440000000-4-40000000000000000022−2222−2222−2222−22000000000000000000000000
χ584-44-4-44-44440000000-4-400000000000000000−2222−2222−2222−2222000000000000000000000000
χ594-44-4-44-44-4-40000000440000000000000000022−2222−22−2222−2222000000000000000000000000
χ604-44-4-44-44-4-400000004400000000000000000−2222−222222−2222−22000000000000000000000000
χ614-4-44-444-40000000000000000004i−4i2i2−2i22i2−2i20000000022−22−2222000000000000000000000000
χ624-4-44-444-40000000000000000004i−4i−2i22i2−2i22i200000000−222222−22000000000000000000000000
χ634-4-44-444-4000000000000000000−4i4i2i2−2i22i2−2i200000000−222222−22000000000000000000000000
χ644-4-44-444-4000000000000000000−4i4i−2i22i2−2i22i20000000022−22−2222000000000000000000000000
χ654-4-4-44-444004-4-440000000000000022−22−2222000022−22−22220000000000000000000000000000
χ664-4-4-44-444004-4-4400000000000000−222222−220000−222222−220000000000000000000000000000
χ674-4-4-44-44400-444-40000000000000022−22−22220000−222222−220000000000000000000000000000
χ684-4-4-44-44400-444-400000000000000−222222−22000022−22−22220000000000000000000000000000

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