Finite Group Databasebeta

← Group #11774783

Character table — Group #11774783

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54
size1111228888999916161818181818181818181818181818181818181818181818181818242424244848484872727272
order1244243612122244612244444444488888888888888888888242424244444
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
χ51111-1-111111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1
χ61111-1-111111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111
χ71111-1-111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-111
χ81111-1-111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-1
χ911-1-11-111-1-111-1-11-11-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−ii−ii−ii−ii−i1-11-1
χ1011-1-11-111-1-111-1-11-11-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−ii−ii−ii−ii-11-11
χ1111-1-11-111-1-111-1-11-11-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiii−ii−ii−ii−i-11-11
χ1211-1-11-111-1-111-1-11-11-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−ii−ii−ii−ii1-11-1
χ1311-1-1-1111-1-111-1-1-11-1111-1-111-1-1iiii−i−i−i−i−i−i−i−iiiiii−i−iii−i−ii1-1-11
χ1411-1-1-1111-1-111-1-1-11-1111-1-111-1-1iiii−i−i−i−i−i−i−i−iiiii−iii−i−iii−i-111-1
χ1511-1-1-1111-1-111-1-1-11-1111-1-111-1-1−i−i−i−iiiiiiiii−i−i−i−ii−i−iii−i−ii-111-1
χ1611-1-1-1111-1-111-1-1-11-1111-1-111-1-1−i−i−i−iiiiiiiii−i−i−i−i−iii−i−iii−i1-1-11
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
χ202222-2-222222222-2-2-2-2-2-22222-2-20000000000000000000000000000
χ212222-2-22222-2-2-2-2-2-22200000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2000000000000
χ222222-2-22222-2-2-2-2-2-22200000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2000000000000
χ2322-2-22-222-2-222-2-22-22-2-2-2-2-222220000000000000000000000000000
χ2422-2-22-222-2-2-2-2222-2-220000000022−2−2−2−22222−2−2−2−222000000000000
χ2522-2-22-222-2-2-2-2222-2-2200000000−2−22222−2−2−2−22222−2−2000000000000
χ2622-2-2-2222-2-222-2-2-22-22-2-222-2-2220000000000000000000000000000
χ2722-2-2-2222-2-2-2-222-222-20000000022−2−2−2−222−2−22222−2−2000000000000
χ2822-2-2-2222-2-2-2-222-222-200000000−2−22222−2−222−2−2−2−222000000000000
χ292-22i−2i002-22i−2i2-22i−2i0000002i−2i2-2001+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
χ302-22i−2i002-22i−2i2-22i−2i0000002i−2i2-200−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000
χ312-22i−2i002-22i−2i2-22i−2i000000−2i2i-22001+i−1−i1+i−1−i1−i−1+i1−i−1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000
χ322-22i−2i002-22i−2i2-22i−2i000000−2i2i-2200−1−i1+i−1−i1+i−1+i1−i−1+i1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
χ332-22i−2i002-22i−2i-22−2i2i00002-200002i−2i000000002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ3000000000000
χ342-22i−2i002-22i−2i-22−2i2i00002-200002i−2i00000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ3000000000000
χ352-22i−2i002-22i−2i-22−2i2i0000-220000−2i2i2ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ00000000000000000000
χ362-22i−2i002-22i−2i-22−2i2i0000-220000−2i2i−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ00000000000000000000
χ372-2−2i2i002-2−2i2i2-2−2i2i0000002i−2i-22001−i−1+i1−i−1+i1+i−1−i1+i−1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
χ382-2−2i2i002-2−2i2i2-2−2i2i0000002i−2i-2200−1+i1−i−1+i1−i−1−i1+i−1−i1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000
χ392-2−2i2i002-2−2i2i2-2−2i2i000000−2i2i2-2001−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000
χ402-2−2i2i002-2−2i2i2-2−2i2i000000−2i2i2-200−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
χ412-2−2i2i002-2−2i2i-222i−2i00002-20000−2i2i000000002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ000000000000
χ422-2−2i2i002-2−2i2i-222i−2i00002-20000−2i2i00000000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ000000000000
χ432-2−2i2i002-2−2i2i-222i−2i0000-2200002i−2i2ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ300000000000000000000
χ442-2−2i2i002-2−2i2i-222i−2i0000-2200002i−2i−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ300000000000000000000
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 8 (ζ8 = 1); i = ζ2.