Finite Group Databasebeta

← Group #11645

Character table — Group #11645

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58
size11111111222222222222222244444444444444444444448888888816161616
order12224444224444448888888844888816161616161616161616161616161616888888882244
χ11111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111-1-111-1-11111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11-11-1
χ611111111-1-111-1-11111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-11-11
χ711111111-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-11-11
χ811111111-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111-11-1
χ91111-1-1-1-111-1-1-1-1111111-1-1-1-11-111-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i1-1-11
χ101111-1-1-1-111-1-1-1-1111111-1-1-1-11-111-1-1iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii-111-1
χ111111-1-1-1-111-1-1-1-1111111-1-1-1-11-111-1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i-111-1
χ121111-1-1-1-111-1-1-1-1111111-1-1-1-11-111-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii1-1-11
χ131111-1-1-1-1-1-1-1-111111111-1-1-1-1-11-1-111iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii11-1-1
χ141111-1-1-1-1-1-1-1-111111111-1-1-1-1-11-1-111iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i-1-111
χ151111-1-1-1-1-1-1-1-111111111-1-1-1-1-11-1-111−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii-1-111
χ161111-1-1-1-1-1-1-1-111111111-1-1-1-1-11-1-111−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i11-1-1
χ172222222222222222-2-2-2-2-2-2-2-222-2-2-2-20000000000000000000000000000
χ182222222222-2-222-2-200000000-2-2000022−2−222−2−222−2−222−2−2000000000000
χ192222222222-2-222-2-200000000-2-20000−2−222−2−222−2−222−2−222000000000000
χ2022222222-2-222-2-222-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000
χ2122222222-2-2-2-2-2-2-2-20000000022000022−2−222−2−2−2−222−2−222000000000000
χ2222222222-2-2-2-2-2-2-2-200000000220000−2−222−2−22222−2−222−2−2000000000000
χ232222-2-2-2-22222-2-2-2-200000000-220000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2000000000000
χ242222-2-2-2-22222-2-2-2-200000000-220000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2000000000000
χ252222-2-2-2-222-2-2-2-222-2-2-2-222222-2-2-2220000000000000000000000000000
χ262222-2-2-2-2-2-22222-2-2000000002-20000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2000000000000
χ272222-2-2-2-2-2-22222-2-2000000002-20000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2000000000000
χ282222-2-2-2-2-2-2-2-22222-2-2-2-22222-2222-2-20000000000000000000000000000
χ2922-2-22i−2i2i−2i002i−2i002-222-2-22i2i−2i−2i000000000000000000000000002ζ6−2ζ62ζ2−2ζ20000
χ3022-2-22i−2i2i−2i002i−2i002-222-2-22i2i−2i−2i00000000000000000000000000−2ζ62ζ6−2ζ22ζ20000
χ3122-2-22i−2i2i−2i002i−2i002-2-2-222−2i−2i2i2i00000000000000000000002ζ6−2ζ62ζ2−2ζ200000000
χ3222-2-22i−2i2i−2i002i−2i002-2-2-222−2i−2i2i2i0000000000000000000000−2ζ62ζ6−2ζ22ζ200000000
χ3322-2-2−2i2i−2i2i00−2i2i002-222-2-2−2i−2i2i2i000000000000000000000000002ζ2−2ζ22ζ6−2ζ60000
χ3422-2-2−2i2i−2i2i00−2i2i002-222-2-2−2i−2i2i2i00000000000000000000000000−2ζ22ζ2−2ζ62ζ60000
χ3522-2-2−2i2i−2i2i00−2i2i002-2-2-2222i2i−2i−2i00000000000000000000002ζ2−2ζ22ζ6−2ζ600000000
χ3622-2-2−2i2i−2i2i00−2i2i002-2-2-2222i2i−2i−2i0000000000000000000000−2ζ22ζ2−2ζ62ζ600000000
χ372-2-2222-2-22-2002-2002−22−22−22−2002−22−2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5000000000000
χ382-2-2222-2-22-2002-2002−22−22−22−2002−22−2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5000000000000
χ392-2-2222-2-22-2002-200−22−22−22−2200−22−22ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7000000000000
χ402-2-2222-2-22-2002-200−22−22−22−2200−22−22−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7000000000000
χ412-2-2222-2-2-2200-22002−22−22−22−200−22−22ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5000000000000
χ422-2-2222-2-2-2200-22002−22−22−22−200−22−22−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5000000000000
χ432-2-2222-2-2-2200-2200−22−22−22−22002−22−2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7000000000000
χ442-2-2222-2-2-2200-2200−22−22−22−22002−22−2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7000000000000
χ452-2-22-2-2222-200-22002−22−2−22−22002−2−22ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7000000000000
χ462-2-22-2-2222-200-22002−22−2−22−22002−2−22−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7000000000000
χ472-2-22-2-2222-200-2200−22−222−22−200−222−2ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ482-2-22-2-2222-200-2200−22−222−22−200−222−2−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ492-2-22-2-222-22002-2002−22−2−22−2200−222−2ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7000000000000
χ502-2-22-2-222-22002-2002−22−2−22−2200−222−2−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7000000000000
χ512-2-22-2-222-22002-200−22−222−22−2002−2−22ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ522-2-22-2-222-22002-200−22−222−22−2002−2−22−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ5344-4-44i−4i4i−4i00−4i4i00-44000000000000000000000000000000000000000000
χ5444-4-4−4i4i−4i4i004i−4i00-44000000000000000000000000000000000000000000
χ554-44-44i−4i−4i4i0000000022−22−22222i2−2i2−2i22i20000000000000000000000000000000000
χ564-44-44i−4i−4i4i00000000−222222−22−2i22i22i2−2i20000000000000000000000000000000000
χ574-44-4−4i4i4i−4i0000000022−22−2222−2i22i22i2−2i20000000000000000000000000000000000
χ584-44-4−4i4i4i−4i00000000−222222−222i2−2i2−2i22i20000000000000000000000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.