Finite Group Databasebeta

← Group #296826

Character table — Group #296826

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111111112222222244444444448888888888888888888816161616161616161616161616163232
order12222222444444444444444444224444444444888888884444448888888844
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111-1-1-1-111111111-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-11111-1-1
χ6111111111111111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111
χ7111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111111111-1-11111-1-1-1-1-1-1-1-111
χ8111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
χ91111111111111111-1-11111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-11-111-1-111-1-111-1-11-1
χ101111111111111111-1-11111-1-11111-1-1-1-1-1-1-1-111-1-1-1-111111-111-1-1-1-111-1-111-11
χ111111111111111111-1-11111-1-111-1-111-1-1-1-1-1-1111111-1-1-1-1-11-1-11111-1-1-1-111-11
χ121111111111111111-1-11111-1-111-1-111-1-1-1-1-1-111-1-1-1-11111-11-1-111-1-11111-1-11-1
χ131111111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-11-1-1-111-1-11111-1-1-11
χ141111111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111111-1-1-11111-1-1-1-1111-1
χ151111111111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-1111-1-1-1-111-1-1111-1
χ161111111111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1111-1-111-1-111-1-1-11
χ172222222222-2-2-222-222000022-2-222220000-2-20000000000-2-200000000000000
χ182222222222-2-2-222-222000022-2-2-2-2-2-20000-2-200000000002200000000000000
χ192222222222-2-2-222-2-2-20000-2-2-2-222-2-20000220000000000-2200000000000000
χ202222222222-2-2-222-2-2-20000-2-2-2-2-2-22200002200000000002-200000000000000
χ2122222222-2-2222-2-22222222-2-2-2-2000022-2-22-2-2-2000000000000000000000000
χ2222222222-2-2222-2-2222-2-2-2-2-2-2-2-20000-2-2222-222000000000000000000000000
χ2322222222-2-2222-2-22-2-2222222-2-20000-2-222-22-2-2000000000000000000000000
χ2422222222-2-2222-2-22-2-2-2-2-2-222-2-2000022-2-2-2222000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-2220000-2-22200000000-220000000000002-22-20000000000
χ2622222222-2-2-2-2-2-2-2-2220000-2-22200000000-22000000000000-22-220000000000
χ2722222222-2-2-2-2-2-2-2-2-2-200002222000000002-20000000000002-2-220000000000
χ2822222222-2-2-2-2-2-2-2-2-2-200002222000000002-2000000000000-222-20000000000
χ29222-2-2-2-22-2-20002202-200002-2002-22-200000000i2i2−i2−i2i2i2−i2−i20000000000i2−i2i2−i200
χ30222-2-2-2-22-2-20002202-200002-2002-22-200000000−i2−i2i2i2−i2−i2i2i20000000000−i2i2−i2i200
χ31222-2-2-2-22-2-20002202-200002-200-22-2200000000i2i2−i2−i2i2i2−i2−i20000000000−i2i2−i2i200
χ32222-2-2-2-22-2-20002202-200002-200-22-2200000000−i2−i2i2i2−i2−i2i2i20000000000i2−i2i2−i200
χ33222-2-2-2-22-2-2000220-220000-22002-2-2200000000i2i2−i2−i2−i2−i2i2i20000000000i2−i2−i2i200
χ34222-2-2-2-22-2-2000220-220000-22002-2-2200000000−i2−i2i2i2i2i2−i2−i20000000000−i2i2i2−i200
χ35222-2-2-2-22-2-2000220-220000-2200-222-200000000i2i2−i2−i2−i2−i2i2i20000000000−i2i2i2−i200
χ36222-2-2-2-22-2-2000220-220000-2200-222-200000000−i2−i2i2i2i2i2−i2−i20000000000i2−i2−i2i200
χ372-2222-2-2-22-22-2-22-22002i2i−2i−2i002-200000000002i−2i00002-22-2000000002i−2i000000
χ382-2222-2-2-22-22-2-22-22002i2i−2i−2i002-200000000002i−2i0000-22-2200000000−2i2i000000
χ392-2222-2-2-22-22-2-22-2200−2i−2i2i2i002-20000000000−2i2i00002-22-200000000−2i2i000000
χ402-2222-2-2-22-22-2-22-2200−2i−2i2i2i002-20000000000−2i2i0000-22-22000000002i−2i000000
χ412-2222-2-2-2-222-2-2-222002i2i−2i−2i00-220000000000−2i2i2-22-200000000002i−2i00000000
χ422-2222-2-2-2-222-2-2-222002i2i−2i−2i00-220000000000−2i2i-22-220000000000−2i2i00000000
χ432-2222-2-2-2-222-2-2-22200−2i−2i2i2i00-2200000000002i−2i2-22-20000000000−2i2i00000000
χ442-2222-2-2-2-222-2-2-22200−2i−2i2i2i00-2200000000002i−2i-22-2200000000002i−2i00000000
χ45444-4-4-4-4444000-4-404-40000-4400000000000000000000000000000000000000
χ46444-4-4-4-4444000-4-40-4400004-400000000000000000000000000000000000000
χ4744-44-44-4-40044-400-400000000000000004-40000000000000000000000000000
χ4844-44-44-4-40044-400-40000000000000000-440000000000000000000000000000
χ4944-44-44-4-400-4-44004004i−4i4i−4i0000000000000000000000000000000000000000
χ5044-44-44-4-400-4-4400400−4i4i−4i4i0000000000000000000000000000000000000000
χ514-4444-4-4-44-4-4444-4-400000000-44000000000000000000000000000000000000
χ524-4444-4-4-4-44-444-44-4000000004-4000000000000000000000000000000000000
χ534-44-4-444-44-4000-44000000000000000000000002i2−2i2−2i22i200000000000000000000
χ544-44-4-444-44-4000-4400000000000000000000000−2i22i22i2−2i200000000000000000000
χ554-44-4-444-4-440004-40000000000000000000000000002i2−2i2−2i22i20000000000000000
χ564-44-4-444-4-440004-4000000000000000000000000000−2i22i22i2−2i20000000000000000
χ574-4-44-4-444004-4400-4000000000000004i−4i000000000000000000000000000000
χ584-4-44-4-444004-4400-400000000000000−4i4i000000000000000000000000000000
χ594-4-44-4-44400-44-4004004-4-440000000000000000000000000000000000000000
χ604-4-44-4-44400-44-400400-444-40000000000000000000000000000000000000000
χ6188-8-88-88-8000000000000000000000000000000000000000000000000000000
χ628-8-8-888-88000000000000000000000000000000000000000000000000000000

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