Finite Group Databasebeta

← Group #287293

Character table — Group #287293

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222444444444444444444444444888888888888888881616161616161616161616163232
order12222222444444444444444488888888888888882222444448888888844448888888844
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111
χ6111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ91111111111111111-1-1-1-111-1-1111111111111-1-1-1-111-1-1-111-1-1-1-1-1-111-1-111-1-111-1-111-1-11-1
χ101111111111111111-1-1-1-111-1-1111111111111-1-1-1-111-1-1-111-1-1-1-1-1-111-1-1-1-111-1-111-1-111-11
χ111111111111111111-1-1-1-111-1-111111111-1-1-1-11111-1-111-1-1-111-1-1-1-1-1-11111-1-111-1-1-1-111-11
χ121111111111111111-1-1-1-111-1-111111111-1-1-1-11111-1-111-1-1-111-1-1-1-1-1-111-1-111-1-11111-1-11-1
χ131111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-111111111-1-111-1-1-1-111-1-1111-1
χ141111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-111111111-1-1-1-11111-1-111-1-1-11
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-111-1-11111-1-11111-1-1-1-11111-1-1-11
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-111-1-11111-1-111-1-11111-1-1-1-1111-1
χ172222222222-22-2-2-222222-2-2-2-200000000000000002222-2-2-2-2-20000000000000000000000
χ182222222222-22-2-2-222222-2-2-2-20000000000000000-2-2-2-2-222220000000000000000000000
χ192222222222-22-2-2-22-2-2-2-2-2-222000000000000000022-2-22-2-2220000000000000000000000
χ202222222222-22-2-2-22-2-2-2-2-2-2220000000000000000-2-222222-2-20000000000000000000000
χ2122222222-2-22-2222-222-2-2-2-22200000000222222220000-200000000-2-2-2-200000000000000
χ2222222222-2-22-2222-222-2-2-2-22200000000-2-2-2-2-2-2-2-20000-200000000222200000000000000
χ2322222222-2-22-2222-2-2-222-2-2-2-2000000002222-2-2-2-20000200000000-2-22200000000000000
χ2422222222-2-22-2222-2-2-222-2-2-2-200000000-2-2-2-22222000020000000022-2-200000000000000
χ2522222222-2-2-2-2-2-2-2-222-2-222-2-22i2i2i2i−2i−2i−2i−2i000000000000200002i2i−2i−2i000000000000000000
χ2622222222-2-2-2-2-2-2-2-222-2-222-2-2−2i−2i−2i−2i2i2i2i2i00000000000020000−2i−2i2i2i000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-22222222i2i2i2i−2i−2i−2i−2i000000000000-20000−2i−2i2i2i000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2222222−2i−2i−2i−2i2i2i2i2i000000000000-200002i2i−2i−2i000000000000000000
χ292222-2-2-2-2220-2000-22-22-2000022−2−222−2−222−2−222−2−22-22-2000002−22−22−22−200000000000000
χ302222-2-2-2-2220-2000-22-22-2000022−2−222−2−2−2−222−2−222-22-22000002−22−2−22−2200000000000000
χ312222-2-2-2-2220-2000-22-22-20000−2−222−2−22222−2−222−2−2-22-2200000−22−222−22−200000000000000
χ322222-2-2-2-2220-2000-22-22-20000−2−222−2−222−2−222−2−2222-22-200000−22−22−22−2200000000000000
χ332222-2-2-2-2220-2000-2-22-22000022−2−222−2−222−2−2−2−2222-2-2200000−22−222−2−2200000000000000
χ342222-2-2-2-2220-2000-2-22-22000022−2−222−2−2−2−22222−2−2-222-200000−22−22−222−200000000000000
χ352222-2-2-2-2220-2000-2-22-220000−2−222−2−22222−2−2−2−222-222-2000002−22−22−2−2200000000000000
χ362222-2-2-2-2220-2000-2-22-220000−2−222−2−222−2−22222−2−22-2-22000002−22−2−222−200000000000000
χ372222-2-2-2-2-2-20200022-2-220000i2i2−i2−i2−i2−i2i2i222−2−222−2−2000002i−2i2i−2ii2−i2−i2i2−22−2200000000000000
χ382222-2-2-2-2-2-20200022-2-220000i2i2−i2−i2−i2−i2i2i2−2−222−2−22200000−2i2i−2i2ii2−i2−i2i22−22−200000000000000
χ392222-2-2-2-2-2-20200022-2-220000−i2−i2i2i2i2i2−i2−i222−2−222−2−200000−2i2i−2i2i−i2i2i2−i2−22−2200000000000000
χ402222-2-2-2-2-2-20200022-2-220000−i2−i2i2i2i2i2−i2−i2−2−222−2−222000002i−2i2i−2i−i2i2i2−i22−22−200000000000000
χ412222-2-2-2-2-2-2020002-222-20000i2i2−i2−i2−i2−i2i2i222−2−2−2−222000002i−2i−2i2i−i2i2i2−i2−222−200000000000000
χ422222-2-2-2-2-2-2020002-222-20000i2i2−i2−i2−i2−i2i2i2−2−22222−2−200000−2i2i2i−2i−i2i2i2−i22−2−2200000000000000
χ432222-2-2-2-2-2-2020002-222-20000−i2−i2i2i2i2i2−i2−i222−2−2−2−22200000−2i2i2i−2ii2−i2−i2i2−222−200000000000000
χ442222-2-2-2-2-2-2020002-222-20000−i2−i2i2i2i2i2−i2−i2−2−22222−2−2000002i−2i−2i2ii2−i2−i2i22−2−2200000000000000
χ4522-2-222-2-22-22-22-2-2200002-2002i−2i2i−2i2i−2i2i−2i00000000000000000000000002-2002i−2i00000000
χ4622-2-222-2-22-22-22-2-2200002-2002i−2i2i−2i2i−2i2i−2i0000000000000000000000000-2200−2i2i00000000
χ4722-2-222-2-22-22-22-2-2200002-200−2i2i−2i2i−2i2i−2i2i00000000000000000000000002-200−2i2i00000000
χ4822-2-222-2-22-22-22-2-2200002-200−2i2i−2i2i−2i2i−2i2i0000000000000000000000000-22002i−2i00000000
χ4922-2-222-2-2-22-22-222-200002-2002-22-2-22-220000000000000000000000000002i−2i002i−2i000000
χ5022-2-222-2-2-22-22-222-200002-2002-22-2-22-22000000000000000000000000000−2i2i00−2i2i000000
χ5122-2-222-2-2-22-22-222-200002-200-22-222-22-20000000000000000000000000002i−2i00−2i2i000000
χ5222-2-222-2-2-22-22-222-200002-200-22-222-22-2000000000000000000000000000−2i2i002i−2i000000
χ5344-4-444-4-44-4-4-4-44440000-440000000000000000000000000000000000000000000000000
χ5444-4-444-4-4-44444-4-4-40000-440000000000000000000000000000000000000000000000000
χ5544-4-4-4-4444-404000-4000000002i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000000000000000000000000
χ5644-4-4-4-4444-404000-400000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000000000000000000000000
χ5744-4-4-4-444-440-400040000000022−22−2222−222222−22000000000000000000000000000000000000000
χ5844-4-4-4-444-440-4000400000000−222222−2222−22−2222000000000000000000000000000000000000000
χ594-44-44-44-4000000000000004i−4i0000000022−2222−222i2−2i22i2−2i20000000000000000000000000000000
χ604-44-44-44-4000000000000004i−4i00000000−2222−2222−2i22i2−2i22i20000000000000000000000000000000
χ614-44-44-44-400000000000000−4i4i0000000022−2222−22−2i22i2−2i22i20000000000000000000000000000000
χ624-44-44-44-400000000000000−4i4i00000000−2222−22222i2−2i22i2−2i20000000000000000000000000000000
χ634-44-4-44-440040-44-40000000000000000000004i−4i−4i4i0000000000000000000000000000000
χ644-44-4-44-440040-44-4000000000000000000000−4i4i4i−4i0000000000000000000000000000000
χ654-44-4-44-4400-404-44000000000000000004-4-4400000000000000000000000000000000000
χ664-44-4-44-4400-404-4400000000000000000-444-400000000000000000000000000000000000
χ674-4-44-444-40040-4-4400000000000000000000000000000000000000000000000000002i2−2i200
χ684-4-44-444-40040-4-440000000000000000000000000000000000000000000000000000−2i22i200
χ694-4-44-444-400-4044-4000000000000000000000000000000000000000000000000002i2−2i20000
χ704-4-44-444-400-4044-400000000000000000000000000000000000000000000000000−2i22i20000
χ718-8-888-8-88000000000000000000000000000000000000000000000000000000000000000

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