Finite Group Databasebeta

← Group #136993

Character table — Group #136993

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11112222222244444444488888888888888888161616161616161616161616161616163232
order12222244444444488888822448888816161616161616168888888888881616161644
χ111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-11111-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111
χ5111111111111111111111-1-1-1-1111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1
χ6111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111
χ7111111111111111111111-1-1-1-11-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
χ91111-1-1-1-11-11-11-1111-1-1-1-11-11-11ii−i−iiiii−i−i−i−ii−i1-1ii−i−i11-1-1ii−i−i1-1
χ101111-1-1-1-11-11-11-1111-1-1-1-11-11-11ii−i−i−i−i−i−iiiiii−i1-1ii−i−i-1-111−i−iii-11
χ111111-1-1-1-11-11-11-1111-1-1-1-11-11-11−i−iiiiiii−i−i−i−i−ii1-1−i−iii-1-111ii−i−i-11
χ121111-1-1-1-11-11-11-1111-1-1-1-11-11-11−i−iii−i−i−i−iiiii−ii1-1−i−iii11-1-1−i−iii1-1
χ131111-1-1-1-11-11-11-1111-1-1-1-1-11-111ii−i−iiiii−i−i−i−ii−i-11−i−iii11-1-1−i−iii-11
χ141111-1-1-1-11-11-11-1111-1-1-1-1-11-111ii−i−i−i−i−i−iiiiii−i-11−i−iii-1-111ii−i−i1-1
χ151111-1-1-1-11-11-11-1111-1-1-1-1-11-111−i−iiiiiii−i−i−i−i−ii-11ii−i−i-1-111−i−iii1-1
χ161111-1-1-1-11-11-11-1111-1-1-1-1-11-111−i−iii−i−i−i−iiiii−ii-11ii−i−i11-1-1ii−i−i-11
χ17222222222222222-2-2-2-2-2-22222-200000000000000-2-200000000000000
χ18222222222222222-2-2-2-2-2-2-2-2-2-2-2000000000000002200000000000000
χ1922222222-2-2-2-2-2-2200000022-2-200000i2i2−i2−i2i2i2−i2−i2000000000000i2−i2i2−i200
χ2022222222-2-2-2-2-2-2200000022-2-200000−i2−i2i2i2−i2−i2i2i2000000000000−i2i2−i2i200
χ2122222222-2-2-2-2-2-22000000-2-22200000i2i2−i2−i2i2i2−i2−i2000000000000−i2i2−i2i200
χ2222222222-2-2-2-2-2-22000000-2-22200000−i2−i2i2i2−i2−i2i2i2000000000000i2−i2i2−i200
χ23222222-2-22222-2-2-2222-2-220000-2222200000000-2-20000000000000000
χ24222222-2-22222-2-2-2222-2-220000-2-2-2-2-200000000220000000000000000
χ25222222-2-22222-2-2-2-2-2-222-20000200000000000000002-22-20000000000
χ26222222-2-22222-2-2-2-2-2-222-2000020000000000000000-22-220000000000
χ272222-2-2222-22-2-22-222-222-20000-22i2i−2i−2i00000000−2i2i0000000000000000
χ282222-2-2222-22-2-22-222-222-20000-2−2i−2i2i2i000000002i−2i0000000000000000
χ292222-2-2222-22-2-22-2-2-22-2-220000200000000000000002i−2i−2i2i0000000000
χ302222-2-2222-22-2-22-2-2-22-2-22000020000000000000000−2i2i2i−2i0000000000
χ312222-2-2-2-22-22-22-22-2-222222-22-2-200000000000000-2200000000000000
χ322222-2-2-2-22-22-22-22-2-22222-22-22-2000000000000002-200000000000000
χ332222-2-2-2-2-22-22-2220000002-2-220000022−2−2−2−2220000000000002−2−2200
χ342222-2-2-2-2-22-22-2220000002-2-2200000−2−22222−2−2000000000000−222−200
χ352222-2-2-2-2-22-22-222000000-222-20000022−2−2−2−222000000000000−222−200
χ362222-2-2-2-2-22-22-222000000-222-200000−2−22222−2−20000000000002−2−2200
χ372-22-22-200-222-20002-2-2002000002i−2i2i−2i2−22−22−22−200000000i2−i2i2−i2000000
χ382-22-22-200-222-20002-2-2002000002i−2i2i−2i−22−22−22−2200000000−i2i2−i2i2000000
χ392-22-22-200-222-20002-2-200200000−2i2i−2i2i2−22−22−22−200000000−i2i2−i2i2000000
χ402-22-22-200-222-20002-2-200200000−2i2i−2i2i−22−22−22−2200000000i2−i2i2−i2000000
χ412-22-2-2200-2-2220002-2200-2000002-2-22i2−i2i2−i2−i2i2−i2i200000000−i2i2i2−i2000000
χ422-22-2-2200-2-2220002-2200-2000002-2-22−i2i2−i2i2i2−i2i2−i200000000i2−i2−i2i2000000
χ432-22-2-2200-2-2220002-2200-200000-222-2i2−i2i2−i2−i2i2−i2i200000000i2−i2−i2i2000000
χ442-22-2-2200-2-2220002-2200-200000-222-2−i2i2−i2i2i2−i2i2−i200000000−i2i2i2−i2000000
χ45444444-4-4-4-4-4-444-400000000000000000000000000000000000000000
χ464444-4-444-44-444-4-400000000000000000000000000000000000000000
χ474-44-44-4004-4-440000000000000000002i−2i−2i2i2i−2i−2i2i000000000000000000
χ484-44-44-4004-4-44000000000000000000−2i2i2i−2i−2i2i2i−2i000000000000000000
χ494-44-44-400-444-4000-44400-400000000000000000000000000000000000
χ504-44-4-440044-4-40000000000000000002-2-22-222-2000000000000000000
χ514-44-4-440044-4-4000000000000000000-222-22-2-22000000000000000000
χ524-44-4-4400-4-444000-44-400400000000000000000000000000000000000
χ5388-8-8008-8000000000000000000000000000000000000000000000000
χ5488-8-800-88000000000000000000000000000000000000000000000000
χ558-8-880000000000000042−42000000000000000000000000000000000000
χ568-8-8800000000000000−4242000000000000000000000000000000000000

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