Finite Group Databasebeta

← Group #4534

Character table — Group #4534

Order 192.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48
size1111111122222222222244444444444444446666666612121212
order122244443444466612121212224466661212121212121212888888888888
χ1111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ411111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111-1-1-1-1111-1-1111-1-1-1-111-1-1111111-1-1-1-1-1-1iiii−i−i−i−iii−i−i
χ61111-1-1-1-1111-1-1111-1-1-1-111-1-1111111-1-1-1-1-1-1−i−i−i−iiiii−i−iii
χ71111-1-1-1-1111-1-1111-1-1-1-1-1-111-1-1-1-111-1-11111iiii−i−i−i−i−i−iii
χ81111-1-1-1-1111-1-1111-1-1-1-1-1-111-1-1-1-111-1-11111−i−i−i−iiiiiii−i−i
χ911-1-1i−ii−i11-1i−i1-1-1ii−i−i1-1i−i11-1-11-1i−iii−i−iζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13
χ1011-1-1i−ii−i11-1i−i1-1-1ii−i−i1-1i−i11-1-11-1i−iii−i−i−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13
χ1111-1-1i−ii−i11-1i−i1-1-1ii−i−i-11−ii-1-1111-1i−i−i−iiiζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13
χ1211-1-1i−ii−i11-1i−i1-1-1ii−i−i-11−ii-1-1111-1i−i−i−iii−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13
χ1311-1-1−ii−ii11-1−ii1-1-1−i−iii1-1−ii11-1-11-1−ii−i−iii−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23
χ1411-1-1−ii−ii11-1−ii1-1-1−i−iii1-1−ii11-1-11-1−ii−i−iiiζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23
χ1511-1-1−ii−ii11-1−ii1-1-1−i−iii-11i−i-1-1111-1−iiii−i−i−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23
χ1611-1-1−ii−ii11-1−ii1-1-1−i−iii-11i−i-1-1111-1−iiii−i−iζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23
χ17222222222-2-2-2-2222222200000000-2-2-2-20000000000000000
χ1822222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ1922222222-12222-1-1-1-1-1-1-1-2-2-2-21111-1-1-1-11111000000000000
χ2022222222-1-2-2-2-2-1-1-1-1-1-1-10000−i3i3−i3i31111−i3i3−i3i3000000000000
χ2122222222-1-2-2-2-2-1-1-1-1-1-1-10000i3−i3i3−i31111i3−i3i3−i3000000000000
χ222222-2-2-2-22-2-222222-2-2-2-200000000-2-2220000000000000000
χ232222-2-2-2-2-122-2-2-1-1-1111122-2-2-1-1-1-1-1-1111111000000000000
χ242222-2-2-2-2-122-2-2-1-1-11111-2-2221111-1-111-1-1-1-1000000000000
χ252222-2-2-2-2-1-2-222-1-1-111110000−i3i3−i3i311-1-1i3−i3i3−i3000000000000
χ262222-2-2-2-2-1-2-222-1-1-111110000i3−i3i3−i311-1-1−i3i3−i3i3000000000000
χ2722-2-22i−2i2i−2i2-22−2i2i2-2-22i2i−2i−2i00000000-22−2i2i0000000000000000
χ2822-2-22i−2i2i−2i-12-22i−2i-111−i−iii2-22i−2i-1-111-11−ii−i−iii000000000000
χ2922-2-22i−2i2i−2i-12-22i−2i-111−i−iii-22−2i2i11-1-1-11−iiii−i−i000000000000
χ3022-2-22i−2i2i−2i-1-22−2i2i-111−i−iii0000−i3i3i3−i31-1i−i3−3−33000000000000
χ3122-2-22i−2i2i−2i-1-22−2i2i-111−i−iii0000i3−i3−i3i31-1i−i−333−3000000000000
χ3222-2-2−2i2i−2i2i2-222i−2i2-2-2−2i−2i2i2i00000000-222i−2i0000000000000000
χ3322-2-2−2i2i−2i2i-12-2−2i2i-111ii−i−i2-2−2i2i-1-111-11i−iii−i−i000000000000
χ3422-2-2−2i2i−2i2i-12-2−2i2i-111ii−i−i-222i−2i11-1-1-11i−i−i−iii000000000000
χ3522-2-2−2i2i−2i2i-1-222i−2i-111ii−i−i0000−i3i3i3−i31-1−ii−333−3000000000000
χ3622-2-2−2i2i−2i2i-1-222i−2i-111ii−i−i0000i3−i3−i3i31-1−ii3−3−33000000000000
χ372-22-22i−2i−2i2i20000-22-22i−2i2i−2i00000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000
χ382-22-22i−2i−2i2i20000-22-22i−2i2i−2i0000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000
χ392-22-2−2i2i2i−2i20000-22-2−2i2i−2i2i00000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000
χ402-22-2−2i2i2i−2i20000-22-2−2i2i−2i2i0000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000
χ412-2-2222-2-220000-2-222-2-220000000000000000−i2i2i2−i2i2−i2−i2i20000
χ422-2-2222-2-220000-2-222-2-220000000000000000i2−i2−i2i2−i2i2i2−i20000
χ432-2-22-2-22220000-2-22-222-200000000000000002−2−222−2−220000
χ442-2-22-2-22220000-2-22-222-20000000000000000−222−2−222−20000
χ454-44-44i−4i−4i4i-200002-22−2i2i−2i2i0000000000000000000000000000
χ464-44-4−4i4i4i−4i-200002-222i−2i2i−2i0000000000000000000000000000
χ474-4-4444-4-4-2000022-2-222-20000000000000000000000000000
χ484-4-44-4-444-2000022-22-2-220000000000000000000000000000

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