Finite Group Databasebeta

← Group #11786120

Character table — Group #11786120

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11111111444444444444444444888888881818181824242424242424242424242424242424242424242424242436363636363636363636
order12224444334466666612121212121212121212121212121212224488888888242424242424242424242424242424244488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
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
χ51111111111-1-111111111111111-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1
χ61111111111-1-111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111
χ71111111111-1-111111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111
χ81111111111-1-111111111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1
χ91111-1-1-1-1111-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111i−ii−ii−ii−iii−i−iii−i−iii−i−iii−i−i1-111-1-111-1-1
χ101111-1-1-1-1111-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111i−ii−i−ii−iiii−i−iii−i−i−i−iii−i−iii1-1-1-111-1-111
χ111111-1-1-1-1111-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111−ii−iii−ii−i−i−iii−i−iiiii−i−iii−i−i1-1-1-111-1-111
χ121111-1-1-1-1111-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111−ii−ii−ii−ii−i−iii−i−iii−i−iii−i−iii1-111-1-111-1-1
χ131111-1-1-1-111-11111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111i−i−iii−i−iiii−i−i−i−iiiii−i−i−i−iii-1111-1-1-1-111
χ141111-1-1-1-111-11111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111i−i−ii−iii−iii−i−i−i−iii−i−iiiii−i−i-11-1-11111-1-1
χ151111-1-1-1-111-11111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111−iii−ii−i−ii−i−iiiii−i−iii−i−i−i−iii-11-1-11111-1-1
χ161111-1-1-1-111-11111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111−iii−i−iii−i−i−iiiii−i−i−i−iiiii−i−i-1111-1-1-1-111
χ172222222222222222222222222222222222-2-2-2-2000000000000000000000000-2-200000000
χ182222222222-2-222222222222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000002200000000
χ192222-2-2-2-2222-2222222-2-2-2-2-2-2-2-22222-2-2-2-222-2-2000000000000000000000000-2200000000
χ202222-2-2-2-222-22222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2-20000000000000000000000002-200000000
χ2122-2-222-2-2220022-2-2-2-222-2-222-2-2000000002-22-20000000000000000000000000000002i−2i2i−2i
χ2222-2-222-2-2220022-2-2-2-222-2-222-2-2000000002-22-2000000000000000000000000000000−2i2i−2i2i
χ2322-2-222-2-2220022-2-2-2-222-2-222-2-200000000-22-22000000000000000000000000002i−2i2i−2i0000
χ2422-2-222-2-2220022-2-2-2-222-2-222-2-200000000-22-2200000000000000000000000000−2i2i−2i2i0000
χ2522-2-2-2-222220022-2-2-2-2-2-222-2-222000000002-2-22000000000000000000000000002i−2i−2i2i0000
χ2622-2-2-2-222220022-2-2-2-2-2-222-2-222000000002-2-2200000000000000000000000000−2i2i2i−2i0000
χ2722-2-2-2-222220022-2-2-2-2-2-222-2-22200000000-222-20000000000000000000000000000002i−2i−2i2i
χ2822-2-2-2-222220022-2-2-2-2-2-222-2-22200000000-222-2000000000000000000000000000000−2i2i2i−2i
χ29444444441-2441-211-2-211-2-2-2-21111-2-211-2-200000000222200000000-1-1-1-1-1-1-1-10000000000
χ30444444441-2441-211-2-211-2-2-2-21111-2-211-2-200000000-2-2-2-200000000111111110000000000
χ31444444441-2-4-41-211-2-211-2-2-2-211-1-122-1-1220000000022-2-200000000-1-1-1-111110000000000
χ32444444441-2-4-41-211-2-211-2-2-2-211-1-122-1-12200000000-2-222000000001111-1-1-1-10000000000
χ3344444444-2144-21-2-211-2-21111-2-2-2-211-2-211000022220000-1-1-1-1-1-1-1-1000000000000000000
χ3444444444-2144-21-2-211-2-21111-2-2-2-211-2-2110000-2-2-2-2000011111111000000000000000000
χ3544444444-21-4-4-21-2-211-2-21111-2-222-1-122-1-1000022-2-20000-1-1-1-11111000000000000000000
χ3644444444-21-4-4-21-2-211-2-21111-2-222-1-122-1-10000-2-22200001111-1-1-1-1000000000000000000
χ374444-4-4-4-41-24-41-211-2-2-1-12222-1-111-2-2-1-122000000002i−2i2i−2i00000000−i−iii−i−iii0000000000
χ384444-4-4-4-41-24-41-211-2-2-1-12222-1-111-2-2-1-12200000000−2i2i−2i2i00000000ii−i−iii−i−i0000000000
χ394444-4-4-4-41-2-441-211-2-2-1-12222-1-1-1-12211-2-2000000002i−2i−2i2i00000000−i−iiiii−i−i0000000000
χ404444-4-4-4-41-2-441-211-2-2-1-12222-1-1-1-12211-2-200000000−2i2i2i−2i00000000ii−i−i−i−iii0000000000
χ414444-4-4-4-4-214-4-21-2-21122-1-1-1-122-2-21122-1-100002i−2i2i−2i0000−i−iii−i−iii000000000000000000
χ424444-4-4-4-4-214-4-21-2-21122-1-1-1-122-2-21122-1-10000−2i2i−2i2i0000ii−i−iii−i−i000000000000000000
χ434444-4-4-4-4-21-44-21-2-21122-1-1-1-12222-1-1-2-21100002i−2i−2i2i0000−i−iiiii−i−i000000000000000000
χ444444-4-4-4-4-21-44-21-2-21122-1-1-1-12222-1-1-2-2110000−2i2i2i−2i0000ii−i−i−i−iii000000000000000000
χ454-44-44i−4i4i−4i1-200-121-12-2i−i2i−2i2i−2ii−i3-3003i−3i0000000000000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000000000
χ464-44-44i−4i4i−4i1-200-121-12-2i−i2i−2i2i−2ii−i3-3003i−3i0000000000000000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000000000
χ474-44-44i−4i4i−4i1-200-121-12-2i−i2i−2i2i−2ii−i-3300−3i3i0000000000000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000000000
χ484-44-44i−4i4i−4i1-200-121-12-2i−i2i−2i2i−2ii−i-3300−3i3i0000000000000000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000000000
χ494-44-44i−4i4i−4i4400-4-44-4-444i−4i−4i4i−4i4i4i−4i0000000000000000000000000000000000000000000000
χ504-44-4−4i4i−4i4i1-200-121-12-2−ii−2i2i−2i2i−ii3-300−3i3i0000000000000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000000000
χ514-44-4−4i4i−4i4i1-200-121-12-2−ii−2i2i−2i2i−ii3-300−3i3i0000000000000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000000000
χ524-44-4−4i4i−4i4i1-200-121-12-2−ii−2i2i−2i2i−ii-33003i−3i0000000000000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000000000
χ534-44-4−4i4i−4i4i1-200-121-12-2−ii−2i2i−2i2i−ii-33003i−3i0000000000000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000000000
χ544-44-4−4i4i−4i4i4400-4-44-4-44−4i4i4i−4i4i−4i−4i4i0000000000000000000000000000000000000000000000
χ554-4-444i−4i−4i4i4400-4-4-444-44i−4i4i−4i−4i4i−4i4i0000000000000000000000000000000000000000000000
χ564-4-444i−4i−4i4i-21002-12-21-1−2i2ii−i−ii2i−2i003i−3i003-3000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000000000000000
χ574-4-444i−4i−4i4i-21002-12-21-1−2i2ii−i−ii2i−2i003i−3i003-3000000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000000000000000
χ584-4-444i−4i−4i4i-21002-12-21-1−2i2ii−i−ii2i−2i00−3i3i00-33000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000000000000000
χ594-4-444i−4i−4i4i-21002-12-21-1−2i2ii−i−ii2i−2i00−3i3i00-33000000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000000000000000
χ604-4-44−4i4i4i−4i4400-4-4-444-4−4i4i−4i4i4i−4i4i−4i0000000000000000000000000000000000000000000000
χ614-4-44−4i4i4i−4i-21002-12-21-12i−2i−iii−i−2i2i003i−3i00-33000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000000000000000
χ624-4-44−4i4i4i−4i-21002-12-21-12i−2i−iii−i−2i2i003i−3i00-33000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000000000000000
χ634-4-44−4i4i4i−4i-21002-12-21-12i−2i−iii−i−2i2i00−3i3i003-3000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000000000000000
χ644-4-44−4i4i4i−4i-21002-12-21-12i−2i−iii−i−2i2i00−3i3i003-3000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000000000000000
χ6588-8-888-8-82-4002-4-2-2442244-4-4-2-20000000000000000000000000000000000000000000000
χ6688-8-888-8-8-4200-4244-2-2-4-4-2-222440000000000000000000000000000000000000000000000
χ6788-8-8-8-8882-4002-4-2-244-2-2-4-444220000000000000000000000000000000000000000000000
χ6888-8-8-8-888-4200-4244-2-24422-2-2-4-40000000000000000000000000000000000000000000000
χ698-88-88i−8i8i−8i-42004-2-44-22−4i4i−2i2i−2i2i−4i4i0000000000000000000000000000000000000000000000
χ708-88-8−8i8i−8i8i-42004-2-44-224i−4i2i−2i2i−2i4i−4i0000000000000000000000000000000000000000000000
χ718-8-888i−8i−8i8i2-400-24-22-442i−2i−4i4i4i−4i−2i2i0000000000000000000000000000000000000000000000
χ728-8-88−8i8i8i−8i2-400-24-22-44−2i2i4i−4i−4i4i2i−2i0000000000000000000000000000000000000000000000

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