Finite Group Databasebeta

← Group #11777911

Character table — Group #11777911

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11111111444444444444444444888888881818181824242424242424242424242424242424242424242424242436363636363636363636
order122244443366666688121212121212121224242424242424244444244466888812121212121224242424242424248888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-111-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1
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
χ51111111111111111-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111
χ71111111111111111-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-11111
χ81111111111111111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-11111-1-1-1-1
χ91111-1-1-1-111111111i−i-1-1-1-1-1-1-1-1iiii−i−i−i−i11-1-11-11-111i−ii−i11-1-1-1-1ii−i−iii−i−ii−i11-1-1ii−i−i
χ101111-1-1-1-111111111i−i-1-1-1-1-1-1-1-1iiii−i−i−i−i11-1-11-1-1111i−i−ii-1-111-1-1ii−i−i−i−iiii−i-1-111−i−iii
χ111111-1-1-1-111111111i−i-1-1-1-1-1-1-1-1iiii−i−i−i−i11-1-1-111-1-1-1−iii−i11-1-111−i−iiiii−i−ii−i-1-111−i−iii
χ121111-1-1-1-111111111i−i-1-1-1-1-1-1-1-1iiii−i−i−i−i11-1-1-11-11-1-1−ii−ii-1-11111−i−iii−i−iiii−i11-1-1ii−i−i
χ131111-1-1-1-111111111−ii-1-1-1-1-1-1-1-1−i−i−i−iiiii11-1-11-11-111−ii−ii11-1-1-1-1−i−iii−i−iii−ii11-1-1−i−iii
χ141111-1-1-1-111111111−ii-1-1-1-1-1-1-1-1−i−i−i−iiiii11-1-11-1-1111−iii−i-1-111-1-1−i−iiiii−i−i−ii-1-111ii−i−i
χ151111-1-1-1-111111111−ii-1-1-1-1-1-1-1-1−i−i−i−iiiii11-1-1-111-1-1-1i−i−ii11-1-111ii−i−i−i−iii−ii-1-111ii−i−i
χ161111-1-1-1-111111111−ii-1-1-1-1-1-1-1-1−i−i−i−iiiii11-1-1-11-11-1-1i−ii−i-1-11111ii−i−iii−i−i−ii11-1-1−i−iii
χ172222222222222222222222222222222222-2-2-2-2000000000000000000000000-2-200000000
χ182222222222222222-2-222222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000002200000000
χ192222-2-2-2-2222222222i−2i-2-2-2-2-2-2-2-22i2i2i2i−2i−2i−2i−2i-2-222000000000000000000000000−2i2i00000000
χ202222-2-2-2-222222222−2i2i-2-2-2-2-2-2-2-2−2i−2i−2i−2i2i2i2i2i-2-2220000000000000000000000002i−2i00000000
χ212-22-22i−2i2i−2i222-2-22-2-2002i−2i2i−2i2i−2i2i−2i000000002-22i−2i000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23
χ222-22-22i−2i2i−2i222-2-22-2-2002i−2i2i−2i2i−2i2i−2i000000002-22i−2i0000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23
χ232-22-22i−2i2i−2i222-2-22-2-2002i−2i2i−2i2i−2i2i−2i00000000-22−2i2i000000000000000000000000002-22i−2i0000
χ242-22-22i−2i2i−2i222-2-22-2-2002i−2i2i−2i2i−2i2i−2i00000000-22−2i2i00000000000000000000000000-22−2i2i0000
χ252-22-2−2i2i−2i2i222-2-22-2-200−2i2i−2i2i−2i2i−2i2i000000002-2−2i2i0000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13
χ262-22-2−2i2i−2i2i222-2-22-2-200−2i2i−2i2i−2i2i−2i2i000000002-2−2i2i000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13
χ272-22-2−2i2i−2i2i222-2-22-2-200−2i2i−2i2i−2i2i−2i2i00000000-222i−2i000000000000000000000000002-2−2i2i0000
χ282-22-2−2i2i−2i2i222-2-22-2-200−2i2i−2i2i−2i2i−2i2i00000000-222i−2i00000000000000000000000000-222i−2i0000
χ29444444441-2-2-2111-24411-2-211-2-211-2-211-2-200000022000022-1-1-1-1000000-1-1-1-10000000000
χ30444444441-2-2-2111-24411-2-211-2-211-2-211-2-2000000-2-20000-2-2111100000011110000000000
χ31444444441-2-2-2111-2-4-411-2-211-2-2-1-122-1-122000000220000-2-2-1-1-1-100000011110000000000
χ32444444441-2-2-2111-2-4-411-2-211-2-2-1-122-1-122000000-2-20000221111000000-1-1-1-10000000000
χ3344444444-2111-2-2-2144-2-211-2-211-2-211-2-21100002200-1-122000000-1-1-1-1-1-100000000000000
χ3444444444-2111-2-2-2144-2-211-2-211-2-211-2-2110000-2-20011-2-200000011111100000000000000
χ3544444444-2111-2-2-21-4-4-2-211-2-21122-1-122-1-100002200-1-1-2-2000000-1-1111100000000000000
χ3644444444-2111-2-2-21-4-4-2-211-2-21122-1-122-1-10000-2-200112200000011-1-1-1-100000000000000
χ374444-4-4-4-41-2-2-2111-24i−4i-1-122-1-122ii−2i−2i−i−i2i2i0000002-200002i−2i-1-111000000−i−iii0000000000
χ384444-4-4-4-41-2-2-2111-24i−4i-1-122-1-122ii−2i−2i−i−i2i2i000000-220000−2i2i11-1-1000000ii−i−i0000000000
χ394444-4-4-4-41-2-2-2111-2−4i4i-1-122-1-122−i−i2i2iii−2i−2i0000002-20000−2i2i-1-111000000ii−i−i0000000000
χ404444-4-4-4-41-2-2-2111-2−4i4i-1-122-1-122−i−i2i2iii−2i−2i000000-2200002i−2i11-1-1000000−i−iii0000000000
χ414444-4-4-4-4-2111-2-2-214i−4i22-1-122-1-1−2i−2iii2i2i−i−i00002-200-1-12i−2i00000011−i−iii00000000000000
χ424444-4-4-4-4-2111-2-2-214i−4i22-1-122-1-1−2i−2iii2i2i−i−i0000-220011−2i2i000000-1-1ii−i−i00000000000000
χ434444-4-4-4-4-2111-2-2-21−4i4i22-1-122-1-12i2i−i−i−2i−2iii00002-200-1-1−2i2i00000011ii−i−i00000000000000
χ444444-4-4-4-4-2111-2-2-21−4i4i22-1-122-1-12i2i−i−i−2i−2iii0000-2200112i−2i000000-1-1−i−iii00000000000000
χ4544-4-444-4-41-2221-1-1-20011-2-2-1-1223-3003-300000000000000003−33−30000003−33−30000000000
χ4644-4-444-4-41-2221-1-1-20011-2-2-1-1223-3003-30000000000000000−33−33000000−33−330000000000
χ4744-4-444-4-41-2221-1-1-20011-2-2-1-122-3300-3300000000000000003−33−3000000−33−330000000000
χ4844-4-444-4-41-2221-1-1-20011-2-2-1-122-3300-330000000000000000−33−330000003−33−30000000000
χ4944-4-444-4-444-4-44-4-44004444-4-4-4-40000000000000000000000000000000000000000000000
χ5044-4-4-4-4441-2221-1-1-200-1-12211-2-23i−3i00−3i3i00000000000000003−3−33000000i3−i3−i3i30000000000
χ5144-4-4-4-4441-2221-1-1-200-1-12211-2-23i−3i00−3i3i0000000000000000−333−3000000−i3i3i3−i30000000000
χ5244-4-4-4-4441-2221-1-1-200-1-12211-2-2−3i3i003i−3i00000000000000003−3−33000000−i3i3i3−i30000000000
χ5344-4-4-4-4441-2221-1-1-200-1-12211-2-2−3i3i003i−3i0000000000000000−333−3000000i3−i3−i3i30000000000
χ5444-4-4-4-44444-4-44-4-4400-4-4-4-444440000000000000000000000000000000000000000000000
χ554-4-444i−4i−4i4i44-44-4-44-4004i−4i4i−4i−4i4i−4i4i0000000000000000000000000000000000000000000000
χ564-4-444i−4i−4i4i-21-1122-2-100−2i2ii−i2i−2i−ii003ζ7+3ζ23−3ζ7−3ζ2300−3ζ5−3ζ133ζ5+3ζ1300000000−i3i3000000003−3−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ1300000000000000
χ574-4-444i−4i−4i4i-21-1122-2-100−2i2ii−i2i−2i−ii003ζ7+3ζ23−3ζ7−3ζ2300−3ζ5−3ζ133ζ5+3ζ1300000000i3−i300000000−33ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ1300000000000000
χ584-4-444i−4i−4i4i-21-1122-2-100−2i2ii−i2i−2i−ii00−3ζ7−3ζ233ζ7+3ζ23003ζ5+3ζ13−3ζ5−3ζ1300000000−i3i3000000003−3ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ1300000000000000
χ594-4-444i−4i−4i4i-21-1122-2-100−2i2ii−i2i−2i−ii00−3ζ7−3ζ233ζ7+3ζ23003ζ5+3ζ13−3ζ5−3ζ1300000000i3−i300000000−33−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ1300000000000000
χ604-4-44−4i4i4i−4i44-44-4-44-400−4i4i−4i4i4i−4i4i−4i0000000000000000000000000000000000000000000000
χ614-4-44−4i4i4i−4i-21-1122-2-1002i−2i−ii−2i2ii−i00−3ζ5−3ζ133ζ5+3ζ13003ζ7+3ζ23−3ζ7−3ζ2300000000−i3i300000000−33−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ2300000000000000
χ624-4-44−4i4i4i−4i-21-1122-2-1002i−2i−ii−2i2ii−i00−3ζ5−3ζ133ζ5+3ζ13003ζ7+3ζ23−3ζ7−3ζ2300000000i3−i3000000003−3ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ2300000000000000
χ634-4-44−4i4i4i−4i-21-1122-2-1002i−2i−ii−2i2ii−i003ζ5+3ζ13−3ζ5−3ζ1300−3ζ7−3ζ233ζ7+3ζ2300000000−i3i300000000−33ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ2300000000000000
χ644-4-44−4i4i4i−4i-21-1122-2-1002i−2i−ii−2i2ii−i003ζ5+3ζ13−3ζ5−3ζ1300−3ζ7−3ζ233ζ7+3ζ2300000000i3−i3000000003−3−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ2300000000000000
χ6588-8-888-8-8-42-2-2-444200-4-42244-2-20000000000000000000000000000000000000000000000
χ6688-8-8-8-888-42-2-2-44420044-2-2-4-4220000000000000000000000000000000000000000000000
χ678-88-88i−8i8i−8i2-4-44-22-24002i−2i−4i4i2i−2i−4i4i0000000000000000000000000000000000000000000000
χ688-88-88i−8i8i−8i-422-24-44-200−4i4i2i−2i−4i4i2i−2i0000000000000000000000000000000000000000000000
χ698-88-8−8i8i−8i8i2-4-44-22-2400−2i2i4i−4i−2i2i4i−4i0000000000000000000000000000000000000000000000
χ708-88-8−8i8i−8i8i-422-24-44-2004i−4i−2i2i4i−4i−2i2i0000000000000000000000000000000000000000000000
χ718-8-888i−8i−8i8i2-44-4-2-224002i−2i−4i4i−2i2i4i−4i0000000000000000000000000000000000000000000000
χ728-8-88−8i8i8i−8i2-44-4-2-22400−2i2i4i−4i2i−2i−4i4i0000000000000000000000000000000000000000000000

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