Finite Group Databasebeta

← Group #11790014

Character table — Group #11790014

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11111111444444444444444444888888881818181824242424242424242424242424242424242424242424242436363636363636363636
order122244443366666688121212121212121224242424242424242244244466888812121212121224242424242424244444888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1
χ311111111111111111111111111111111111111-111-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111
χ51111111111111111-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ61111111111111111-1-111111111-1-1-1-1-1-1-1-111111-1-1111-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1
χ71111111111111111-1-111111111-1-1-1-1-1-1-1-11111-111-1-1-111-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-1
χ81111111111111111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-11111
χ91111-1-1-1-111111111i−i-1-1-1-1-1-1-1-1ii−i−iii−i−i-1-11111-1-111i−ii−i11-1-1-1-1ii−i−iii−i−iii−i−ii−i11-1-1
χ101111-1-1-1-111111111i−i-1-1-1-1-1-1-1-1ii−i−iii−i−i-1-1111-11-111i−i−ii-1-111-1-1ii−i−i−i−iii−i−iiii−i-1-111
χ111111-1-1-1-111111111i−i-1-1-1-1-1-1-1-1ii−i−iii−i−i-1-111-11-11-1-1−iii−i11-1-111−i−iiiii−i−i−i−iiii−i-1-111
χ121111-1-1-1-111111111i−i-1-1-1-1-1-1-1-1ii−i−iii−i−i-1-111-1-111-1-1−ii−ii-1-11111−i−iii−i−iiiii−i−ii−i11-1-1
χ131111-1-1-1-111111111−ii-1-1-1-1-1-1-1-1−i−iii−i−iii-1-11111-1-111−ii−ii11-1-1-1-1−i−iii−i−iii−i−iii−ii11-1-1
χ141111-1-1-1-111111111−ii-1-1-1-1-1-1-1-1−i−iii−i−iii-1-1111-11-111−iii−i-1-111-1-1−i−iiiii−i−iii−i−i−ii-1-111
χ151111-1-1-1-111111111−ii-1-1-1-1-1-1-1-1−i−iii−i−iii-1-111-11-11-1-1i−i−ii11-1-111ii−i−i−i−iiiii−i−i−ii-1-111
χ161111-1-1-1-111111111−ii-1-1-1-1-1-1-1-1−i−iii−i−iii-1-111-1-111-1-1i−ii−i-1-11111ii−i−iii−i−i−i−iii−ii11-1-1
χ172222222222222222222222222222222222-2-2-2-20000000000000000000000000000-2-20000
χ182222222222222222-2-222222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000220000
χ192222-2-2-2-2222222222i−2i-2-2-2-2-2-2-2-22i2i−2i−2i2i2i−2i−2i22-2-20000000000000000000000000000−2i2i0000
χ202222-2-2-2-222222222−2i2i-2-2-2-2-2-2-2-2−2i−2i2i2i−2i−2i2i2i22-2-200000000000000000000000000002i−2i0000
χ212-2-2222-2-222-2-22-2-220022-2-222-2-2000000002-2-220000000000000000000000002i−2i2i−2i000000
χ222-2-2222-2-222-2-22-2-220022-2-222-2-2000000002-2-22000000000000000000000000−2i2i−2i2i000000
χ232-2-2222-2-222-2-22-2-220022-2-222-2-200000000-222-20000000000000000000000000000002i−2i2i−2i
χ242-2-2222-2-222-2-22-2-220022-2-222-2-200000000-222-2000000000000000000000000000000−2i2i−2i2i
χ252-2-22-2-22222-2-22-2-2200-2-222-2-222000000002-22-20000000000000000000000000000002i−2i−2i2i
χ262-2-22-2-22222-2-22-2-2200-2-222-2-222000000002-22-2000000000000000000000000000000−2i2i2i−2i
χ272-2-22-2-22222-2-22-2-2200-2-222-2-22200000000-22-220000000000000000000000002-2-22000000
χ282-2-22-2-22222-2-22-2-2200-2-222-2-22200000000-22-22000000000000000000000000-222-2000000
χ29444444441-2-2-2111-24411-2-2-2-211-2-2-2-2111100000220000022-1-1-1-1000000-1-1-1-10000000000
χ30444444441-2-2-2111-24411-2-2-2-211-2-2-2-2111100000-2-200000-2-2111100000011110000000000
χ31444444441-2-2-2111-2-4-411-2-2-2-2112222-1-1-1-1000002200000-2-2-1-1-1-100000011110000000000
χ32444444441-2-2-2111-2-4-411-2-2-2-2112222-1-1-1-100000-2-200000221111000000-1-1-1-10000000000
χ3344444444-2111-2-2-2144-2-21111-2-21111-2-2-2-200002002-1-122000000-1-1-1-1-1-100000000000000
χ3444444444-2111-2-2-2144-2-21111-2-21111-2-2-2-20000-200-211-2-200000011111100000000000000
χ3544444444-2111-2-2-21-4-4-2-21111-2-2-1-1-1-1222200002002-1-1-2-2000000-1-1111100000000000000
χ3644444444-2111-2-2-21-4-4-2-21111-2-2-1-1-1-122220000-200-2112200000011-1-1-1-100000000000000
χ374444-4-4-4-41-2-2-2111-24i−4i-1-12222-1-1−2i−2i2i2iii−i−i000002-2000002i−2i-1-111000000−i−iii0000000000
χ384444-4-4-4-41-2-2-2111-24i−4i-1-12222-1-1−2i−2i2i2iii−i−i00000-2200000−2i2i11-1-1000000ii−i−i0000000000
χ394444-4-4-4-41-2-2-2111-2−4i4i-1-12222-1-12i2i−2i−2i−i−iii000002-200000−2i2i-1-111000000ii−i−i0000000000
χ404444-4-4-4-41-2-2-2111-2−4i4i-1-12222-1-12i2i−2i−2i−i−iii00000-22000002i−2i11-1-1000000−i−iii0000000000
χ414444-4-4-4-4-2111-2-2-214i−4i22-1-1-1-122ii−i−i−2i−2i2i2i0000200-2-1-12i−2i00000011−i−iii00000000000000
χ424444-4-4-4-4-2111-2-2-214i−4i22-1-1-1-122ii−i−i−2i−2i2i2i0000-200211−2i2i000000-1-1ii−i−i00000000000000
χ434444-4-4-4-4-2111-2-2-21−4i4i22-1-1-1-122−i−iii2i2i−2i−2i0000200-2-1-1−2i2i00000011ii−i−i00000000000000
χ444444-4-4-4-4-2111-2-2-21−4i4i22-1-1-1-122−i−iii2i2i−2i−2i0000-2002112i−2i000000-1-1−i−iii00000000000000
χ4544-4-44i−4i4i−4i1-22-2-11-1200i−i2i−2i2i−2ii−i00003ζ7+3ζ23−3ζ7−3ζ23−3ζ5−3ζ133ζ5+3ζ1300000000000000−i3i33−3000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000000000
χ4644-4-44i−4i4i−4i1-22-2-11-1200i−i2i−2i2i−2ii−i00003ζ7+3ζ23−3ζ7−3ζ23−3ζ5−3ζ133ζ5+3ζ1300000000000000i3−i3−33000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000000000
χ4744-4-44i−4i4i−4i1-22-2-11-1200i−i2i−2i2i−2ii−i0000−3ζ7−3ζ233ζ7+3ζ233ζ5+3ζ13−3ζ5−3ζ1300000000000000−i3i33−3000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000000000
χ4844-4-44i−4i4i−4i1-22-2-11-1200i−i2i−2i2i−2ii−i0000−3ζ7−3ζ233ζ7+3ζ233ζ5+3ζ13−3ζ5−3ζ1300000000000000i3−i3−33000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000000000
χ4944-4-44i−4i4i−4i44-44-44-4-4004i−4i−4i4i−4i4i4i−4i0000000000000000000000000000000000000000000000
χ5044-4-4−4i4i−4i4i1-22-2-11-1200−ii−2i2i−2i2i−ii0000−3ζ5−3ζ133ζ5+3ζ133ζ7+3ζ23−3ζ7−3ζ2300000000000000−i3i3−33000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000000000
χ5144-4-4−4i4i−4i4i1-22-2-11-1200−ii−2i2i−2i2i−ii0000−3ζ5−3ζ133ζ5+3ζ133ζ7+3ζ23−3ζ7−3ζ2300000000000000i3−i33−3000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000000000
χ5244-4-4−4i4i−4i4i1-22-2-11-1200−ii−2i2i−2i2i−ii00003ζ5+3ζ13−3ζ5−3ζ13−3ζ7−3ζ233ζ7+3ζ2300000000000000−i3i3−33000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000000000
χ5344-4-4−4i4i−4i4i1-22-2-11-1200−ii−2i2i−2i2i−ii00003ζ5+3ζ13−3ζ5−3ζ13−3ζ7−3ζ233ζ7+3ζ2300000000000000i3−i33−3000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000000000
χ5444-4-4−4i4i−4i4i44-44-44-4-400−4i4i4i−4i4i−4i−4i4i0000000000000000000000000000000000000000000000
χ554-44-44i−4i−4i4i444-4-4-44-4004i−4i4i−4i−4i4i−4i4i0000000000000000000000000000000000000000000000
χ564-44-44i−4i−4i4i-211-122-2-100−2i2ii−i−ii2i−2i−3ζ5−3ζ133ζ5+3ζ133ζ7+3ζ23−3ζ7−3ζ23000000000000−i3i3000000003−3ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ2300000000000000
χ574-44-44i−4i−4i4i-211-122-2-100−2i2ii−i−ii2i−2i−3ζ5−3ζ133ζ5+3ζ133ζ7+3ζ23−3ζ7−3ζ23000000000000i3−i300000000−33−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ2300000000000000
χ584-44-44i−4i−4i4i-211-122-2-100−2i2ii−i−ii2i−2i3ζ5+3ζ13−3ζ5−3ζ13−3ζ7−3ζ233ζ7+3ζ23000000000000−i3i3000000003−3−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ2300000000000000
χ594-44-44i−4i−4i4i-211-122-2-100−2i2ii−i−ii2i−2i3ζ5+3ζ13−3ζ5−3ζ13−3ζ7−3ζ233ζ7+3ζ23000000000000i3−i300000000−33ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ2300000000000000
χ604-44-4−4i4i4i−4i444-4-4-44-400−4i4i−4i4i4i−4i4i−4i0000000000000000000000000000000000000000000000
χ614-44-4−4i4i4i−4i-211-122-2-1002i−2i−iii−i−2i2i3ζ7+3ζ23−3ζ7−3ζ23−3ζ5−3ζ133ζ5+3ζ13000000000000−i3i300000000−33ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ1300000000000000
χ624-44-4−4i4i4i−4i-211-122-2-1002i−2i−iii−i−2i2i3ζ7+3ζ23−3ζ7−3ζ23−3ζ5−3ζ133ζ5+3ζ13000000000000i3−i3000000003−3−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ1300000000000000
χ634-44-4−4i4i4i−4i-211-122-2-1002i−2i−iii−i−2i2i−3ζ7−3ζ233ζ7+3ζ233ζ5+3ζ13−3ζ5−3ζ13000000000000−i3i300000000−33−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ1300000000000000
χ644-44-4−4i4i4i−4i-211-122-2-1002i−2i−iii−i−2i2i−3ζ7−3ζ233ζ7+3ζ233ζ5+3ζ13−3ζ5−3ζ13000000000000i3−i3000000003−3ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ1300000000000000
χ6588-8-88i−8i8i−8i-42-224-44-200−4i4i−2i2i−2i2i−4i4i0000000000000000000000000000000000000000000000
χ6688-8-8−8i8i−8i8i-42-224-44-2004i−4i2i−2i2i−2i4i−4i0000000000000000000000000000000000000000000000
χ678-88-88i−8i−8i8i2-4-44-2-224002i−2i−4i4i4i−4i−2i2i0000000000000000000000000000000000000000000000
χ688-88-8−8i8i8i−8i2-4-44-2-22400−2i2i4i−4i−4i4i2i−2i0000000000000000000000000000000000000000000000
χ698-8-8888-8-82-4442-2-2-4002244-4-4-2-20000000000000000000000000000000000000000000000
χ708-8-8888-8-8-42-2-2-444200-4-4-2-222440000000000000000000000000000000000000000000000
χ718-8-88-8-8882-4442-2-2-400-2-2-4-444220000000000000000000000000000000000000000000000
χ728-8-88-8-888-42-2-2-4442004422-2-2-4-40000000000000000000000000000000000000000000000

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