Finite Group Databasebeta

← Group #11771039

Character table — Group #11771039

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size111122224444444444444444488888888121212121212121218181818181824242424242424242424242424242424242424243672727272
order1222444423366666612121212121212126666121212128888888822444488882424242424242424242424242424242428888
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1
χ4111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111
χ5111111-1-1-11111111111-1-1-1-111-1-1-1-111-1-1iiii−i−i−i−i-1-111-1-111-1-1iiii−i−i−i−i1111-1-1-1-11ii−i−i
χ6111111-1-1-11111111111-1-1-1-111-1-1-1-111-1-1iiii−i−i−i−i-1-111-1-1-1-111iiii−i−i−i−i-1-1-1-111111−i−iii
χ7111111-1-1-11111111111-1-1-1-111-1-1-1-111-1-1−i−i−i−iiiii-1-111-1-111-1-1−i−i−i−iiiii1111-1-1-1-11−i−iii
χ8111111-1-1-11111111111-1-1-1-111-1-1-1-111-1-1−i−i−i−iiiii-1-111-1-1-1-111−i−i−i−iiiii-1-1-1-111111ii−i−i
χ91111-1-111-111111111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1i−ii−i11-1-111-1-1ii−i−iii−i−i-1i−ii−i
χ101111-1-111-111111111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1−ii−ii11-1-111-1-1−i−iii−i−iii-1−ii−ii
χ111111-1-111-111111111-1-11111-1-1-1-1-1-1-1-111-1-111-1-1111111-1-1i−ii−i-1-111-1-111ii−i−iii−i−i-1−ii−ii
χ121111-1-111-111111111-1-11111-1-1-1-1-1-1-1-111-1-111-1-1111111-1-1−ii−ii-1-111-1-111−i−iii−i−iii-1i−ii−i
χ131111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1ii−i−i−i−iii-1-11111i−i−iiii−i−i−i−iiiii−i−i−i−iii-1-111-1
χ141111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1ii−i−i−i−iii-1-11111−iii−iii−i−i−i−iii−i−iiiii−i−i-11-1-11
χ151111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1−i−iiiii−i−i-1-11111i−i−ii−i−iiiii−i−iii−i−i−i−iii-11-1-11
χ161111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1−i−iiiii−i−i-1-11111−iii−i−i−iiiii−i−i−i−iiiii−i−i-1-111-1
χ1722222222222222222222222222222222200000000-2-2-2-2-2-200000000000000000000-20000
χ18222222-2-2-22222222222-2-2-2-222-2-2-2-222-2-20000000022-2-22200000000000000000000-20000
χ192222-2-222-222222222-2-22222-2-2-2-2-2-2-2-22200000000-2-2-2-2220000000000000000000020000
χ202222-2-2-2-2222222222-2-2-2-2-2-2-2-22222-2-2-2-20000000022-2-2-2-20000000000000000000020000
χ2122-2-22i−2i0002222-2-2-2-22i−2i00002i−2i00002i−2i002−2−i2i22−2−i2i22-2002i−2i00002−2−i2i22−2−i2i20000000000000
χ2222-2-22i−2i0002222-2-2-2-22i−2i00002i−2i00002i−2i00−i2i2−22i2−i22−2-2200−2i2i0000−i2i2−22i2−i22−20000000000000
χ2322-2-22i−2i0002222-2-2-2-22i−2i00002i−2i00002i−2i00i2−i22−2−i2i2−22-2200−2i2i0000i2−i22−2−i2i2−220000000000000
χ2422-2-22i−2i0002222-2-2-2-22i−2i00002i−2i00002i−2i00−22i2−i2−22i2−i22-2002i−2i0000−22i2−i2−22i2−i20000000000000
χ2522-2-2−2i2i0002222-2-2-2-2−2i2i0000−2i2i0000−2i2i002−2i2−i22−2i2−i22-200−2i2i00002−2i2−i22−2i2−i20000000000000
χ2622-2-2−2i2i0002222-2-2-2-2−2i2i0000−2i2i0000−2i2i00−i2i22−2i2−i2−22-22002i−2i0000−i2i22−2i2−i2−220000000000000
χ2722-2-2−2i2i0002222-2-2-2-2−2i2i0000−2i2i0000−2i2i00i2−i2−22−i2i22−2-22002i−2i0000i2−i2−22−i2i22−20000000000000
χ2822-2-2−2i2i0002222-2-2-2-2−2i2i0000−2i2i0000−2i2i00−22−i2i2−22−i2i22-200−2i2i0000−22−i2i2−22−i2i20000000000000
χ294444444441-21-21-21-211-2-2-2-21111-2-2-2-21100000000000000222200000000-1-1-1-1-1-1-1-100000
χ304444444441-21-21-21-211-2-2-2-21111-2-2-2-21100000000000000-2-2-2-2000000001111111100000
χ31444444444-21-21-21-21-2-21111-2-2-2-21111-2-2222222220000000000-1-1-1-1-1-1-1-10000000000000
χ32444444444-21-21-21-21-2-21111-2-2-2-21111-2-2-2-2-2-2-2-2-2-20000000000111111110000000000000
χ33444444-4-4-41-21-21-21-211222211-1-122-2-2-1-10000000000000022-2-200000000-1-1-1-1111100000
χ34444444-4-4-41-21-21-21-211222211-1-122-2-2-1-100000000000000-2-222000000001111-1-1-1-100000
χ35444444-4-4-4-21-21-21-21-2-2-1-1-1-1-2-222-1-111222i2i2i2i−2i−2i−2i−2i0000000000−i−i−i−iiiii0000000000000
χ36444444-4-4-4-21-21-21-21-2-2-1-1-1-1-2-222-1-11122−2i−2i−2i−2i2i2i2i2i0000000000iiii−i−i−i−i0000000000000
χ374444-4-444-41-21-21-21-2-1-1-2-2-2-2-1-1-1-1222211000000000000002i−2i2i−2i00000000−i−iii−i−iii00000
χ384444-4-444-41-21-21-21-2-1-1-2-2-2-2-1-1-1-122221100000000000000−2i2i−2i2i00000000ii−i−iii−i−i00000
χ394444-4-444-4-21-21-21-212211112222-1-1-1-1-2-222-2-222-2-20000000000-1-111-1-1110000000000000
χ404444-4-444-4-21-21-21-212211112222-1-1-1-1-2-2-2-222-2-222000000000011-1-111-1-10000000000000
χ414444-4-4-4-441-21-21-21-2-1-12222-1-111-2-222-1-1000000000000002i−2i−2i2i00000000−i−iiiii−i−i00000
χ424444-4-4-4-441-21-21-21-2-1-12222-1-111-2-222-1-100000000000000−2i2i2i−2i00000000ii−i−i−i−iii00000
χ434444-4-4-4-44-21-21-21-2122-1-1-1-122-2-211-1-1222i2i−2i−2i−2i−2i2i2i0000000000−i−iiiii−i−i0000000000000
χ444444-4-4-4-44-21-21-21-2122-1-1-1-122-2-211-1-122−2i−2i2i2i2i2i−2i−2i0000000000ii−i−i−i−iii0000000000000
χ4544-4-44i−4i000-21-212-12-1−2i2i3i3i−3i−3i−2i2i003-3i−i002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ7−2ζ232ζ7+2ζ230000000000−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ230000000000000
χ4644-4-44i−4i000-21-212-12-1−2i2i3i3i−3i−3i−2i2i003-3i−i00−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ7+2ζ23−2ζ7−2ζ230000000000ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ230000000000000
χ4744-4-44i−4i000-21-212-12-1−2i2i−3i−3i3i3i−2i2i00-33i−i00−2ζ5−2ζ132ζ5+2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000ζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ130000000000000
χ4844-4-44i−4i000-21-212-12-1−2i2i−3i−3i3i3i−2i2i00-33i−i002ζ5+2ζ13−2ζ5−2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ130000000000000
χ4944-4-4−4i4i000-21-212-12-12i−2i3i3i−3i−3i2i−2i00-33−ii002ζ7+2ζ23−2ζ7−2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000000000−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ230000000000000
χ5044-4-4−4i4i000-21-212-12-12i−2i3i3i−3i−3i2i−2i00-33−ii00−2ζ7−2ζ232ζ7+2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000000000ζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ230000000000000
χ5144-4-4−4i4i000-21-212-12-12i−2i−3i−3i3i3i2i−2i003-3−ii00−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ130000000000000
χ5244-4-4−4i4i000-21-212-12-12i−2i−3i−3i3i3i2i−2i003-3−ii002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23ζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ130000000000000
χ534-44-40000044-4-444-4-4000000000000000000000000004i−4i000000000000000000000000000
χ544-44-40000044-4-444-4-400000000000000000000000000−4i4i000000000000000000000000000
χ554-4-44004-401-2-12-121-2332-22-2-3-33-300001-100000000000000000000000000−i3i3−i3i3−i3i3−i3i300000
χ564-4-44004-401-2-12-121-2332-22-2-3-33-300001-100000000000000000000000000i3−i3i3−i3i3−i3i3−i300000
χ574-4-44004-401-2-12-121-2-3-32-22-233-3300001-1000000000000000000000000003−3−333−3−3300000
χ584-4-44004-401-2-12-121-2-3-32-22-233-3300001-100000000000000000000000000−333−3−333−300000
χ594-4-44004-4044-4-4-4-44400-44-44000000004-4000000000000000000000000000000000000000
χ604-4-4400-4401-2-12-121-233-22-22-3-3-330000-1100000000000000000000000000−i3i3−i3i3i3−i3i3−i300000
χ614-4-4400-4401-2-12-121-233-22-22-3-3-330000-1100000000000000000000000000i3−i3i3−i3−i3i3−i3i300000
χ624-4-4400-4401-2-12-121-2-3-3-22-22333-30000-11000000000000000000000000003−3−33−333−300000
χ634-4-4400-4401-2-12-121-2-3-3-22-22333-30000-1100000000000000000000000000−333−33−3−3300000
χ644-4-4400-44044-4-4-4-444004-44-400000000-44000000000000000000000000000000000000000
χ6588-8-88i−8i0002-42-4-24-242i−2i00002i−2i0000−4i4i00000000000000000000000000000000000000000
χ6688-8-8−8i8i0002-42-4-24-24−2i2i0000−2i2i00004i−4i00000000000000000000000000000000000000000
χ678-88-8000002-4-242-4-246i−6i0000−6i6i00000000000000000000000000000000000000000000000
χ688-88-8000002-4-242-4-24−6i6i00006i−6i00000000000000000000000000000000000000000000000
χ698-88-800000-424-2-424-2006i−6i−6i6i0000000000000000000000000000000000000000000000000
χ708-88-800000-424-2-424-200−6i6i6i−6i0000000000000000000000000000000000000000000000000
χ718-8-88008-80-424-24-2-4200-22-2200000000-44000000000000000000000000000000000000000
χ728-8-8800-880-424-24-2-42002-22-2000000004-4000000000000000000000000000000000000000

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