Finite Group Databasebeta

← Group #11771004

Character table — Group #11771004

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size111122224444444444444444488888888888888888888888888181818181818363636363636363636727272727272
order12224444334666666121212121212121288121212121212121224242424242424242424242424242424444444288888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1
χ3111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1iiii−i−i−i−i-1-1ii−i−i
χ4111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1−i−i−i−iiiii-1-1−i−iii
χ51111111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1
χ61111111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i11−i−iii
χ81111111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii11ii−i−i
χ9111111-1-111-1111111-1-1-1-1-1-1-1-1i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-111-1-111-1-1i−ii−ii−i
χ10111111-1-111-1111111-1-1-1-1-1-1-1-1i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1-111-1-111i−i−ii−ii
χ11111111-1-111-1111111-1-1-1-1-1-1-1-1i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1111ii−i−i−i−iii−ii-111-1
χ12111111-1-111-1111111-1-1-1-1-1-1-1-1i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1111−i−iiiii−i−i−ii1-1-11
χ13111111-1-111-1111111-1-1-1-1-1-1-1-1−ii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-111-1-111-1-1−ii−ii−ii
χ14111111-1-111-1111111-1-1-1-1-1-1-1-1−ii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1-111-1-111−iii−ii−i
χ15111111-1-111-1111111-1-1-1-1-1-1-1-1−ii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1111ii−i−i−i−iiii−i1-1-11
χ16111111-1-111-1111111-1-1-1-1-1-1-1-1−ii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1111−i−iiiii−i−ii−i-111-1
χ172222-2-22222-22222222222222200-2-2-2-2-2-2-2-2000000000000000022-2-222-200000000000000
χ182222-2-22222-22222222222222200-2-2-2-2-2-2-2-20000000000000000-2-222-2-2200000000000000
χ192222-2-2-2-2222222222-2-2-2-2-2-2-2-200-2-2-2-22222000000000000000022-2-2-2-2200000000000000
χ202222-2-2-2-2222222222-2-2-2-2-2-2-2-200-2-2-2-222220000000000000000-2-22222-200000000000000
χ2122-2-2002-222022-2-2-2-2-2-2-2-22222000000000000000000000000002i−2i002i−2i01+i−1−i1+i−1−i1−i−1+i1−i−1+i000000
χ2222-2-2002-222022-2-2-2-2-2-2-2-22222000000000000000000000000002i−2i002i−2i0−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000
χ2322-2-2002-222022-2-2-2-2-2-2-2-2222200000000000000000000000000−2i2i00−2i2i01−i−1+i1−i−1+i1+i−1−i1+i−1−i000000
χ2422-2-2002-222022-2-2-2-2-2-2-2-2222200000000000000000000000000−2i2i00−2i2i0−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000
χ2522-2-200-2222022-2-2-2-22222-2-2-2-2000000000000000000000000002i−2i00−2i2i01+i−1−i−1−i1+i1−i−1+i−1+i1−i000000
χ2622-2-200-2222022-2-2-2-22222-2-2-2-2000000000000000000000000002i−2i00−2i2i0−1−i1+i1+i−1−i−1+i1−i1−i−1+i000000
χ2722-2-200-2222022-2-2-2-22222-2-2-2-200000000000000000000000000−2i2i002i−2i01−i−1+i−1+i1−i1+i−1−i−1−i1+i000000
χ2822-2-200-2222022-2-2-2-22222-2-2-2-200000000000000000000000000−2i2i002i−2i0−1+i1−i1−i−1+i−1−i1+i1+i−1−i000000
χ29444444441-241-211-2-211-2-211-2-24411-2-211-2-21111-2-2-2-21111-2-2-2-2000000000000000000000
χ30444444441-241-211-2-211-2-211-2-2-4-411-2-211-2-2-1-1-1-12222-1-1-1-12222000000000000000000000
χ3144444444-214-21-2-211-2-211-2-21144-2-211-2-211-2-2-2-21111-2-2-2-21111000000000000000000000
χ3244444444-214-21-2-211-2-211-2-211-4-4-2-211-2-2112222-1-1-1-12222-1-1-1-1000000000000000000000
χ33444444-4-41-2-41-211-2-2-1-122-1-1224i−4i11-2-2-1-122iiii−2i−2i−2i−2i−i−i−i−i2i2i2i2i000000000000000000000
χ34444444-4-41-2-41-211-2-2-1-122-1-122−4i4i11-2-2-1-122−i−i−i−i2i2i2i2iiiii−2i−2i−2i−2i000000000000000000000
χ35444444-4-4-21-4-21-2-21122-1-122-1-14i−4i-2-21122-1-1−2i−2i−2i−2iiiii2i2i2i2i−i−i−i−i000000000000000000000
χ36444444-4-4-21-4-21-2-21122-1-122-1-1−4i4i-2-21122-1-12i2i2i2i−i−i−i−i−2i−2i−2i−2iiiii000000000000000000000
χ374444-4-4441-2-41-211-2-211-2-211-2-200-1-122-1-12233-3-3000033-3-30000000000000000000000000
χ384444-4-4441-2-41-211-2-211-2-211-2-200-1-122-1-122-3-3330000-3-3330000000000000000000000000
χ394444-4-444-21-4-21-2-211-2-211-2-2110022-1-122-1-1000033-3-3000033-3-3000000000000000000000
χ404444-4-444-21-4-21-2-211-2-211-2-2110022-1-122-1-10000-3-3330000-3-333000000000000000000000
χ414444-4-4-4-41-241-211-2-2-1-122-1-12200-1-12211-2-23i3i−3i−3i0000−3i−3i3i3i0000000000000000000000000
χ424444-4-4-4-41-241-211-2-2-1-122-1-12200-1-12211-2-2−3i−3i3i3i00003i3i−3i−3i0000000000000000000000000
χ434444-4-4-4-4-214-21-2-21122-1-122-1-10022-1-1-2-21100003i3i−3i−3i0000−3i−3i3i3i000000000000000000000
χ444444-4-4-4-4-214-21-2-21122-1-122-1-10022-1-1-2-2110000−3i−3i3i3i00003i3i−3i−3i000000000000000000000
χ454-44-40000440-4-44-44-40000000000000000000000000000000000004i−4i00000000000000000
χ464-44-40000440-4-44-44-4000000000000000000000000000000000000−4i4i00000000000000000
χ474-4-444i−4i001-20-12-112-23i−3i003i−3i0000i−i2i−2i3-300ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ236−6i6−i6−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ136−6i6−i6000000000000000000000
χ484-4-444i−4i001-20-12-112-23i−3i003i−3i0000i−i2i−2i3-300−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−66−i6i6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−66−i6i6000000000000000000000
χ494-4-444i−4i001-20-12-112-2−3i3i00−3i3i0000i−i2i−2i-3300−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13−i6i66−6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23i6−i6−66000000000000000000000
χ504-4-444i−4i001-20-12-112-2−3i3i00−3i3i0000i−i2i−2i-3300ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13i6−i6−66−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23−i6i66−6000000000000000000000
χ514-4-444i−4i00440-4-4-44-4400000000004i−4i−4i4i00000000000000000000000000000000000000000
χ524-4-444i−4i00-2102-12-2-11003i−3i003i−3i00−2i2i−ii003-36−6−i6i6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ136−6i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23000000000000000000000
χ534-4-444i−4i00-2102-12-2-11003i−3i003i−3i00−2i2i−ii003-3−66i6−i6−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−66−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23000000000000000000000
χ544-4-444i−4i00-2102-12-2-1100−3i3i00−3i3i00−2i2i−ii00-33i6−i66−6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23−i6i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000000000000000000
χ554-4-444i−4i00-2102-12-2-1100−3i3i00−3i3i00−2i2i−ii00-33−i6i6−66ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23i6−i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000000000000000000
χ564-4-44−4i4i001-20-12-112-23i−3i003i−3i0000−ii−2i2i-3300ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23i6−i66−6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13−i6i6−66000000000000000000000
χ574-4-44−4i4i001-20-12-112-23i−3i003i−3i0000−ii−2i2i-3300−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23−i6i6−66ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13i6−i66−6000000000000000000000
χ584-4-44−4i4i001-20-12-112-2−3i3i00−3i3i0000−ii−2i2i3-300−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ136−6−i6i6ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ236−6−i6i6000000000000000000000
χ594-4-44−4i4i001-20-12-112-2−3i3i00−3i3i0000−ii−2i2i3-300ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−66i6−i6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−66i6−i6000000000000000000000
χ604-4-44−4i4i00440-4-4-44-440000000000−4i4i4i−4i00000000000000000000000000000000000000000
χ614-4-44−4i4i00-2102-12-2-11003i−3i003i−3i002i−2ii−i00-33i6−i6−66−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13−i6i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000000000000000000
χ624-4-44−4i4i00-2102-12-2-11003i−3i003i−3i002i−2ii−i00-33−i6i66−6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13i6−i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000000000000000000
χ634-4-44−4i4i00-2102-12-2-1100−3i3i00−3i3i002i−2ii−i003-36−6i6−i6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ236−6−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13000000000000000000000
χ644-4-44−4i4i00-2102-12-2-1100−3i3i00−3i3i002i−2ii−i003-3−66−i6i6ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−66i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13000000000000000000000
χ6588-8-8008-82-402-4-2-244-2-24422-4-400000000000000000000000000000000000000000000000
χ6688-8-8008-8-420-4244-2-244-2-2-4-42200000000000000000000000000000000000000000000000
χ6788-8-800-882-402-4-2-24422-4-4-2-24400000000000000000000000000000000000000000000000
χ6888-8-800-88-420-4244-2-2-4-42244-2-200000000000000000000000000000000000000000000000
χ698-88-800002-40-242-2-446i−6i00−6i6i0000000000000000000000000000000000000000000000000
χ708-88-800002-40-242-2-44−6i6i006i−6i0000000000000000000000000000000000000000000000000
χ718-88-80000-4204-2-442-2006i−6i00−6i6i00000000000000000000000000000000000000000000000
χ728-88-80000-4204-2-442-200−6i6i006i−6i00000000000000000000000000000000000000000000000

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