Finite Group Databasebeta

← Group #138261

Character table — Group #138261

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112222222222444444444444448888888888888888888888161616161616161632323232
order1222222244444422222444448888888888888888888888888816161616161616162444
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−i11-1-1
χ6111111111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiii-1-111
χ7111111111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i-1-111
χ8111111111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii11-1-1
χ91111-1-111111-1-11-111-1-1-111-1-1-1-1-1-111-1-111iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i1-11-1
χ101111-1-111111-1-11-111-1-1-111-1-1-1-1-1-111-1-111iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii-11-11
χ111111-1-111111-1-11-111-1-1-111-1-1-1-1-1-111-1-111−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i-11-11
χ121111-1-111111-1-11-111-1-1-111-1-1-1-1-1-111-1-111−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii1-11-1
χ131111-1-111111-1-11-1-1-111-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1111-1-11
χ141111-1-111111-1-11-1-1-111-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-111-1
χ151111-1-111111-1-11-1-1-111-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111-111-1
χ161111-1-111111-1-11-1-1-111-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-11-1-11
χ17222222222222222222222222-2-2-2-2-2-2-2-2-2-20000000000000000000000000000
χ18222222222222222-2-2-2-22-2-2-2-22222-2-2-2-2220000000000000000000000000000
χ1922222222-2-2-2-2-2-222222-2-2-2-2-200000000000000000000000000i2−i2i2−i2i2−i2i2−i20000
χ2022222222-2-2-2-2-2-222222-2-2-2-2-200000000000000000000000000−i2i2−i2i2−i2i2−i2i20000
χ2122222222-2-2-2-2-2-22-2-2-2-2-22222000000000000000000000000002−22−2−22−220000
χ2222222222-2-2-2-2-2-22-2-2-2-2-2222200000000000000000000000000−22−222−22−20000
χ23222222-2-222-222-2-20000-200002i2i−2i−2i00002i−2i1+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i000000000000
χ24222222-2-222-222-2-20000-200002i2i−2i−2i00002i−2i−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i000000000000
χ25222222-2-222-222-2-20000-20000−2i−2i2i2i0000−2i2i1−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i000000000000
χ26222222-2-222-222-2-20000-20000−2i−2i2i2i0000−2i2i−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i000000000000
χ272222-2-222222-2-22-222-2-2-222-2-22222-2-222-2-20000000000000000000000000000
χ282222-2-222222-2-22-2-2-222-2-2-222-2-2-2-2-2-222220000000000000000000000000000
χ292222-2-222-2-2-222-2-222-2-22-2-222000000000000000000000000002−2−222−2−220000
χ302222-2-222-2-2-222-2-222-2-22-2-22200000000000000000000000000−222−2−222−20000
χ312222-2-222-2-2-222-2-2-2-222222-2-200000000000000000000000000i2−i2−i2i2−i2i2i2−i20000
χ322222-2-222-2-2-222-2-2-2-222222-2-200000000000000000000000000−i2i2i2−i2i2−i2−i2i20000
χ332222-2-2-2-222-2-2-2-220000200002i2i−2i−2i0000−2i2i1+i1+i−1−i−1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i1−i1−i−1+i−1+i000000000000
χ342222-2-2-2-222-2-2-2-220000200002i2i−2i−2i0000−2i2i−1−i−1−i1+i1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i−1+i−1+i1−i1−i000000000000
χ352222-2-2-2-222-2-2-2-22000020000−2i−2i2i2i00002i−2i1−i1−i−1+i−1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i1+i1+i−1−i−1−i000000000000
χ362222-2-2-2-222-2-2-2-22000020000−2i−2i2i2i00002i−2i−1+i−1+i1−i1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i−1−i−1−i1+i1+i000000000000
χ372-22-2002-22-2200-202-20002-2002i−2i2i−2i002i−2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000
χ382-22-2002-22-2200-202-20002-2002i−2i2i−2i002i−2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
χ392-22-2002-22-2200-202-20002-200−2i2i−2i2i00−2i2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
χ402-22-2002-22-2200-202-20002-200−2i2i−2i2i00−2i2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000
χ412-22-2002-22-2200-20-22000-22002i−2i2i−2i00−2i2i001+i−1−i1+i−1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i1−i−1+i1−i−1+i000000000000
χ422-22-2002-22-2200-20-22000-22002i−2i2i−2i00−2i2i00−1−i1+i−1−i1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i−1+i1−i−1+i1−i000000000000
χ432-22-2002-22-2200-20-22000-2200−2i2i−2i2i002i−2i001−i−1+i1−i−1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i1+i−1−i1+i−1−i000000000000
χ442-22-2002-22-2200-20-22000-2200−2i2i−2i2i002i−2i00−1+i1−i−1+i1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i−1−i1+i−1−i1+i000000000000
χ452-22-200-222-2-20020002-20002-22-2-222-2000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ462-22-200-222-2-20020002-20002-22-2-222-200000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ472-22-200-222-2-20020002-20002-2-222-2-2200002i−2i−2i2i00000000−2i2i2i−2i000000000000
χ482-22-200-222-2-20020002-20002-2-222-2-220000−2i2i2i−2i000000002i−2i−2i2i000000000000
χ492-22-200-222-2-2002000-22000-222-2-22-2200002-2-22000000002-2-22000000000000
χ502-22-200-222-2-2002000-22000-222-2-22-220000-222-200000000-222-2000000000000
χ512-22-200-222-2-2002000-22000-22-222-22-2000000002-2-222-2-220000000000000000
χ522-22-200-222-2-2002000-22000-22-222-22-200000000-222-2-222-20000000000000000
χ53444444-4-4-4-44-4-44-400004000000000000000000000000000000000000000000
χ544444-4-4-4-4-4-4444440000-4000000000000000000000000000000000000000000
χ554-44-4004-4-44-400404-4000-440000000000000000000000000000000000000000
χ564-44-4004-4-44-40040-440004-40000000000000000000000000000000000000000
χ574-44-400-44-44400-40004-4000-4400000000000000000000000000000000000000
χ584-44-400-44-44400-4000-440004-400000000000000000000000000000000000000
χ5988-8-800000008i−8i0000000000000000000000000000000000000000000000000
χ6088-8-80000000−8i8i0000000000000000000000000000000000000000000000000
χ618-8-888-800000000000000000000000000000000000000000000000000000000
χ628-8-88-8800000000000000000000000000000000000000000000000000000000

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