Finite Group Databasebeta

← Group #11770880

Character table — Group #11770880

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size111122224444444444444444488888888888888888888888888181818181818363636363636363636727272727272
order122222443346666666666666644121212121212121212121212121212121212121212121212224444244444444448888
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
χ91111-1-11111-11111-1-1-1-111-1-1-1-1i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-111-1-111-1-1i−ii−ii−i
χ101111-1-11111-11111-1-1-1-111-1-1-1-1i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1-111-1-111i−i−ii−ii
χ111111-1-11111-11111-1-1-1-111-1-1-1-1i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1111ii−i−i−i−iii−ii-111-1
χ121111-1-11111-11111-1-1-1-111-1-1-1-1i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1111−i−iiiii−i−i−ii1-1-11
χ131111-1-11111-11111-1-1-1-111-1-1-1-1−ii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-111-1-111-1-1−ii−ii−ii
χ141111-1-11111-11111-1-1-1-111-1-1-1-1−ii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1-111-1-111−iii−ii−i
χ151111-1-11111-11111-1-1-1-111-1-1-1-1−ii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1111ii−i−i−i−iiii−i1-1-11
χ161111-1-11111-11111-1-1-1-111-1-1-1-1−ii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1111−i−iiiii−i−ii−i-111-1
χ17222222-2-222-22222222222222200-2-2-2-2-2-2-2-2000000000000000022-2-2-2-2200000000000000
χ18222222-2-222-22222222222222200-2-2-2-2-2-2-2-20000000000000000-2-22222-200000000000000
χ192222-2-2-2-22222222-2-2-2-222-2-2-2-200-2-2-2-22222000000000000000022-2-222-200000000000000
χ202222-2-2-2-22222222-2-2-2-222-2-2-2-200-2-2-2-222220000000000000000-2-222-2-2200000000000000
χ2122-2-22-20022022-2-2-2-2-2-2-2-2222200000000000000000000000000002i−2i2i−2i01+i−1−i1+i−1−i1−i−1+i1−i−1+i000000
χ2222-2-22-20022022-2-2-2-2-2-2-2-2222200000000000000000000000000002i−2i2i−2i0−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000
χ2322-2-22-20022022-2-2-2-2-2-2-2-222220000000000000000000000000000−2i2i−2i2i01−i−1+i1−i−1+i1+i−1−i1+i−1−i000000
χ2422-2-22-20022022-2-2-2-2-2-2-2-222220000000000000000000000000000−2i2i−2i2i0−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000
χ2522-2-2-220022022-2-22222-2-2-2-2-2-200000000000000000000000000002i−2i−2i2i01+i−1−i−1−i1+i1−i−1+i−1+i1−i000000
χ2622-2-2-220022022-2-22222-2-2-2-2-2-200000000000000000000000000002i−2i−2i2i0−1−i1+i1+i−1−i−1+i1−i1−i−1+i000000
χ2722-2-2-220022022-2-22222-2-2-2-2-2-20000000000000000000000000000−2i2i2i−2i01−i−1+i−1+i1−i1+i−1−i−1−i1+i000000
χ2822-2-2-220022022-2-22222-2-2-2-2-2-20000000000000000000000000000−2i2i2i−2i0−1+i1−i1−i−1+i−1−i1+i1+i−1−i000000
χ29444444441-241-21-211-2-21-211-2-24411-2-211-2-21111-2-2-2-21111-2-2-2-2000000000000000000000
χ30444444441-241-21-211-2-21-211-2-2-4-411-2-211-2-2-1-1-1-12222-1-1-1-12222000000000000000000000
χ3144444444-214-21-21-2-211-21-2-21144-2-211-2-211-2-2-2-21111-2-2-2-21111000000000000000000000
χ3244444444-214-21-21-2-211-21-2-211-4-4-2-211-2-2112222-1-1-1-12222-1-1-1-1000000000000000000000
χ33444444-4-41-2-41-21-211-2-21-211-2-200-1-122-1-12233-3-3000033-3-30000000000000000000000000
χ34444444-4-41-2-41-21-211-2-21-211-2-200-1-122-1-122-3-3330000-3-3330000000000000000000000000
χ35444444-4-4-21-4-21-21-2-211-21-2-2110022-1-122-1-1000033-3-3000033-3-3000000000000000000000
χ36444444-4-4-21-4-21-21-2-211-21-2-2110022-1-122-1-10000-3-3330000-3-333000000000000000000000
χ374444-4-4441-2-41-21-2-1-1221-2-1-1224i−4i11-2-2-1-122iiii−2i−2i−2i−2i−i−i−i−i2i2i2i2i000000000000000000000
χ384444-4-4441-2-41-21-2-1-1221-2-1-122−4i4i11-2-2-1-122−i−i−i−i2i2i2i2iiiii−2i−2i−2i−2i000000000000000000000
χ394444-4-444-21-4-21-2122-1-1-2122-1-14i−4i-2-21122-1-1−2i−2i−2i−2iiiii2i2i2i2i−i−i−i−i000000000000000000000
χ404444-4-444-21-4-21-2122-1-1-2122-1-1−4i4i-2-21122-1-12i2i2i2i−i−i−i−i−2i−2i−2i−2iiiii000000000000000000000
χ414444-4-4-4-41-241-21-2-1-1221-2-1-12200-1-12211-2-23i3i−3i−3i0000−3i−3i3i3i0000000000000000000000000
χ424444-4-4-4-41-241-21-2-1-1221-2-1-12200-1-12211-2-2−3i−3i3i3i00003i3i−3i−3i0000000000000000000000000
χ434444-4-4-4-4-214-21-2122-1-1-2122-1-10022-1-1-2-21100003i3i−3i−3i0000−3i−3i3i3i000000000000000000000
χ444444-4-4-4-4-214-21-2122-1-1-2122-1-10022-1-1-2-2110000−3i−3i3i3i00003i3i−3i−3i000000000000000000000
χ454-44-4004i−4i1-20-121-23-300-123-30000i−i2i−2i3i−3i00−i3i33−3−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−i3i33−3−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11000000000000000000000
χ464-44-4004i−4i1-20-121-23-300-123-30000i−i2i−2i3i−3i00i3−i3−33ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11i3−i3−33ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11000000000000000000000
χ474-44-4004i−4i1-20-121-2-3300-12-330000i−i2i−2i−3i3i003−3i3−i3ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−33−i3i3ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11000000000000000000000
χ484-44-4004i−4i1-20-121-2-3300-12-330000i−i2i−2i−3i3i00−33−i3i3−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ113−3i3−i3−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11000000000000000000000
χ494-44-4004i−4i440-4-4440000-4-40000004i−4i−4i4i00000000000000000000000000000000000000000
χ504-44-4004i−4i-2102-1-21003-32-1003-300−2i2i−ii003i−3i−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11−33i3−i3−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ113−3i3−i3000000000000000000000
χ514-44-4004i−4i-2102-1-21003-32-1003-300−2i2i−ii003i−3iζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ113−3−i3i3ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11−33−i3i3000000000000000000000
χ524-44-4004i−4i-2102-1-2100-332-100-3300−2i2i−ii00−3i3i−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11i3−i33−3−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11i3−i3−33000000000000000000000
χ534-44-4004i−4i-2102-1-2100-332-100-3300−2i2i−ii00−3i3iζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11−i3i3−33ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−i3i33−3000000000000000000000
χ544-44-400−4i4i1-20-121-23-300-123-30000−ii−2i2i−3i3i00−i3i3−33−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−i3i3−33−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11000000000000000000000
χ554-44-400−4i4i1-20-121-23-300-123-30000−ii−2i2i−3i3i00i3−i33−3ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11i3−i33−3ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11000000000000000000000
χ564-44-400−4i4i1-20-121-2-3300-12-330000−ii−2i2i3i−3i003−3−i3i3−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11−33i3−i3−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11000000000000000000000
χ574-44-400−4i4i1-20-121-2-3300-12-330000−ii−2i2i3i−3i00−33i3−i3ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ113−3−i3i3ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11000000000000000000000
χ584-44-400−4i4i440-4-4440000-4-4000000−4i4i4i−4i00000000000000000000000000000000000000000
χ594-44-400−4i4i-2102-1-21003-32-1003-3002i−2ii−i00−3i3i−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ113−3i3−i3−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−33i3−i3000000000000000000000
χ604-44-400−4i4i-2102-1-21003-32-1003-3002i−2ii−i00−3i3iζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−33−i3i3ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ113−3−i3i3000000000000000000000
χ614-44-400−4i4i-2102-1-2100-332-100-33002i−2ii−i003i−3i−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11i3−i3−33−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11i3−i33−3000000000000000000000
χ624-44-400−4i4i-2102-1-2100-332-100-33002i−2ii−i003i−3iζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11−i3i33−3ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−i3i3−33000000000000000000000
χ634-4-440000440-4-4-4-40000440000000000000000000000000000004-40000000000000000000
χ644-4-440000440-4-4-4-4000044000000000000000000000000000000-440000000000000000000
χ6588-8-88-8002-402-4-24-2-244-2422-4-400000000000000000000000000000000000000000000000
χ6688-8-88-800-420-424-244-2-24-2-4-42200000000000000000000000000000000000000000000000
χ6788-8-8-88002-402-4-2422-4-4-24-2-24400000000000000000000000000000000000000000000000
χ6888-8-8-8800-420-424-2-4-4224-244-2-200000000000000000000000000000000000000000000000
χ698-8-8800002-40-24-246-6002-4-660000000000000000000000000000000000000000000000000
χ708-8-8800002-40-24-24-66002-46-60000000000000000000000000000000000000000000000000
χ718-8-880000-4204-24-2006-6-4200-6600000000000000000000000000000000000000000000000
χ728-8-880000-4204-24-200-66-42006-600000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.