Finite Group Databasebeta

← Group #13166224

Character table — Group #13166224

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63
size1122244448888889999991616161616161616161818181818181818183636363636363636363636365454545454545454108108108108
order1234641212123336662244441212121212121212124446612121212444121212121212121212888888888888
χ1111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111-1-1-1-11111111111-1-111-1-1-1-11-1-1111-1-1-1-1-1-1iiii−i−i−i−iii−i−i
χ411111111111111111-1-1-1-11111111111-1-111-1-1-1-11-1-1111-1-1-1-1-1-1−i−i−i−iiiii−i−iii
χ5111111111111111-1-1i−ii−i111111111-1i−i-1-1ii−i−i-1i−i-1-1-1iii−i−i−iζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13
χ6111111111111111-1-1i−ii−i111111111-1i−i-1-1ii−i−i-1i−i-1-1-1iii−i−i−i−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13
χ7111111111111111-1-1−ii−ii111111111-1−ii-1-1−i−iii-1−ii-1-1-1−i−i−iiii−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23
χ8111111111111111-1-1−ii−ii111111111-1−ii-1-1−i−iii-1−ii-1-1-1−i−i−iiiiζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23
χ911111-11-1-1111111111111111-1-1-1-1-1-1111111111-1-1-11-1-11-1-11-1-111111111-1-1-1-1
χ1011111-11-1-1111111111111111-1-1-1-1-1-1111111111-1-1-11-1-11-1-11-1-1-1-1-1-1-1-1-1-11111
χ1111111-11-1-111111111-1-1-1-1111-1-1-1-1-1-11-1-111-1-1-1-1-1111-1-1-111-111iiii−i−i−i−i−i−iii
χ1211111-11-1-111111111-1-1-1-1111-1-1-1-1-1-11-1-111-1-1-1-1-1111-1-1-111-111−i−i−i−iiiiiii−i−i
χ1311111-11-1-1111111-1-1i−ii−i111-1-1-1-1-1-1-1i−i-1-1ii−i−i1−ii-111i−i−i−iiiζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13
χ1411111-11-1-1111111-1-1i−ii−i111-1-1-1-1-1-1-1i−i-1-1ii−i−i1−ii-111i−i−i−iii−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13
χ1511111-11-1-1111111-1-1−ii−ii111-1-1-1-1-1-1-1−ii-1-1−i−iii1i−i-111−iiii−i−i−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23
χ1611111-11-1-1111111-1-1−ii−ii111-1-1-1-1-1-1-1−ii-1-1−i−iii1i−i-111−iiii−i−iζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23
χ17222-220-200222222222222-2-2-2000000-2-2-2222222000-200-200-200000000000000
χ18222-220-20022222222-2-2-2-2-2-2-2000000-22222-2-2-2-2000-200200200000000000000
χ19222-220-200222222-2-22i−2i2i−2i-2-2-20000002−2i2i-2-22i2i−2i−2i000200−2i002i00000000000000
χ20222-220-200222222-2-2−2i2i−2i2i-2-2-200000022i−2i-2-2−2i−2i2i2i0002002i00−2i00000000000000
χ2122-12-12-1-1-12-1-12-1-12222222-1-122-1-1-1-1222-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1000000000000
χ2222-12-12-1-1-12-1-12-1-122-2-2-2-22-1-122-1-1-1-12-2-2-1-111112-2-2-1-1-1111111000000000000
χ2322-12-12-1-1-12-1-12-1-1-2-22i−2i2i−2i2-1-122-1-1-1-1-22i−2i11−i−iii-22i−2i111−i−i−iiii000000000000
χ2422-12-12-1-1-12-1-12-1-1-2-2−2i2i−2i2i2-1-122-1-1-1-1-2−2i2i11ii−i−i-2−2i2i111iii−i−i−i000000000000
χ2522-12-1-2-1112-1-12-1-12222222-1-1-2-21111222-1-1-1-1-1-1-2-2-2-111-111-111000000000000
χ2622-12-1-2-1112-1-12-1-122-2-2-2-22-1-1-2-211112-2-2-1-11111-222-1111-1-11-1-1000000000000
χ2722-12-1-2-1112-1-12-1-1-2-22i−2i2i−2i2-1-1-2-21111-22i−2i11−i−iii2−2i2i1-1-1−iiii−i−i000000000000
χ2822-12-1-2-1112-1-12-1-1-2-2−2i2i−2i2i2-1-1-2-21111-2−2i2i11ii−i−i22i−2i1-1-1i−i−i−iii000000000000
χ2922-1-2-101−i3i32-1-12-1-1222222-21100−i3−i3i3i3-2-2-2-1-1-1-1-1-10001−i3i31−i3i31−i3i3000000000000
χ3022-1-2-101−i3i32-1-12-1-122-2-2-2-2-21100−i3−i3i3i3-222-1-111110001−i3i3-1i3−i3-1i3−i3000000000000
χ3122-1-2-101−i3i32-1-12-1-1-2-22i−2i2i−2i-21100−i3−i3i3i32−2i2i11−i−iii000-1i3−i3i3−3−i−33000000000000
χ3222-1-2-101−i3i32-1-12-1-1-2-2−2i2i−2i2i-21100−i3−i3i3i322i−2i11ii−i−i000-1i3−i3−i−33i3−3000000000000
χ3322-1-2-101i3−i32-1-12-1-1222222-21100i3i3−i3−i3-2-2-2-1-1-1-1-1-10001i3−i31i3−i31i3−i3000000000000
χ3422-1-2-101i3−i32-1-12-1-122-2-2-2-2-21100i3i3−i3−i3-222-1-111110001i3−i3-1−i3i3-1−i3i3000000000000
χ3522-1-2-101i3−i32-1-12-1-1-2-22i−2i2i−2i-21100i3i3−i3−i32−2i2i11−i−iii000-1−i3i3i−33−i3−3000000000000
χ3622-1-2-101i3−i32-1-12-1-1-2-2−2i2i−2i2i-21100i3i3−i3−i322i−2i11ii−i−i000-1−i3i3−i3−3i−33000000000000
χ372-220-20000222-2-2-22-222-2-20000000000002-22-22-20000000000002−22−22−22−20000
χ382-220-20000222-2-2-22-222-2-20000000000002-22-22-2000000000000−22−22−22−220000
χ392-220-20000222-2-2-22-2-2-2220000000000002-2-22-22000000000000−i2i2−i2i2i2−i2i2−i20000
χ402-220-20000222-2-2-22-2-2-2220000000000002-2-22-22000000000000i2−i2i2−i2−i2i2−i2i20000
χ412-220-20000222-2-2-2-222i−2i−2i2i000000000000-222i−2i−2i2i0000000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i0000
χ422-220-20000222-2-2-2-222i−2i−2i2i000000000000-222i−2i−2i2i000000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i0000
χ432-220-20000222-2-2-2-22−2i2i2i−2i000000000000-22−2i2i2i−2i0000000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i0000
χ442-220-20000222-2-2-2-22−2i2i2i−2i000000000000-22−2i2i2i−2i000000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i0000
χ454-4-20200004-2-2-4224-444-4-4000000000000-22-22-22000000000000000000000000
χ464-4-20200004-2-2-4224-4-4-444000000000000-222-22-2000000000000000000000000
χ474-4-20200004-2-2-422-444i−4i−4i4i0000000000002-2−2i2i2i−2i000000000000000000000000
χ484-4-20200004-2-2-422-44−4i4i4i−4i0000000000002-22i−2i−2i2i000000000000000000000000
χ49888888888-1-1-1-1-1-1000000-1-1-1-1-1-1-1-1-1000000000000000000000000000000000
χ5088888-88-8-8-1-1-1-1-1-1000000-1-1-1111111000000000000000000000000000000000
χ51888-880-800-1-1-1-1-1-10000001113-33-33-3000000000000000000000000000000000
χ52888-880-800-1-1-1-1-1-1000000111-33-33-33000000000000000000000000000000000
χ5388-48-48-4-4-4-11−3i321+3i32-11−3i321+3i32000000-11−3i321+3i32-1-11−3i321+3i321+3i321−3i32000000000000000000000000000000000
χ5488-48-48-4-4-4-11+3i321−3i32-11+3i321−3i32000000-11+3i321−3i32-1-11+3i321−3i321−3i321+3i32000000000000000000000000000000000
χ5588-48-4-8-444-11−3i321+3i32-11−3i321+3i32000000-11−3i321+3i3211−1+3i32−1−3i32−1−3i32−1+3i32000000000000000000000000000000000
χ5688-48-4-8-444-11+3i321−3i32-11+3i321−3i32000000-11+3i321−3i3211−1−3i32−1+3i32−1+3i32−1−3i32000000000000000000000000000000000
χ5788-4-8-404−4i34i3-11−3i321+3i32-11−3i321+3i320000001−1+3i32−1−3i323-3−3+i323+i32−3−i323−i32000000000000000000000000000000000
χ5888-4-8-404−4i34i3-11+3i321−3i32-11+3i321−3i320000001−1−3i32−1+3i32-333+i32−3+i323−i32−3−i32000000000000000000000000000000000
χ5988-4-8-4044i3−4i3-11−3i321+3i32-11−3i321+3i320000001−1+3i32−1−3i32-333−i32−3−i323+i32−3+i32000000000000000000000000000000000
χ6088-4-8-4044i3−4i3-11+3i321−3i32-11+3i321−3i320000001−1−3i32−1+3i323-3−3−i323−i32−3+i323+i32000000000000000000000000000000000
χ6116-16160-160000-2-2-2222000000000000000000000000000000000000000000000000
χ6216-16-8080000-21−3i31+3i32−1+3i3−1−3i3000000000000000000000000000000000000000000000000
χ6316-16-8080000-21+3i31−3i32−1−3i3−1+3i3000000000000000000000000000000000000000000000000

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