Finite Group Databasebeta

← Group #11772392

Character table — Group #11772392

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54
size1111228888999916161818181818181818181818181818181818181818181818181818242424244848484872727272
order12442436121222446122488888888161616161616161616161616161616168888242424248888
χ1111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111-1-11111-1-1-1-1-1-1111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-111-1-1ii−i−i
χ61111-1-11111-1-1-1-1-1-1111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-111-1-111−i−iii
χ71111-1-11111-1-1-1-1-1-1111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-111-1-1−i−iii
χ81111-1-11111-1-1-1-1-1-1111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-111-1-111ii−i−i
χ911-1-11-111-1-1-1-1111-1-1111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−ii−ii−ii−ii−i1-11-1
χ1011-1-11-111-1-1-1-1111-1-1111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i−ii−ii−ii−ii-11-11
χ1111-1-11-111-1-1-1-1111-1-1111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiiii−ii−ii−ii−i-11-11
χ1211-1-11-111-1-1-1-1111-1-1111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii−ii−ii−ii−ii1-11-1
χ1311-1-1-1111-1-111-1-1-11-1111-1-1-1-1111111-1-1-1-1-1-1-1-11111i−i−iii−i−ii−iii−i
χ1411-1-1-1111-1-111-1-1-11-1111-1-1-1-1111111-1-1-1-1-1-1-1-11111−iii−i−iii−ii−i−ii
χ1511-1-1-1111-1-111-1-1-11-1111-1-1-1-111-1-1-1-111111111-1-1-1-1i−i−iii−i−iii−i−ii
χ1611-1-1-1111-1-111-1-1-11-1111-1-1-1-111-1-1-1-111111111-1-1-1-1−iii−i−iii−i−iii−i
χ17222222222222222222-2-2-2-2-2-2-2-20000000000000000000000000000
χ182222222222-2-2-2-222-2-200000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2000000000000
χ192222222222-2-2-2-222-2-200000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2000000000000
χ202222-2-222222222-2-2-2-20000000022−2−222−2−2−2−222−2−222000000000000
χ212222-2-222222222-2-2-2-200000000−2−222−2−22222−2−222−2−2000000000000
χ222222-2-22222-2-2-2-2-2-222-2-2-2-222220000000000000000000000000000
χ2322-2-22-222-2-222-2-22-22-20000000022−2−2−2−22222−2−2−2−222000000000000
χ2422-2-22-222-2-222-2-22-22-200000000−2−22222−2−2−2−22222−2−2000000000000
χ2522-2-22-222-2-2-2-2222-2-22-2-222-2-2220000000000000000000000000000
χ2622-2-2-2222-2-222-2-2-22-22-2-22222-2-20000000000000000000000000000
χ2722-2-2-2222-2-2-2-222-222-200000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2000000000000
χ2822-2-2-2222-2-2-2-222-222-200000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2000000000000
χ292-22i−2i002-22i−2i2-22i−2i00002−2i2−i2i2−i22−2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7000000000000
χ302-22i−2i002-22i−2i2-22i−2i00002−2i2−i2i2−i22−2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7000000000000
χ312-22i−2i002-22i−2i2-22i−2i0000−22−i2i2−i2i2−22ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5000000000000
χ322-22i−2i002-22i−2i2-22i−2i0000−22−i2i2−i2i2−22−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5000000000000
χ332-22i−2i002-22i−2i-22−2i2i00002−2i2−i2−i2i2−22ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ342-22i−2i002-22i−2i-22−2i2i00002−2i2−i2−i2i2−22−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ352-22i−2i002-22i−2i-22−2i2i0000−22−i2i2i2−i22−2ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7000000000000
χ362-22i−2i002-22i−2i-22−2i2i0000−22−i2i2i2−i22−2−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7000000000000
χ372-2−2i2i002-2−2i2i2-2−2i2i00002−2−i2i2−i2i22−2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7000000000000
χ382-2−2i2i002-2−2i2i2-2−2i2i00002−2−i2i2−i2i22−2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7000000000000
χ392-2−2i2i002-2−2i2i2-2−2i2i0000−22i2−i2i2−i2−22ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5000000000000
χ402-2−2i2i002-2−2i2i2-2−2i2i0000−22i2−i2i2−i2−22−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5000000000000
χ412-2−2i2i002-2−2i2i-222i−2i00002−2−i2i2i2−i2−22ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ422-2−2i2i002-2−2i2i-222i−2i00002−2−i2i2i2−i2−22−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ432-2−2i2i002-2−2i2i-222i−2i0000−22i2−i2−i2i22−2ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7000000000000
χ442-2−2i2i002-2−2i2i-222i−2i0000−22i2−i2−i2i22−2−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7000000000000
χ45888888-1-1-1-10000-1-1000000000000000000000000002222-1-1-1-10000
χ46888888-1-1-1-10000-1-100000000000000000000000000-2-2-2-211110000
χ478888-8-8-1-1-1-10000110000000000000000000000000022-2-2-1-1110000
χ488888-8-8-1-1-1-100001100000000000000000000000000-2-22211-1-10000
χ4988-8-88-8-1-1110000-11000000000000000000000000002i−2i2i−2i−ii−ii0000
χ5088-8-88-8-1-1110000-1100000000000000000000000000−2i2i−2i2ii−ii−i0000
χ5188-8-8-88-1-11100001-1000000000000000000000000002i−2i−2i2i−iii−i0000
χ5288-8-8-88-1-11100001-100000000000000000000000000−2i2i2i−2ii−i−ii0000
χ5316-1616i−16i00-22−2i2i00000000000000000000000000000000000000000000
χ5416-16−16i16i00-222i−2i00000000000000000000000000000000000000000000

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