Finite Group Databasebeta

← Group #11788221

Character table — Group #11788221

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11111111444444444444444444888888881818181824242424242424242424242424242424242424242424242436363636363636363636
order12224444233466666612121212121212126666121212122244244466888812121212121224242424242424242444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
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
χ511111111-111-111111111111111-1-1-1-1-1-1-1-111111-1-111111-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1
χ611111111-111-111111111111111-1-1-1-1-1-1-1-111111-1-1111-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111
χ711111111-111-111111111111111-1-1-1-1-1-1-1-11111-111-1-1-111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-11111
χ811111111-111-111111111111111-1-1-1-1-1-1-1-11111-111-1-1-1-1-1111111-1-1-1-1-1-11111-1-11111-1-1-1-1
χ91111-1-1-1-1111-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-111i−ii−i11-1-1-1-1ii−i−iii−i−i-11ii−i−iii−i−i
χ101111-1-1-1-1111-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-111−ii−ii11-1-1-1-1−i−iii−i−iii-11−i−iii−i−iii
χ111111-1-1-1-1111-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-1i−ii−i-1-11111ii−i−iii−i−i-11−i−iii−i−iii
χ121111-1-1-1-1111-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-1−ii−ii-1-11111−i−iii−i−iii-11ii−i−iii−i−i
χ131111-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111-11-111i−i−ii-1-111-1-1ii−i−i−i−iii1-1ii−i−i−i−iii
χ141111-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111-11-111−iii−i-1-111-1-1−i−iiiii−i−i1-1−i−iiiii−i−i
χ151111-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-11-11-1-1i−i−ii11-1-111ii−i−i−i−iii1-1−i−iiiii−i−i
χ161111-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-11-11-1-1−iii−i11-1-111−i−iiiii−i−i1-1ii−i−i−i−iii
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
χ212-2-2222-2-20220-2-22-2-2222-2-222-2-2000000002-22-20000000000000000000000000000002i−2i2i−2i
χ222-2-2222-2-20220-2-22-2-2222-2-222-2-2000000002-22-2000000000000000000000000000000−2i2i−2i2i
χ232-2-2222-2-20220-2-22-2-2222-2-222-2-200000000-22-22000000000000000000000000002-22-20000
χ242-2-2222-2-20220-2-22-2-2222-2-222-2-200000000-22-2200000000000000000000000000-22-220000
χ252-2-22-2-2220220-2-22-2-22-2-222-2-222000000002-2-22000000000000000000000000002i−2i−2i2i0000
χ262-2-22-2-2220220-2-22-2-22-2-222-2-222000000002-2-2200000000000000000000000000−2i2i2i−2i0000
χ272-2-22-2-2220220-2-22-2-22-2-222-2-22200000000-222-20000000000000000000000000000002-2-22
χ282-2-22-2-2220220-2-22-2-22-2-222-2-22200000000-222-2000000000000000000000000000000-222-2
χ294444444441-24111-2-2-2-2-2-2-2111111-2-211-2-200000000002222000000-1-1-1-1-1-1-1-10000000000
χ304444444441-24111-2-2-2-2-2-2-2111111-2-211-2-20000000000-2-2-2-2000000111111110000000000
χ31444444444-214-2-2-21111111-2-2-2-2-2-211-2-21100002222-1-10000-1-1-1-1-1-1000000000000000000
χ32444444444-214-2-2-21111111-2-2-2-2-2-211-2-2110000-2-2-2-2110000111111000000000000000000
χ3344444444-41-2-4111-2-2-2-2-2-2-21111-1-122-1-122000000000022-2-2000000-1-1-1-111110000000000
χ3444444444-41-2-4111-2-2-2-2-2-2-21111-1-122-1-1220000000000-2-2220000001111-1-1-1-10000000000
χ3544444444-4-21-4-2-2-21111111-2-2-2-222-1-122-1-100002-2-22-1-100001111-1-1000000000000000000
χ3644444444-4-21-4-2-2-21111111-2-2-2-222-1-122-1-10000-222-2110000-1-1-1-111000000000000000000
χ374444-4-4-4-441-2-4111-2-2-22222-1-1-1-111-2-2-1-12200000000002i−2i2i−2i000000−i−iii−i−iii0000000000
χ384444-4-4-4-441-2-4111-2-2-22222-1-1-1-111-2-2-1-1220000000000−2i2i−2i2i000000ii−i−iii−i−i0000000000
χ394444-4-4-4-44-21-4-2-2-2111-1-1-1-12222-2-21122-1-1000022-2-2-1-10000-1-11111000000000000000000
χ404444-4-4-4-44-21-4-2-2-2111-1-1-1-12222-2-21122-1-10000-2-22211000011-1-1-1-1000000000000000000
χ414444-4-4-4-4-41-24111-2-2-22222-1-1-1-1-1-12211-2-200000000002i−2i−2i2i000000−i−iiiii−i−i0000000000
χ424444-4-4-4-4-41-24111-2-2-22222-1-1-1-1-1-12211-2-20000000000−2i2i2i−2i000000ii−i−i−i−iii0000000000
χ434444-4-4-4-4-4-214-2-2-2111-1-1-1-1222222-1-1-2-21100002-22-2-1-1000011-1-111000000000000000000
χ444444-4-4-4-4-4-214-2-2-2111-1-1-1-1222222-1-1-2-2110000-22-22110000-1-111-1-1000000000000000000
χ4544-4-44i−4i4i−4i01-201-1-12-222i−2i2i−2ii−ii−i3-3003i−3i0000000000000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000000000
χ4644-4-44i−4i4i−4i01-201-1-12-222i−2i2i−2ii−ii−i3-3003i−3i0000000000000000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000000000
χ4744-4-44i−4i4i−4i01-201-1-12-222i−2i2i−2ii−ii−i-3300−3i3i0000000000000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000000000
χ4844-4-44i−4i4i−4i01-201-1-12-222i−2i2i−2ii−ii−i-3300−3i3i0000000000000000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000000000
χ4944-4-44i−4i4i−4i04404-4-4-44-4−4i4i−4i4i4i−4i4i−4i0000000000000000000000000000000000000000000000
χ5044-4-4−4i4i−4i4i01-201-1-12-22−2i2i−2i2i−ii−ii3-300−3i3i0000000000000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000000000
χ5144-4-4−4i4i−4i4i01-201-1-12-22−2i2i−2i2i−ii−ii3-300−3i3i0000000000000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000000000
χ5244-4-4−4i4i−4i4i01-201-1-12-22−2i2i−2i2i−ii−ii-33003i−3i0000000000000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000000000
χ5344-4-4−4i4i−4i4i01-201-1-12-22−2i2i−2i2i−ii−ii-33003i−3i0000000000000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000000000
χ5444-4-4−4i4i−4i4i04404-4-4-44-44i−4i4i−4i−4i4i−4i4i0000000000000000000000000000000000000000000000
χ554-44-44i−4i−4i4i0440-44-44-4-4−4i4i4i−4i4i−4i−4i4i0000000000000000000000000000000000000000000000
χ564-44-44i−4i−4i4i0-2102-221-1-1−iii−i−2i2i2i−2i003-3003i−3i00000000−i3i30000−i3i33−33−3000000000000000000
χ574-44-44i−4i−4i4i0-2102-221-1-1−iii−i−2i2i2i−2i003-3003i−3i00000000i3−i30000i3−i3−33−33000000000000000000
χ584-44-44i−4i−4i4i0-2102-221-1-1−iii−i−2i2i2i−2i00-3300−3i3i00000000−i3i30000i3−i3−333−3000000000000000000
χ594-44-44i−4i−4i4i0-2102-221-1-1−iii−i−2i2i2i−2i00-3300−3i3i00000000i3−i30000−i3i33−3−33000000000000000000
χ604-44-4−4i4i4i−4i0440-44-44-4-44i−4i−4i4i−4i4i4i−4i0000000000000000000000000000000000000000000000
χ614-44-4−4i4i4i−4i0-2102-221-1-1i−i−ii2i−2i−2i2i003-300−3i3i00000000−i3i30000−i3i3−33−33000000000000000000
χ624-44-4−4i4i4i−4i0-2102-221-1-1i−i−ii2i−2i−2i2i003-300−3i3i00000000i3−i30000i3−i33−33−3000000000000000000
χ634-44-4−4i4i4i−4i0-2102-221-1-1i−i−ii2i−2i−2i2i00-33003i−3i00000000−i3i30000i3−i33−3−33000000000000000000
χ644-44-4−4i4i4i−4i0-2102-221-1-1i−i−ii2i−2i−2i2i00-33003i−3i00000000i3−i30000−i3i3−333−3000000000000000000
χ6588-8-88i−8i8i−8i0-420-444-22-2−2i2i−2i2i−4i4i−4i4i0000000000000000000000000000000000000000000000
χ6688-8-8−8i8i−8i8i0-420-444-22-22i−2i2i−2i4i−4i4i−4i0000000000000000000000000000000000000000000000
χ678-88-88i−8i−8i8i02-40-22-2-4444i−4i−4i4i2i−2i−2i2i0000000000000000000000000000000000000000000000
χ688-88-8−8i8i8i−8i02-40-22-2-444−4i4i4i−4i−2i2i2i−2i0000000000000000000000000000000000000000000000
χ698-8-8888-8-802-40-2-2244-4-4-44422-2-20000000000000000000000000000000000000000000000
χ708-8-8888-8-80-42044-4-2-2222-2-2-4-4440000000000000000000000000000000000000000000000
χ718-8-88-8-88802-40-2-2244-444-4-4-2-2220000000000000000000000000000000000000000000000
χ728-8-88-8-8880-42044-4-2-22-2-22244-4-40000000000000000000000000000000000000000000000

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