Finite Group Databasebeta

← Group #72259930

Character table — Group #72259930

Order 2592.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11222244666888888999999161616161616181818181818181818181818242424242424363636363636545454545454545454545454545454545454545454162162162162
order1233663641212333666224444333666666612121212121212121212121212126612121212444888812121212121224242424242424248888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1ii−i−i11-1-1-1-1iiii−i−i−i−iii−i−i
χ41111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1−i−iii11-1-1-1-1−i−i−i−iiiii−i−iii
χ511111111111111111-1-1i−ii−i111111-1-1-1-1iii−i−i−ii−i111111-1-1ii−i−i-1i−iζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13-1-1ii−i−iζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13
χ611111111111111111-1-1i−ii−i111111-1-1-1-1iii−i−i−ii−i111111-1-1ii−i−i-1i−i−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13-1-1ii−i−i−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13
χ711111111111111111-1-1−ii−ii111111-1-1-1-1−i−i−iiii−ii111111-1-1−i−iii-1−ii−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23-1-1−i−iii−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23
χ811111111111111111-1-1−ii−ii111111-1-1-1-1−i−i−iiii−ii111111-1-1−i−iii-1−iiζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23-1-1−i−iiiζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23
χ911111111-1-1-1111111111111111111111111111111-1-1-1-1-1-1111111-1-1-11111-1-1-1-1-1-111111111-1-1-1-1
χ1011111111-1-1-1111111111111111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ1111111111-1-1-111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111ii−i−i-1-11111iiii−i−i−i−i−i−iii
χ1211111111-1-1-111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111−i−iii-1-11111−i−i−i−iiiiiii−i−i
χ1311111111-1-1-1111111-1-1i−ii−i111111-1-1-1-1iii−i−i−ii−i-1-1-1-1-1-1-1-1ii−i−i1−iiζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ1311−i−iiiζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13
χ1411111111-1-1-1111111-1-1i−ii−i111111-1-1-1-1iii−i−i−ii−i-1-1-1-1-1-1-1-1ii−i−i1−ii−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ1311−i−iii−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13
χ1511111111-1-1-1111111-1-1−ii−ii111111-1-1-1-1−i−i−iiii−ii-1-1-1-1-1-1-1-1−i−iii1i−i−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ2311ii−i−i−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23
χ1611111111-1-1-1111111-1-1−ii−ii111111-1-1-1-1−i−i−iiii−ii-1-1-1-1-1-1-1-1−i−iii1i−iζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ2311ii−i−iζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23
χ17222-12-1-1-12-1-12-1-12-1-12222222-1-12-1-122-1-12-1-12-1-12222-1-1-1-1-1-1-1-1-1-12220000-1-1-1-1-1-1000000000000
χ18222-12-1-1-12-1-12-1-12-1-122-2-2-2-22-1-12-1-122-1-1-211-211-2-222-1-1-1-1-1-111112-2-20000-1-11111000000000000
χ19222-12-1-1-12-1-12-1-12-1-1-2-22i−2i2i−2i2-1-12-1-1-2-2112i−i−i−2iii2i−2i22-1-1-1-111−i−iii-22i−2i000011−i−iii000000000000
χ20222-12-1-1-12-1-12-1-12-1-1-2-2−2i2i−2i2i2-1-12-1-1-2-211−2iii2i−i−i−2i2i22-1-1-1-111ii−i−i-2−2i2i000011ii−i−i000000000000
χ21222-12-1-1-1-2112-1-12-1-12222222-1-12-1-122-1-12-1-12-1-122-2-21111-1-1-1-1-1-1-2-2-20000111111000000000000
χ22222-12-1-1-1-2112-1-12-1-122-2-2-2-22-1-12-1-122-1-1-211-211-2-2-2-21111-1-11111-222000011-1-1-1-1000000000000
χ23222-12-1-1-1-2112-1-12-1-1-2-22i−2i2i−2i2-1-12-1-1-2-2112i−i−i−2iii2i−2i-2-2111111−i−iii2−2i2i0000-1-1ii−i−i000000000000
χ24222-12-1-1-1-2112-1-12-1-1-2-2−2i2i−2i2i2-1-12-1-1-2-211−2iii2i−i−i−2i2i-2-2111111ii−i−i22i−2i0000-1-1−i−iii000000000000
χ2522-12-12-1-1000222222222222-1-1-1-1-1-1-1-122-122-122-1-1000000-1-1-1-1-1-10002222000000-1-1-1-1-1-1-1-10000
χ2622-12-12-1-1000222222222222-1-1-1-1-1-1-1-122-122-122-1-1000000-1-1-1-1-1-1000-2-2-2-2000000111111110000
χ2722-12-12-1-100022222222-2-2-2-2-1-1-1-1-1-1-1-1221-2-21-2-211000000-1-111110002i2i−2i−2i000000−i−i−i−iiiii0000
χ2822-12-12-1-100022222222-2-2-2-2-1-1-1-1-1-1-1-1221-2-21-2-211000000-1-11111000−2i−2i2i2i000000iiii−i−i−i−i0000
χ2922-12-12-1-1000222222-2-22i−2i2i−2i-1-1-1-1-1-111-2-2−i2i2ii−2i−2i−ii00000011−i−iii0002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ130000
χ3022-12-12-1-1000222222-2-22i−2i2i−2i-1-1-1-1-1-111-2-2−i2i2ii−2i−2i−ii00000011−i−iii000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ130000
χ3122-12-12-1-1000222222-2-2−2i2i−2i2i-1-1-1-1-1-111-2-2i−2i−2i−i2i2ii−i00000011ii−i−i000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ230000
χ3222-12-12-1-1000222222-2-2−2i2i−2i2i-1-1-1-1-1-111-2-2i−2i−2i−i2i2ii−i00000011ii−i−i0002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ230000
χ332-222-2-22-2000222-2-2-22-222-2-2222-2-2-2-222-222-222-2-2-2000000-222-22-20000000000000000000000000
χ342-222-2-22-2000222-2-2-22-2-2-222222-2-2-2-222-2-2-22-2-2222000000-22-22-220000000000000000000000000
χ352-222-2-22-2000222-2-2-2-222i−2i−2i2i222-2-2-22-2-222i2i−2i−2i−2i2i−2i2i0000002-22i−2i−2i2i0000000000000000000000000
χ362-222-2-22-2000222-2-2-2-22−2i2i2i−2i222-2-2-22-2-22−2i−2i2i2i2i−2i2i−2i0000002-2−2i2i2i−2i0000000000000000000000000
χ372-22-1-21-1103−32-1-1-2112-222-2-22-1-1-211-22-112-112-11-2-20033−3−31-1-11-1100000003−33−33−3000000000000
χ382-22-1-21-1103−32-1-1-2112-2-2-2222-1-1-211-22-11-21-1-21-1220033−3−31-11-11-100000003−3−33−33000000000000
χ392-22-1-21-1103−32-1-1-211-222i−2i−2i2i2-1-1-2112-21-12i−ii−2ii−i−2i2i0033−3−3-11−iii−i0000000−33i3−i3−i3i3000000000000
χ402-22-1-21-1103−32-1-1-211-22−2i2i2i−2i2-1-1-2112-21-1−2ii−i2i−ii2i−2i0033−3−3-11i−i−ii0000000−33−i3i3i3−i3000000000000
χ412-22-1-21-110−332-1-1-2112-222-2-22-1-1-211-22-112-112-11-2-200−3−3331-1-11-110000000−33−33−33000000000000
χ422-22-1-21-110−332-1-1-2112-2-2-2222-1-1-211-22-11-21-1-21-12200−3−3331-11-11-10000000−333−33−3000000000000
χ432-22-1-21-110−332-1-1-211-222i−2i−2i2i2-1-1-2112-21-12i−ii−2ii−i−2i2i00−3−333-11−iii−i00000003−3−i3i3i3−i3000000000000
χ442-22-1-21-110−332-1-1-211-22−2i2i2i−2i2-1-1-2112-21-1−2ii−i2i−ii2i−2i00−3−333-11i−i−ii00000003−3i3−i3−i3i3000000000000
χ452-2-121-2-11000222-2-2-22-222-2-2-1-1-11111-12-2-12-2-12-2110000001-1-11-1100000000000003−33−33−33−30000
χ462-2-121-2-11000222-2-2-22-222-2-2-1-1-11111-12-2-12-2-12-2110000001-1-11-110000000000000−33−33−33−330000
χ472-2-121-2-11000222-2-2-22-2-2-222-1-1-11111-12-21-221-22-1-10000001-11-11-10000000000000−i3i3−i3i3i3−i3i3−i30000
χ482-2-121-2-11000222-2-2-22-2-2-222-1-1-11111-12-21-221-22-1-10000001-11-11-10000000000000i3−i3i3−i3−i3i3−i3i30000
χ492-2-121-2-11000222-2-2-2-222i−2i−2i2i-1-1-1111-11-22−i2i−2ii−2i2ii−i000000-11−iii−i0000000000000ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ230000
χ502-2-121-2-11000222-2-2-2-222i−2i−2i2i-1-1-1111-11-22−i2i−2ii−2i2ii−i000000-11−iii−i0000000000000−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ230000
χ512-2-121-2-11000222-2-2-2-22−2i2i2i−2i-1-1-1111-11-22i−2i2i−i2i−2i−ii000000-11i−i−ii0000000000000−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ130000
χ522-2-121-2-11000222-2-2-2-22−2i2i2i−2i-1-1-1111-11-22i−2i2i−i2i−2i−ii000000-11i−i−ii0000000000000ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ130000
χ5344-2-2-2-2110004-2-24-2-2444444-211-211-2-2-2-2-2-2-2-2-2-2-2-20000001111110000000000000000000000000
χ5444-2-2-2-2110004-2-24-2-244-4-4-4-4-211-211-2-2-2-22222222200000011-1-1-1-10000000000000000000000000
χ5544-2-2-2-2110004-2-24-2-2-4-44i−4i4i−4i-211-2112222−2i−2i−2i2i2i2i−2i2i000000-1-1ii−i−i0000000000000000000000000
χ5644-2-2-2-2110004-2-24-2-2-4-4−4i4i−4i4i-211-21122222i2i2i−2i−2i−2i2i−2i000000-1-1−i−iii0000000000000000000000000
χ574-4-2-2221-10004-2-2-4224-444-4-4-2112-1-12-2-22-2-22-2-2222000000-111-11-10000000000000000000000000
χ584-4-2-2221-10004-2-2-4224-4-4-444-2112-1-12-2-2222-222-2-2-2000000-11-11-110000000000000000000000000
χ594-4-2-2221-10004-2-2-422-444i−4i−4i4i-2112-1-1-222-2−2i−2i2i2i2i−2i2i−2i0000001-1i−i−ii0000000000000000000000000
χ604-4-2-2221-10004-2-2-422-44−4i4i4i−4i-2112-1-1-222-22i2i−2i−2i−2i2i−2i2i0000001-1−iii−i0000000000000000000000000
χ6188888888888-1-1-1-1-1-1000000-1-1-1-1-1-1000000000000-1-1-1-1-1-10000000000000000000000000000000
χ6288888888-8-8-8-1-1-1-1-1-1000000-1-1-1-1-1-10000000000001111110000000000000000000000000000000
χ63888-48-4-4-48-4-4-11−3i321+3i32-11−3i321+3i32000000-11−3i321+3i32-11−3i321+3i32000000000000-1-11−3i321+3i321−3i321+3i320000000000000000000000000000000
χ64888-48-4-4-48-4-4-11+3i321−3i32-11+3i321−3i32000000-11+3i321−3i32-11+3i321−3i32000000000000-1-11+3i321−3i321+3i321−3i320000000000000000000000000000000
χ65888-48-4-4-4-844-11−3i321+3i32-11−3i321+3i32000000-11−3i321+3i32-11−3i321+3i3200000000000011−1+3i32−1−3i32−1+3i32−1−3i320000000000000000000000000000000
χ66888-48-4-4-4-844-11+3i321−3i32-11+3i321−3i32000000-11+3i321−3i32-11+3i321−3i3200000000000011−1−3i32−1+3i32−1−3i32−1+3i320000000000000000000000000000000
χ678-888-8-88-8000-1-1-1111000000-1-1-11110000000000003i−3i3i−3i−3i3i0000000000000000000000000000000
χ688-888-8-88-8000-1-1-1111000000-1-1-1111000000000000−3i3i−3i3i3i−3i0000000000000000000000000000000
χ698-88-4-84-44043−43-11−3i321+3i321−1+3i32−1−3i32000000-11−3i321+3i321−1+3i32−1−3i320000000000003i−3i2ζ14+ζ22−ζ14−2ζ22−2ζ14−ζ22ζ14+2ζ220000000000000000000000000000000
χ708-88-4-84-44043−43-11+3i321−3i321−1−3i32−1+3i32000000-11+3i321−3i321−1−3i32−1+3i32000000000000−3i3i−ζ14−2ζ222ζ14+ζ22ζ14+2ζ22−2ζ14−ζ220000000000000000000000000000000
χ718-88-4-84-440−4343-11−3i321+3i321−1+3i32−1−3i32000000-11−3i321+3i321−1+3i32−1−3i32000000000000−3i3i−2ζ14−ζ22ζ14+2ζ222ζ14+ζ22−ζ14−2ζ220000000000000000000000000000000
χ728-88-4-84-440−4343-11+3i321−3i321−1−3i32−1+3i32000000-11+3i321−3i321−1−3i32−1+3i320000000000003i−3iζ14+2ζ22−2ζ14−ζ22−ζ14−2ζ222ζ14+ζ220000000000000000000000000000000
χ731616-816-816-8-8000-2-2-2-2-2-20000001111110000000000000000000000000000000000000000000000000
χ741616-8-8-8-844000-21−3i31+3i3-21−3i31+3i30000001−1+3i32−1−3i321−1+3i32−1−3i320000000000000000000000000000000000000000000000000
χ751616-8-8-8-844000-21+3i31−3i3-21+3i31−3i30000001−1−3i32−1+3i321−1−3i32−1+3i320000000000000000000000000000000000000000000000000
χ7616-16-8168-16-88000-2-2-2222000000111-1-1-10000000000000000000000000000000000000000000000000
χ7716-16-8-8884-4000-21−3i31+3i32−1+3i3−1−3i30000001−1+3i32−1−3i32-11−3i321+3i320000000000000000000000000000000000000000000000000
χ7816-16-8-8884-4000-21+3i31−3i32−1−3i3−1+3i30000001−1−3i32−1+3i32-11+3i321−3i320000000000000000000000000000000000000000000000000

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