Finite Group Databasebeta

← Group #11785473

Character table — Group #11785473

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11111111444444444444444444888888881818181824242424242424242424242424242424242424242424242436363636363636363636
order1222444423346666661212121212121212666612121212224488888888242424242424242424242424242424242488888888
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
χ511111111-111-111111111111111-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1
χ611111111-111-111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111
χ711111111-111-111111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111
χ811111111-111-111111111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1
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−i-1111-1-111-1-1
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−iii-11-1-111-1-111
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−i-11-1-111-1-111
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−iii-1111-1-111-1-1
χ131111-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111i−i−iii−i−iiii−i−i−i−iiiii−i−i−i−iii1-111-1-1-1-111
χ141111-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111i−i−ii−iii−iii−i−i−i−iii−i−iiiii−i−i1-1-1-11111-1-1
χ151111-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111−iii−ii−i−ii−i−iiiii−i−iii−i−i−i−iii1-1-1-11111-1-1
χ161111-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111−iii−i−iii−i−i−iiiii−i−i−i−iiiii−i−i1-111-1-1-1-111
χ172222222222222222222222222222222222-2-2-2-2000000000000000000000000-2-200000000
χ1822222222-222-222222222222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000002200000000
χ192222-2-2-2-2222-2222222-2-2-2-2-2-2-2-22222-2-2-2-222-2-20000000000000000000000002-200000000
χ202222-2-2-2-2-2222222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2-2000000000000000000000000-2200000000
χ212-2-2222-2-20220-2-2-2-2222222-2-2-2-2000000002-22-20000000000000000000000000000002i−2i2i−2i
χ222-2-2222-2-20220-2-2-2-2222222-2-2-2-2000000002-22-2000000000000000000000000000000−2i2i−2i2i
χ232-2-2222-2-20220-2-2-2-2222222-2-2-2-200000000-22-22000000000000000000000000002-22-20000
χ242-2-2222-2-20220-2-2-2-2222222-2-2-2-200000000-22-2200000000000000000000000000-22-220000
χ252-2-22-2-2220220-2-2-2-222-2-2-2-22222000000002-2-22000000000000000000000000002-2-220000
χ262-2-22-2-2220220-2-2-2-222-2-2-2-22222000000002-2-2200000000000000000000000000-222-20000
χ272-2-22-2-2220220-2-2-2-222-2-2-2-2222200000000-222-20000000000000000000000000000002i−2i−2i2i
χ282-2-22-2-2220220-2-2-2-222-2-2-2-2222200000000-222-2000000000000000000000000000000−2i2i2i−2i
χ294444444441-2411-2-21-211-2-211-2-211-2-211-2-200000000222200000000-1-1-1-1-1-1-1-10000000000
χ304444444441-2411-2-21-211-2-211-2-211-2-211-2-200000000-2-2-2-200000000111111110000000000
χ31444444444-214-2-211-21-2-211-2-211-2-211-2-211000022220000-1-1-1-1-1-1-1-1000000000000000000
χ32444444444-214-2-211-21-2-211-2-211-2-211-2-2110000-2-2-2-2000011111111000000000000000000
χ3344444444-41-2-411-2-21-211-2-211-2-2-1-122-1-1220000000022-2-200000000-1-1-1-111110000000000
χ3444444444-41-2-411-2-21-211-2-211-2-2-1-122-1-12200000000-2-222000000001111-1-1-1-10000000000
χ3544444444-4-21-4-2-211-21-2-211-2-21122-1-122-1-1000022-2-20000-1-1-1-11111000000000000000000
χ3644444444-4-21-4-2-211-21-2-211-2-21122-1-122-1-10000-2-22200001111-1-1-1-1000000000000000000
χ374444-4-4-4-441-2-411-2-21-2-1-122-1-12211-2-2-1-122000000002i−2i2i−2i00000000−i−iii−i−iii0000000000
χ384444-4-4-4-441-2-411-2-21-2-1-122-1-12211-2-2-1-12200000000−2i2i−2i2i00000000ii−i−iii−i−i0000000000
χ394444-4-4-4-44-21-4-2-211-2122-1-122-1-1-2-21122-1-100002i−2i2i−2i0000−i−iii−i−iii000000000000000000
χ404444-4-4-4-44-21-4-2-211-2122-1-122-1-1-2-21122-1-10000−2i2i−2i2i0000ii−i−iii−i−i000000000000000000
χ414444-4-4-4-4-41-2411-2-21-2-1-122-1-122-1-12211-2-2000000002i−2i−2i2i00000000−i−iiiii−i−i0000000000
χ424444-4-4-4-4-41-2411-2-21-2-1-122-1-122-1-12211-2-200000000−2i2i2i−2i00000000ii−i−i−i−iii0000000000
χ434444-4-4-4-4-4-214-2-211-2122-1-122-1-122-1-1-2-21100002i−2i−2i2i0000−i−iiiii−i−i000000000000000000
χ444444-4-4-4-4-4-214-2-211-2122-1-122-1-122-1-1-2-2110000−2i2i2i−2i0000ii−i−i−i−iii000000000000000000
χ4544-4-44i−4i4i−4i01-201-12-2-12i−i2i−2ii−i2i−2i3-3003i−3i0000000000000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000000000
χ4644-4-44i−4i4i−4i01-201-12-2-12i−i2i−2ii−i2i−2i3-3003i−3i0000000000000000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000000000
χ4744-4-44i−4i4i−4i01-201-12-2-12i−i2i−2ii−i2i−2i-3300−3i3i0000000000000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000000000
χ4844-4-44i−4i4i−4i01-201-12-2-12i−i2i−2ii−i2i−2i-3300−3i3i0000000000000000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000000000
χ4944-4-44i−4i4i−4i04404-4-44-4-44i−4i−4i4i4i−4i−4i4i0000000000000000000000000000000000000000000000
χ5044-4-4−4i4i−4i4i01-201-12-2-12−ii−2i2i−ii−2i2i3-300−3i3i0000000000000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000000000
χ5144-4-4−4i4i−4i4i01-201-12-2-12−ii−2i2i−ii−2i2i3-300−3i3i0000000000000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000000000
χ5244-4-4−4i4i−4i4i01-201-12-2-12−ii−2i2i−ii−2i2i-33003i−3i0000000000000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000000000
χ5344-4-4−4i4i−4i4i01-201-12-2-12−ii−2i2i−ii−2i2i-33003i−3i0000000000000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000000000
χ5444-4-4−4i4i−4i4i04404-4-44-4-4−4i4i4i−4i−4i4i4i−4i0000000000000000000000000000000000000000000000
χ554-44-44i−4i−4i4i0440-444-4-4-44i−4i−4i4i−4i4i4i−4i0000000000000000000000000000000000000000000000
χ564-44-44i−4i−4i4i0-2102-21-12-1−2i2i−ii2i−2ii−i003-3003i−3i000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000000000000000
χ574-44-44i−4i−4i4i0-2102-21-12-1−2i2i−ii2i−2ii−i003-3003i−3i000000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000000000000000
χ584-44-44i−4i−4i4i0-2102-21-12-1−2i2i−ii2i−2ii−i00-3300−3i3i000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000000000000000
χ594-44-44i−4i−4i4i0-2102-21-12-1−2i2i−ii2i−2ii−i00-3300−3i3i000000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000000000000000
χ604-44-4−4i4i4i−4i0440-444-4-4-4−4i4i4i−4i4i−4i−4i4i0000000000000000000000000000000000000000000000
χ614-44-4−4i4i4i−4i0-2102-21-12-12i−2ii−i−2i2i−ii003-300−3i3i000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000000000000000
χ624-44-4−4i4i4i−4i0-2102-21-12-12i−2ii−i−2i2i−ii003-300−3i3i000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000000000000000
χ634-44-4−4i4i4i−4i0-2102-21-12-12i−2ii−i−2i2i−ii00-33003i−3i000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000000000000000
χ644-44-4−4i4i4i−4i0-2102-21-12-12i−2ii−i−2i2i−ii00-33003i−3i000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000000000000000
χ6588-8-88i−8i8i−8i0-420-44-224-2−4i4i−2i2i−4i4i−2i2i0000000000000000000000000000000000000000000000
χ6688-8-8−8i8i−8i8i0-420-44-224-24i−4i2i−2i4i−4i2i−2i0000000000000000000000000000000000000000000000
χ678-88-88i−8i−8i8i02-40-22-44-242i−2i4i−4i−2i2i−4i4i0000000000000000000000000000000000000000000000
χ688-88-8−8i8i8i−8i02-40-22-44-24−2i2i−4i4i2i−2i4i−4i0000000000000000000000000000000000000000000000
χ698-8-8888-8-802-40-2-2442-422-4-4-2-2440000000000000000000000000000000000000000000000
χ708-8-8888-8-80-42044-2-2-42-4-42244-2-20000000000000000000000000000000000000000000000
χ718-8-88-8-88802-40-2-2442-4-2-24422-4-40000000000000000000000000000000000000000000000
χ728-8-88-8-8880-42044-2-2-4244-2-2-4-4220000000000000000000000000000000000000000000000

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