Finite Group Databasebeta

← Group #11772378

Character table — Group #11772378

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54
size1111228888999916161818181818181818181818181818181818181818181818181818242424244848484872727272
order1222443666222212124488888888161616161616161616161616161616164444121212124444
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
χ91-11-11-11-11-111-1-11-1-1111-1-1-1-1111111-1-1-1-11111-1-1-1-1i−ii−ii−ii−ii−ii−i
χ101-11-11-11-11-111-1-11-1-1111-1-1-1-1111111-1-1-1-11111-1-1-1-1−ii−ii−ii−ii−ii−ii
χ111-11-11-11-11-111-1-11-1-1111-1-1-1-111-1-1-1-11111-1-1-1-11111i−ii−ii−ii−i−ii−ii
χ121-11-11-11-11-111-1-11-1-1111-1-1-1-111-1-1-1-11111-1-1-1-11111−ii−ii−ii−iii−ii−i
χ131-11-1-111-11-1-1-111-11-1111-1-111-1-1iiii−i−i−i−i−i−i−i−iiiiii−i−iii−i−ii-111-1
χ141-11-1-111-11-1-1-111-11-1111-1-111-1-1iiii−i−i−i−i−i−i−i−iiiii−iii−i−iii−i1-1-11
χ151-11-1-111-11-1-1-111-11-1111-1-111-1-1−i−i−i−iiiiiiiii−i−i−i−ii−i−iii−i−ii1-1-11
χ161-11-1-111-11-1-1-111-11-1111-1-111-1-1−i−i−i−iiiiiiiii−i−i−i−i−iii−i−iii−i-111-1
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
χ2322-2-20022-2-22-22-200002−22−22−22−2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7000000000000
χ2422-2-20022-2-22-22-200002−22−22−22−2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7000000000000
χ2522-2-20022-2-22-22-20000−22−22−22−22ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ2622-2-20022-2-22-22-20000−22−22−22−22−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ2722-2-20022-2-2-22-2200002−22−2−22−22ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5000000000000
χ2822-2-20022-2-2-22-2200002−22−2−22−22−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5000000000000
χ2922-2-20022-2-2-22-220000−22−222−22−2ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7000000000000
χ3022-2-20022-2-2-22-220000−22−222−22−2−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7000000000000
χ312-22-22-22-22-222-2-22-2-22-2-22222-2-20000000000000000000000000000
χ322-22-22-22-22-2-2-2222-22-200000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2000000000000
χ332-22-22-22-22-2-2-2222-22-200000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2000000000000
χ342-22-2-222-22-222-2-2-222-20000000022−2−2−2−222−2−22222−2−2000000000000
χ352-22-2-222-22-222-2-2-222-200000000−2−22222−2−222−2−2−2−222000000000000
χ362-22-2-222-22-2-2-222-22-22-2-222-2-2220000000000000000000000000000
χ372-2-22002-2-222-2-2200002−2−22−222−2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7000000000000
χ382-2-22002-2-222-2-2200002−2−22−222−2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7000000000000
χ392-2-22002-2-222-2-220000−222−22−2−22ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ402-2-22002-2-222-2-220000−222−22−2−22−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ412-2-22002-2-22-222-200002−2−222−2−22ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5000000000000
χ422-2-22002-2-22-222-200002−2−222−2−22−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5000000000000
χ432-2-22002-2-22-222-20000−222−2−222−2ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7000000000000
χ442-2-22002-2-22-222-20000−222−2−222−2−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+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
χ498-88-88-8-11-110000-11000000000000000000000000002i−2i2i−2i−ii−ii0000
χ508-88-88-8-11-110000-1100000000000000000000000000−2i2i−2i2ii−ii−i0000
χ518-88-8-88-11-1100001-1000000000000000000000000002i−2i−2i2i−iii−i0000
χ528-88-8-88-11-1100001-100000000000000000000000000−2i2i2i−2ii−i−ii0000
χ531616-16-1600-2-22200000000000000000000000000000000000000000000
χ5416-16-161600-222-200000000000000000000000000000000000000000000

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