Finite Group Databasebeta

← Group #11785749

Character table — Group #11785749

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size111122224444444444444444488888888121212121212121218181818181824242424242424242424242424242424242424243672727272
order1222444423366666612121212121212126666121212124444444422444488881212121212121212242424242424242428888
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
χ5111111-1-1-1111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i-1ii−i−i
χ6111111-1-1-1111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii-1−i−iii
χ7111111-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1ii−i−i-1-1-1-11111iiii−i−i−i−i-1−i−iii
χ8111111-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1−i−iii-1-1-1-11111−i−i−i−iiiii-1ii−i−i
χ91111-1-111-111111111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-111-1-1111-11-111-1-111-1-111-1-111-1-1-11-11-1
χ101111-1-111-111111111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-111-1-111-11-1111-1-111-1-1-1-111-1-111-1-11-11
χ111111-1-111-111111111-1-1-1-11111-1-1-1-1-1-111-1-111-1-11111-1-1111-11-1-1-111-1-11111-1-111-1-1-1-11-11
χ121111-1-111-111111111-1-1-1-11111-1-1-1-1-1-111-1-111-1-11111-1-111-11-11-1-111-1-111-1-111-1-111-11-11-1
χ131111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1i−i−ii11-1-1-1-111ii−i−i−i−iii1i−i−ii
χ141111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1−iii−i11-1-1-1-111−i−iiiii−i−i1−iii−i
χ151111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1-1-1i−i−ii-1-11111-1-1ii−i−i−i−iii1−iii−i
χ161111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1-1-1−iii−i-1-11111-1-1−i−iiiii−i−i1i−i−ii
χ1722222222222222222222222222222222200000000-2-2-2-2-2-200000000000000000000-20000
χ18222222-2-2-2222222222222-2-2-2-2-2-2-2-222-2-200000000-2-2-2-2220000000000000000000020000
χ192222-2-222-222222222-2-2-2-22222-2-2-2-2-2-22200000000-2-222-2-20000000000000000000020000
χ202222-2-2-2-2222222222-2-2-2-2-2-2-2-22222-2-2-2-200000000-2-2222200000000000000000000-20000
χ212-2-22002-2022-2-222-2-2000022-2-20000002-2002i−2i002i−2i2-2002-20000002i−2i002i−2i0000000000000
χ222-2-22002-2022-2-222-2-2000022-2-20000002-200−2i2i00−2i2i2-2002-2000000−2i2i00−2i2i0000000000000
χ232-2-22002-2022-2-222-2-2000022-2-20000002-22i−2i002i−2i00-2200-2200002i−2i002i−2i000000000000000
χ242-2-22002-2022-2-222-2-2000022-2-20000002-2−2i2i00−2i2i00-2200-220000−2i2i00−2i2i000000000000000
χ252-2-2200-22022-2-222-2-20000-2-222000000-22002i−2i00−2i2i2-200-220000002i−2i00−2i2i0000000000000
χ262-2-2200-22022-2-222-2-20000-2-222000000-2200−2i2i002i−2i2-200-22000000−2i2i002i−2i0000000000000
χ272-2-2200-22022-2-222-2-20000-2-222000000-222i−2i00−2i2i00-22002-200002i−2i00−2i2i000000000000000
χ282-2-2200-22022-2-222-2-20000-2-222000000-22−2i2i002i−2i00-22002-20000−2i2i002i−2i000000000000000
χ294444444441-2111-2-2-2-2-2-2-2111111-2-211-2-200000000000000222200000000-1-1-1-1-1-1-1-100000
χ304444444441-2111-2-2-2-2-2-2-2111111-2-211-2-200000000000000-2-2-2-2000000001111111100000
χ31444444444-21-2-2-21111111-2-2-2-2-2-211-2-211222222220000000000-1-1-1-1-1-1-1-10000000000000
χ32444444444-21-2-2-21111111-2-2-2-2-2-211-2-211-2-2-2-2-2-2-2-20000000000111111110000000000000
χ33444444-4-4-41-2111-2-2-2-2-2-2-2-1-1-1-1-1-1221122000000000000002i2i−2i−2i00000000−i−i−i−iiiii00000
χ34444444-4-4-41-2111-2-2-2-2-2-2-2-1-1-1-1-1-122112200000000000000−2i−2i2i2i00000000iiii−i−i−i−i00000
χ35444444-4-4-4-21-2-2-21111111222222-1-1-2-2-1-12222-2-2-2-20000000000-1-1-1-111110000000000000
χ36444444-4-4-4-21-2-2-21111111222222-1-1-2-2-1-1-2-2-2-2222200000000001111-1-1-1-10000000000000
χ374444-4-444-41-2111-2-2-222221111-1-122-1-1-2-2000000000000002-22-200000000-1-111-1-11100000
χ384444-4-444-41-2111-2-2-222221111-1-122-1-1-2-200000000000000-22-220000000011-1-111-1-100000
χ394444-4-444-4-21-2-2-2111-1-1-1-1-2-2-2-222-1-1221122-2-222-2-20000000000-1-111-1-1110000000000000
χ404444-4-444-4-21-2-2-2111-1-1-1-1-2-2-2-222-1-12211-2-222-2-222000000000011-1-111-1-10000000000000
χ414444-4-4-4-441-2111-2-2-22222-1-1-1-111-2-2-1-122000000000000002i−2i−2i2i00000000−i−iiiii−i−i00000
χ424444-4-4-4-441-2111-2-2-22222-1-1-1-111-2-2-1-12200000000000000−2i2i2i−2i00000000ii−i−i−i−iii00000
χ434444-4-4-4-44-21-2-2-2111-1-1-1-12222-2-21122-1-122-2-2-2-2220000000000-1-11111-1-10000000000000
χ444444-4-4-4-44-21-2-2-2111-1-1-1-12222-2-21122-1-1-2-22222-2-2000000000011-1-1-1-1110000000000000
χ4544-4-400000444-4-4-44-4000000000000000000000000004i−4i000000000000000000000000000
χ4644-4-400000444-4-4-44-400000000000000000000000000−4i4i000000000000000000000000000
χ474-44-44i−4i0001-2-11-122-22i2i−2i−2i3i−3i3i−3i3-300i−i0000000000000000000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ1300000
χ484-44-44i−4i0001-2-11-122-22i2i−2i−2i3i−3i3i−3i3-300i−i0000000000000000000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ1300000
χ494-44-44i−4i0001-2-11-122-22i2i−2i−2i−3i3i−3i3i-3300i−i0000000000000000000000000000−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ2300000
χ504-44-44i−4i0001-2-11-122-22i2i−2i−2i−3i3i−3i3i-3300i−i0000000000000000000000000000ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ2300000
χ514-44-44i−4i00044-44-4-4-44−4i−4i4i4i000000004i−4i00000000000000000000000000000000000000000
χ524-44-4−4i4i0001-2-11-122-2−2i−2i2i2i3i−3i3i−3i-3300−ii0000000000000000000000000000ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ1300000
χ534-44-4−4i4i0001-2-11-122-2−2i−2i2i2i3i−3i3i−3i-3300−ii0000000000000000000000000000−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ1300000
χ544-44-4−4i4i0001-2-11-122-2−2i−2i2i2i−3i3i−3i3i3-300−ii0000000000000000000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ2300000
χ554-44-4−4i4i0001-2-11-122-2−2i−2i2i2i−3i3i−3i3i3-300−ii0000000000000000000000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ2300000
χ564-44-4−4i4i00044-44-4-4-444i4i−4i−4i00000000−4i4i00000000000000000000000000000000000000000
χ574-4-44004-40-2122-21-1-13-33-3-2-222003-3001-12i−2i2i−2i2i−2i2i−2i0000000000−ii−ii−ii−ii0000000000000
χ584-4-44004-40-2122-21-1-13-33-3-2-222003-3001-1−2i2i−2i2i−2i2i−2i2i0000000000i−ii−ii−ii−i0000000000000
χ594-4-44004-40-2122-21-1-1-33-33-2-22200-33001-12i−2i−2i2i2i−2i−2i2i0000000000−iii−i−iii−i0000000000000
χ604-4-44004-40-2122-21-1-1-33-33-2-22200-33001-1−2i2i2i−2i−2i2i2i−2i0000000000i−i−iii−i−ii0000000000000
χ614-4-4400-440-2122-21-1-13-33-322-2-200-3300-112i−2i2i−2i−2i2i−2i2i0000000000−ii−iii−ii−i0000000000000
χ624-4-4400-440-2122-21-1-13-33-322-2-200-3300-11−2i2i−2i2i2i−2i2i−2i0000000000i−ii−i−ii−ii0000000000000
χ634-4-4400-440-2122-21-1-1-33-3322-2-2003-300-112i−2i−2i2i−2i2i2i−2i0000000000−iii−ii−i−ii0000000000000
χ644-4-4400-440-2122-21-1-1-33-3322-2-2003-300-11−2i2i2i−2i2i−2i−2i2i0000000000i−i−ii−iii−i0000000000000
χ6588-8-8000002-42-2-24-4400006i−6i−6i6i00000000000000000000000000000000000000000000000
χ6688-8-8000002-42-2-24-440000−6i6i6i−6i00000000000000000000000000000000000000000000000
χ6788-8-800000-42-444-22-26i−6i−6i6i000000000000000000000000000000000000000000000000000
χ6888-8-800000-42-444-22-2−6i6i6i−6i000000000000000000000000000000000000000000000000000
χ698-88-88i−8i000-424-44-2-22−2i−2i2i2i00000000−4i4i00000000000000000000000000000000000000000
χ708-88-8−8i8i000-424-44-2-222i2i−2i−2i000000004i−4i00000000000000000000000000000000000000000
χ718-8-88008-802-4-2-22-444000022-2-2000000-44000000000000000000000000000000000000000
χ728-8-8800-8802-4-2-22-4440000-2-2220000004-4000000000000000000000000000000000000000

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