Finite Group Databasebeta

← Group #11777943

Character table — Group #11777943

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11111111444444444444444444888888881818181824242424242424242424242424242424242424242424242436363636363636363636
order12224444336666668812121212121212122424242424242424444444448888121212121212121224242424242424248888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-111-1-111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1
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
χ51111111111111111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111
χ81111111111111111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1
χ91111-1-1-1-111111111i−i-1-1-1-1-1-1-1-1ii−i−iii−i−i11-1-11-11-1i−ii−i11-1-111-1-1ii−i−iii−i−ii−i11-1-1ii−i−i
χ101111-1-1-1-111111111i−i-1-1-1-1-1-1-1-1ii−i−iii−i−i11-1-11-1-11i−i−ii11-1-1-1-111−i−iiiii−i−ii−i-1-111−i−iii
χ111111-1-1-1-111111111i−i-1-1-1-1-1-1-1-1ii−i−iii−i−i11-1-1-111-1−iii−i-1-11111-1-1ii−i−i−i−iiii−i-1-111−i−iii
χ121111-1-1-1-111111111i−i-1-1-1-1-1-1-1-1ii−i−iii−i−i11-1-1-11-11−ii−ii-1-111-1-111−i−iii−i−iiii−i11-1-1ii−i−i
χ131111-1-1-1-111111111−ii-1-1-1-1-1-1-1-1−i−iii−i−iii11-1-11-11-1−ii−ii11-1-111-1-1−i−iii−i−iii−ii11-1-1−i−iii
χ141111-1-1-1-111111111−ii-1-1-1-1-1-1-1-1−i−iii−i−iii11-1-11-1-11−iii−i11-1-1-1-111ii−i−i−i−iii−ii-1-111ii−i−i
χ151111-1-1-1-111111111−ii-1-1-1-1-1-1-1-1−i−iii−i−iii11-1-1-111-1i−i−ii-1-11111-1-1−i−iiiii−i−i−ii-1-111ii−i−i
χ161111-1-1-1-111111111−ii-1-1-1-1-1-1-1-1−i−iii−i−iii11-1-1-11-11i−ii−i-1-111-1-111ii−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-2-2-2-2-2-2-2-22i2i−2i−2i2i2i−2i−2i-2-222000000000000000000000000−2i2i00000000
χ202222-2-2-2-222222222−2i2i-2-2-2-2-2-2-2-2−2i−2i2i2i−2i−2i2i2i-2-2220000000000000000000000002i−2i00000000
χ212-22-22i−2i2i−2i22-2-222-2-2002i−2i2i−2i2i−2i2i−2i000000002-22i−2i000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23
χ222-22-22i−2i2i−2i22-2-222-2-2002i−2i2i−2i2i−2i2i−2i000000002-22i−2i0000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23
χ232-22-22i−2i2i−2i22-2-222-2-2002i−2i2i−2i2i−2i2i−2i00000000-22−2i2i000000000000000000000000002-22i−2i0000
χ242-22-22i−2i2i−2i22-2-222-2-2002i−2i2i−2i2i−2i2i−2i00000000-22−2i2i00000000000000000000000000-22−2i2i0000
χ252-22-2−2i2i−2i2i22-2-222-2-200−2i2i−2i2i−2i2i−2i2i000000002-2−2i2i0000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13
χ262-22-2−2i2i−2i2i22-2-222-2-200−2i2i−2i2i−2i2i−2i2i000000002-2−2i2i000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13
χ272-22-2−2i2i−2i2i22-2-222-2-200−2i2i−2i2i−2i2i−2i2i00000000-222i−2i000000000000000000000000002-2−2i2i0000
χ282-22-2−2i2i−2i2i22-2-222-2-200−2i2i−2i2i−2i2i−2i2i00000000-222i−2i00000000000000000000000000-222i−2i0000
χ29444444441-21-21-21-24411-2-2-2-211-2-2-2-21111000022002200-1-1-1-100000000-1-1-1-10000000000
χ30444444441-21-21-21-24411-2-2-2-211-2-2-2-211110000-2-200-2-20011110000000011110000000000
χ31444444441-21-21-21-2-4-411-2-2-2-2112222-1-1-1-100002200-2-200-1-1-1-10000000011110000000000
χ32444444441-21-21-21-2-4-411-2-2-2-2112222-1-1-1-10000-2-2002200111100000000-1-1-1-10000000000
χ3344444444-21-21-21-2144-2-21111-2-21111-2-2-2-20000002200220000-1-1-1-1-1-1-1-100000000000000
χ3444444444-21-21-21-2144-2-21111-2-21111-2-2-2-2000000-2-200-2-200001111111100000000000000
χ3544444444-21-21-21-21-4-4-2-21111-2-2-1-1-1-122220000002200-2-20000-1-1-1-1111100000000000000
χ3644444444-21-21-21-21-4-4-2-21111-2-2-1-1-1-12222000000-2-2002200001111-1-1-1-100000000000000
χ374444-4-4-4-41-21-21-21-24i−4i-1-12222-1-1−2i−2i2i2iii−i−i00002-2002i−2i00-1-11100000000−i−iii0000000000
χ384444-4-4-4-41-21-21-21-24i−4i-1-12222-1-1−2i−2i2i2iii−i−i0000-2200−2i2i0011-1-100000000ii−i−i0000000000
χ394444-4-4-4-41-21-21-21-2−4i4i-1-12222-1-12i2i−2i−2i−i−iii00002-200−2i2i00-1-11100000000ii−i−i0000000000
χ404444-4-4-4-41-21-21-21-2−4i4i-1-12222-1-12i2i−2i−2i−i−iii0000-22002i−2i0011-1-100000000−i−iii0000000000
χ414444-4-4-4-4-21-21-21-214i−4i22-1-1-1-122ii−i−i−2i−2i2i2i0000002-2002i−2i0000-1-111−i−iii00000000000000
χ424444-4-4-4-4-21-21-21-214i−4i22-1-1-1-122ii−i−i−2i−2i2i2i000000-2200−2i2i000011-1-1ii−i−i00000000000000
χ434444-4-4-4-4-21-21-21-21−4i4i22-1-1-1-122−i−iii2i2i−2i−2i0000002-200−2i2i0000-1-111ii−i−i00000000000000
χ444444-4-4-4-4-21-21-21-21−4i4i22-1-1-1-122−i−iii2i2i−2i−2i000000-22002i−2i000011-1-1−i−iii00000000000000
χ4544-4-444-4-44444-4-4-4-400-4-444-4-4440000000000000000000000000000000000000000000000
χ4644-4-444-4-4-21-212-12-1002211-1-1-2-23-33-3000000000000000000003−33−33−33−300000000000000
χ4744-4-444-4-4-21-212-12-1002211-1-1-2-23-33-300000000000000000000−33−33−33−3300000000000000
χ4844-4-444-4-4-21-212-12-1002211-1-1-2-2-33-33000000000000000000003−33−3−33−3300000000000000
χ4944-4-444-4-4-21-212-12-1002211-1-1-2-2-33-3300000000000000000000−33−333−33−300000000000000
χ5044-4-4-4-4444444-4-4-4-40044-4-444-4-40000000000000000000000000000000000000000000000
χ5144-4-4-4-444-21-212-12-100-2-2-1-111223i−3i−3i3i000000000000000000003−3−33i3−i3−i3i300000000000000
χ5244-4-4-4-444-21-212-12-100-2-2-1-111223i−3i−3i3i00000000000000000000−333−3−i3i3i3−i300000000000000
χ5344-4-4-4-444-21-212-12-100-2-2-1-11122−3i3i3i−3i000000000000000000003−3−33−i3i3i3−i300000000000000
χ5444-4-4-4-444-21-212-12-100-2-2-1-11122−3i3i3i−3i00000000000000000000−333−3i3−i3−i3i300000000000000
χ554-4-444i−4i−4i4i1-2-12-121-200−ii−2i2i2i−2ii−i00003ζ7+3ζ23−3ζ7−3ζ23−3ζ5−3ζ133ζ5+3ζ130000000000003−3−i3i300000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000000000
χ564-4-444i−4i−4i4i1-2-12-121-200−ii−2i2i2i−2ii−i00003ζ7+3ζ23−3ζ7−3ζ23−3ζ5−3ζ133ζ5+3ζ13000000000000−33i3−i300000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000000000
χ574-4-444i−4i−4i4i1-2-12-121-200−ii−2i2i2i−2ii−i0000−3ζ7−3ζ233ζ7+3ζ233ζ5+3ζ13−3ζ5−3ζ130000000000003−3−i3i300000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000000000
χ584-4-444i−4i−4i4i1-2-12-121-200−ii−2i2i2i−2ii−i0000−3ζ7−3ζ233ζ7+3ζ233ζ5+3ζ13−3ζ5−3ζ13000000000000−33i3−i300000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000000000
χ594-4-444i−4i−4i4i44-4-4-4-44400−4i4i4i−4i−4i4i4i−4i0000000000000000000000000000000000000000000000
χ604-4-44−4i4i4i−4i1-2-12-121-200i−i2i−2i−2i2i−ii0000−3ζ5−3ζ133ζ5+3ζ133ζ7+3ζ23−3ζ7−3ζ230000000000003−3i3−i300000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000000000
χ614-4-44−4i4i4i−4i1-2-12-121-200i−i2i−2i−2i2i−ii0000−3ζ5−3ζ133ζ5+3ζ133ζ7+3ζ23−3ζ7−3ζ23000000000000−33−i3i300000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000000000
χ624-4-44−4i4i4i−4i1-2-12-121-200i−i2i−2i−2i2i−ii00003ζ5+3ζ13−3ζ5−3ζ13−3ζ7−3ζ233ζ7+3ζ230000000000003−3i3−i300000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000000000
χ634-4-44−4i4i4i−4i1-2-12-121-200i−i2i−2i−2i2i−ii00003ζ5+3ζ13−3ζ5−3ζ13−3ζ7−3ζ233ζ7+3ζ23000000000000−33−i3i300000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000000000
χ644-4-44−4i4i4i−4i44-4-4-4-444004i−4i−4i4i4i−4i−4i4i0000000000000000000000000000000000000000000000
χ6588-8-888-8-82-42-4-24-2400-2-2-4-444220000000000000000000000000000000000000000000000
χ6688-8-8-8-8882-42-4-24-24002244-4-4-2-20000000000000000000000000000000000000000000000
χ678-88-88i−8i8i−8i2-4-242-4-24002i−2i−4i4i−4i4i2i−2i0000000000000000000000000000000000000000000000
χ688-88-88i−8i8i−8i-424-2-424-200−4i4i2i−2i2i−2i−4i4i0000000000000000000000000000000000000000000000
χ698-88-8−8i8i−8i8i2-4-242-4-2400−2i2i4i−4i4i−4i−2i2i0000000000000000000000000000000000000000000000
χ708-88-8−8i8i−8i8i-424-2-424-2004i−4i−2i2i−2i2i4i−4i0000000000000000000000000000000000000000000000
χ718-8-888i−8i−8i8i-424-24-2-42004i−4i2i−2i−2i2i−4i4i0000000000000000000000000000000000000000000000
χ728-8-88−8i8i8i−8i-424-24-2-4200−4i4i−2i2i2i−2i4i−4i0000000000000000000000000000000000000000000000

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