Finite Group Databasebeta

← Group #4535

Character table — Group #4535

Order 192.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48
size1111111122222222222244444444444444446666666612121212
order1222444434444666121212124444121212121212121212121212888888888888
χ1111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111-1-1-1-1111-1-1111-1-1-1-111-1-111-1-11111-1-1-1-1iiii−i−i−i−iii−i−i
χ61111-1-1-1-1111-1-1111-1-1-1-111-1-111-1-11111-1-1-1-1−i−i−i−iiiii−i−iii
χ71111-1-1-1-1111-1-1111-1-1-1-1-1-11111-1-1-1-1-1-11111iiii−i−i−i−i−i−iii
χ81111-1-1-1-1111-1-1111-1-1-1-1-1-11111-1-1-1-1-1-11111−i−i−i−iiiiiii−i−i
χ91-11-1i−ii−i11-1i−i-11-1ii−i−i1-1i−i1-1i−i11-1-1ii−i−iζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13
χ101-11-1i−ii−i11-1i−i-11-1ii−i−i1-1i−i1-1i−i11-1-1ii−i−i−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13
χ111-11-1i−ii−i11-1i−i-11-1ii−i−i-11−ii1-1i−i-1-111−i−iiiζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13
χ121-11-1i−ii−i11-1i−i-11-1ii−i−i-11−ii1-1i−i-1-111−i−iii−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13
χ131-11-1−ii−ii11-1−ii-11-1−i−iii1-1−ii1-1−ii11-1-1−i−iii−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23
χ141-11-1−ii−ii11-1−ii-11-1−i−iii1-1−ii1-1−ii11-1-1−i−iiiζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23
χ151-11-1−ii−ii11-1−ii-11-1−i−iii-11i−i1-1−ii-1-111ii−i−i−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23
χ161-11-1−ii−ii11-1−ii-11-1−i−iii-11i−i1-1−ii-1-111ii−i−iζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23
χ17222222222-2-2-2-222222220000-2-2-2-200000000000000000000
χ1822222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ1922222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-111111111000000000000
χ2022222222-1-2-2-2-2-1-1-1-1-1-1-100001111−i3i3−i3i3−i3i3−i3i3000000000000
χ2122222222-1-2-2-2-2-1-1-1-1-1-1-100001111i3−i3i3−i3i3−i3i3−i3000000000000
χ222222-2-2-2-22-2-222222-2-2-2-20000-2-22200000000000000000000
χ232222-2-2-2-2-122-2-2-1-1-1111122-2-2-1-111-1-1-1-11111000000000000
χ242222-2-2-2-2-122-2-2-1-1-11111-2-222-1-1111111-1-1-1-1000000000000
χ252222-2-2-2-2-1-2-222-1-1-11111000011-1-1−i3i3−i3i3i3−i3i3−i3000000000000
χ262222-2-2-2-2-1-2-222-1-1-11111000011-1-1i3−i3i3−i3−i3i3−i3i3000000000000
χ2722-2-222-2-2200002-2-22-22-200000000000000002−22−22−22−20000
χ2822-2-222-2-2200002-2-22-22-20000000000000000−22−22−22−220000
χ2922-2-2-2-222200002-2-2-22-220000000000000000−i2i2−i2i2i2−i2i2−i20000
χ3022-2-2-2-222200002-2-2-22-220000000000000000i2−i2i2−i2−i2i2−i2i20000
χ312-22-22i−2i2i−2i2-22−2i2i-22-22i2i−2i−2i0000-22−2i2i00000000000000000000
χ322-22-22i−2i2i−2i-12-22i−2i1-11−i−iii2-22i−2i-11−ii-1-111−i−iii000000000000
χ332-22-22i−2i2i−2i-12-22i−2i1-11−i−iii-22−2i2i-11−ii11-1-1ii−i−i000000000000
χ342-22-22i−2i2i−2i-1-22−2i2i1-11−i−iii00001-1i−i−i3i3i3−i33−3−33000000000000
χ352-22-22i−2i2i−2i-1-22−2i2i1-11−i−iii00001-1i−ii3−i3−i3i3−333−3000000000000
χ362-22-2−2i2i−2i2i2-222i−2i-22-2−2i−2i2i2i0000-222i−2i00000000000000000000
χ372-22-2−2i2i−2i2i-12-2−2i2i1-11ii−i−i2-2−2i2i-11i−i-1-111ii−i−i000000000000
χ382-22-2−2i2i−2i2i-12-2−2i2i1-11ii−i−i-222i−2i-11i−i11-1-1−i−iii000000000000
χ392-22-2−2i2i−2i2i-1-222i−2i1-11ii−i−i00001-1−ii−i3i3i3−i3−333−3000000000000
χ402-22-2−2i2i−2i2i-1-222i−2i1-11ii−i−i00001-1−iii3−i3−i3i33−3−33000000000000
χ412-2-222i−2i−2i2i20000-2-222i−2i−2i2i00000000000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i0000
χ422-2-222i−2i−2i2i20000-2-222i−2i−2i2i0000000000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i0000
χ432-2-22−2i2i2i−2i20000-2-22−2i2i2i−2i00000000000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i0000
χ442-2-22−2i2i2i−2i20000-2-22−2i2i2i−2i0000000000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i0000
χ4544-4-444-4-4-20000-222-22-220000000000000000000000000000
χ4644-4-4-4-444-20000-2222-22-20000000000000000000000000000
χ474-4-444i−4i−4i4i-2000022-2−2i2i2i−2i0000000000000000000000000000
χ484-4-44−4i4i4i−4i-2000022-22i−2i−2i2i0000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.