Finite Group Databasebeta

← Group #141734

Character table — Group #141734

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size1111222222222244444444448888888888888888888888883232323232323232
order122222444488884444888888888888881616161616161616161616161616161624444488
χ111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1
χ91111-1-1-111-11111-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-1i−ii−i
χ101111-1-1-111-11111-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-11-11−ii−ii
χ111111-1-1-111-11111-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-1−ii−ii
χ121111-1-1-111-11111-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-11-11i−ii−i
χ131111-1-1-111-11111-1-11111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii1-1-11i−i−ii
χ141111-1-1-111-11111-1-11111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-111-1−iii−i
χ151111-1-1-111-11111-1-11111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i1-1-11−iii−i
χ161111-1-1-111-11111-1-11111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-111-1i−i−ii
χ1722222222222222-2-2-2-2-2-222-2-2000000000000000022-2-222-2-200000000
χ1822222222222222-2-2-2-2-2-222-2-20000000000000000-2-222-2-22200000000
χ192222222222-2-2-2-22222-2-2-2-2-2-222-2-222-2-2000000000000000000000000
χ202222222222-2-2-2-22222-2-2-2-2-2-2-2-222-2-222000000000000000000000000
χ212222222222-2-2-2-2-2-2-2-222-2-2220000000022-2-222-2-20000000000000000
χ222222222222-2-2-2-2-2-2-2-222-2-22200000000-2-222-2-2220000000000000000
χ232222-2-2-222-2222222-2-2-2-2-2-22200000000000000002i2i−2i−2i−2i−2i2i2i00000000
χ242222-2-2-222-2222222-2-2-2-2-2-2220000000000000000−2i−2i2i2i2i2i−2i−2i00000000
χ252222-2-2-222-2-2-2-2-222-2-22222-2-2000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ262222-2-2-222-2-2-2-2-222-2-22222-2-200000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ272222-2-2-222-2-2-2-2-2-2-222-2-2222222-2-2-2-222000000000000000000000000
χ282222-2-2-222-2-2-2-2-2-2-222-2-22222-2-22222-2-2000000000000000000000000
χ292-2-222-222-2-222-2-20000002-2002−22−22−22−2i2−i2i2−i2i2−i2i2−i2002i−2i002i−2i00000000
χ302-2-222-222-2-222-2-20000002-2002−22−22−22−2−i2i2−i2i2−i2i2−i2i200−2i2i00−2i2i00000000
χ312-2-222-222-2-222-2-20000002-200−22−22−22−22i2−i2i2−i2i2−i2i2−i200−2i2i00−2i2i00000000
χ322-2-222-222-2-222-2-20000002-200−22−22−22−22−i2i2−i2i2−i2i2−i2i2002i−2i002i−2i00000000
χ332-2-222-222-2-2-2-222000000-22002−2−222−2−22i2−i2−i2i2i2−i2−i2i22i−2i002i−2i0000000000
χ342-2-222-222-2-2-2-222000000-22002−2−222−2−22−i2i2i2−i2−i2i2i2−i2−2i2i00−2i2i0000000000
χ352-2-222-222-2-2-2-222000000-2200−222−2−222−2i2−i2−i2i2i2−i2−i2i2−2i2i00−2i2i0000000000
χ362-2-222-222-2-2-2-222000000-2200−222−2−222−2−i2i2i2−i2−i2i2i2−i22i−2i002i−2i0000000000
χ372-2-22-22-22-2222-2-2000000-22002−22−2−22−222−22−2−22−22002-200-2200000000
χ382-2-22-22-22-2222-2-2000000-22002−22−2−22−22−22−222−22−200-22002-200000000
χ392-2-22-22-22-2222-2-2000000-2200−22−222−22−22−22−2−22−2200-22002-200000000
χ402-2-22-22-22-2222-2-2000000-2200−22−222−22−2−22−222−22−2002-200-2200000000
χ412-2-22-22-22-22-2-2220000002-2002−2−22−222−22−2−22−222−22-200-220000000000
χ422-2-22-22-22-22-2-2220000002-2002−2−22−222−2−222−22−2−22-22002-20000000000
χ432-2-22-22-22-22-2-2220000002-200−222−22−2−222−2−22−222−2-22002-20000000000
χ442-2-22-22-22-22-2-2220000002-200−222−22−2−22−222−22−2−222-200-220000000000
χ45444444-4-4-4-400004-44-400000000000000000000000000000000000000
χ46444444-4-4-4-40000-44-4400000000000000000000000000000000000000
χ474444-4-44-4-4400004-4-4400000000000000000000000000000000000000
χ484444-4-44-4-440000-444-400000000000000000000000000000000000000
χ494-4-444-4-4-444000000004-4004-400000000000000000000000000000000
χ504-4-444-4-4-44400000000-4400-4400000000000000000000000000000000
χ514-4-44-444-44-4000000004-400-4400000000000000000000000000000000
χ524-4-44-444-44-400000000-44004-400000000000000000000000000000000
χ5388-8-800000042−4242−42000000000000000000000000000000000000000000
χ5488-8-8000000−4242−4242000000000000000000000000000000000000000000
χ558-88-800000042−42−4242000000000000000000000000000000000000000000
χ568-88-8000000−424242−42000000000000000000000000000000000000000000

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