Finite Group Databasebeta

← Group #13146446

Character table — Group #13146446

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size11222444499999918181818181818181824243636363636363636363636364848485454545454545454108108108108
order123462661222444444466121212123624466121212121212126612888888888888
χ111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111-1-1-1-11-1-111-1-1-1-1111-1-1111-1-1-1-1-1-1111iiii−i−i−i−iii−i−i
χ411111111111-1-1-1-11-1-111-1-1-1-1111-1-1111-1-1-1-1-1-1111−i−i−i−iiiii−i−iii
χ5111111111-1-1i−ii−i-1i−i-1-1ii−i−i11-1i−i-1-1-1i−iii−i−i111ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13
χ6111111111-1-1i−ii−i-1i−i-1-1ii−i−i11-1i−i-1-1-1i−iii−i−i111−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13
χ7111111111-1-1−ii−ii-1−ii-1-1−i−iii11-1−ii-1-1-1−ii−i−iii111−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23
χ8111111111-1-1−ii−ii-1−ii-1-1−i−iii11-1−ii-1-1-1−ii−i−iii111ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23
χ911111-1-1-1111111111111111111-1-1-1-1-1111-1-1-1-1-1-1111111111-1-1-1-1
χ1011111-1-1-1111111111111111111-1-1-1-1-1111-1-1-1-1-1-11-1-1-1-1-1-1-1-11111
χ1111111-1-1-1111-1-1-1-11-1-111-1-1-1-111-111-1-11-1-11111-1-11iiii−i−i−i−i−i−iii
χ1211111-1-1-1111-1-1-1-11-1-111-1-1-1-111-111-1-11-1-11111-1-11−i−i−i−iiiiiii−i−i
χ1311111-1-1-11-1-1i−ii−i-1i−i-1-1ii−i−i111−ii11-1i−i−i−iii-1-11ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13
χ1411111-1-1-11-1-1i−ii−i-1i−i-1-1ii−i−i111−ii11-1i−i−i−iii-1-11−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13
χ1511111-1-1-11-1-1−ii−ii-1−ii-1-1−i−iii111i−i11-1−iiii−i−i-1-11−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23
χ1611111-1-1-11-1-1−ii−ii-1−ii-1-1−i−iii111i−i11-1−iiii−i−i-1-11ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23
χ17222-22000-2222222-2-2-22222222200000-2-2-2000000-2000000000000
χ18222-22000-222-2-2-2-2-22222-2-2-2-22200000-222000000-2000000000000
χ19222-22000-2-2-22i−2i2i−2i2−2i2i-2-22i2i−2i−2i22000002−2i2i000000-2000000000000
χ20222-22000-2-2-2−2i2i−2i2i22i−2i-2-2−2i−2i2i2i220000022i−2i000000-2000000000000
χ212-220-200002-22i−2i−2i2i0002-22i−2i2i−2i2-20000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000
χ222-220-200002-22i−2i−2i2i0002-22i−2i2i−2i2-2000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000
χ232-220-200002-2−2i2i2i−2i0002-2−2i2i−2i2i2-20000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000
χ242-220-200002-2−2i2i2i−2i0002-2−2i2i−2i2i2-2000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000
χ252-220-20000-2222-2-2000-222-2-222-2000000000000000−i2i2i2−i2i2−i2−i2i20000
χ262-220-20000-2222-2-2000-222-2-222-2000000000000000i2−i2−i2i2−i2i2i2−i20000
χ272-220-20000-22-2-222000-22-222-22-20000000000000002−2−222−2−220000
χ282-220-20000-22-2-222000-22-222-22-2000000000000000−222−2−222−20000
χ2966-36-36-3-3-3222i−2i2i−2i22i−2i-1-1−i−iii0022i−2i-1-1-1−ii−i−iii000000000000000
χ3066-36-36-3-3-322−2i2i−2i2i2−2i2i-1-1ii−i−i002−2i2i-1-1-1i−iii−i−i000000000000000
χ3166-36-36-3-3-3-2-22222-22211-1-1-1-100-222111-1-1-1-1-1-1000000000000000
χ3266-36-36-3-3-3-2-2-2-2-2-2-2-2-211111100-2-2-2111111111000000000000000
χ3366-36-3-633-3222i−2i2i−2i22i−2i-1-1−i−iii00-2−2i2i11-1−iiii−i−i000000000000000
χ3466-36-3-633-322−2i2i−2i2i2−2i2i-1-1ii−i−i00-22i−2i11-1i−i−i−iii000000000000000
χ3566-36-3-633-3-2-22222-22211-1-1-1-1002-2-2-1-11-1-11111000000000000000
χ3666-36-3-633-3-2-2-2-2-2-2-2-2-211111100222-1-1111-1-1-1-1000000000000000
χ3766-3-6-30−3i33i33222i−2i2i−2i-2−2i2i-1-1−i−iii00000−i3i31i−i3−33−3000000000000000
χ3866-3-6-30−3i33i3322−2i2i−2i2i-22i−2i-1-1ii−i−i00000−i3i31−ii−33−33000000000000000
χ3966-3-6-30−3i33i33-2-222222-2-211-1-1-1-100000i3−i3-111−i3i3i3−i3000000000000000
χ4066-3-6-30−3i33i33-2-2-2-2-2-222211111100000i3−i3-1-1-1i3−i3−i3i3000000000000000
χ4166-3-6-303i3−3i33222i−2i2i−2i-2−2i2i-1-1−i−iii00000i3−i31i−i−33−33000000000000000
χ4266-3-6-303i3−3i3322−2i2i−2i2i-22i−2i-1-1ii−i−i00000i3−i31−ii3−33−3000000000000000
χ4366-3-6-303i3−3i33-2-222222-2-211-1-1-1-100000−i3i3-111i3−i3−i3i3000000000000000
χ4466-3-6-303i3−3i33-2-2-2-2-2-222211111100000−i3i3-1-1-1−i3i3i3−i3000000000000000
χ45888888888000000000000000-1-1000000000000-1-1-1000000000000
χ4688888-8-8-88000000000000000-1-100000000000011-1000000000000
χ47888-88000-8000000000000000-1-10000000000003-31000000000000
χ48888-88000-8000000000000000-1-1000000000000-331000000000000
χ4912-12-60600004-444-4-4000-22-222-200000000000000000000000000000
χ5012-12-60600004-4-4-444000-222-2-2200000000000000000000000000000
χ5112-12-6060000-444i−4i−4i4i0002-2−2i2i−2i2i00000000000000000000000000000
χ5212-12-6060000-44−4i4i4i−4i0002-22i−2i2i−2i00000000000000000000000000000
χ5316-16160-160000000000000000000-22000000000000000000000000000

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