Finite Group Databasebeta

← Group #11770960

Character table — Group #11770960

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size111122224444444444444444488888888888888888888888888181818181818363636363636363636727272727272
order12224444334666666121212121212121288121212121212121224242424242424242424242424242424224444488888888444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111
χ3111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1iiii−i−i−i−iii−i−i-1-1
χ4111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1−i−i−i−iiiii−i−iii-1-1
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
χ61111111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1
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−i−i−iii11
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−iiiiiii−i−i11
χ9111111-1-111-1111111-1-1-1-1-1-1-1-1i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-1-1-11ii−i−iii−i−i1-11-1i−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−i11-1-1-1-11−i−iii−i−iii-11-11i−i
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-1-11111-111-1-1-1-111−iii−i−ii
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-1-11111-1-1-11111-1-1i−i−ii−ii
χ13111111-1-111-1111111-1-1-1-1-1-1-1-1−ii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-1-1-11ii−i−iii−i−i-11-11−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−iiiiiiiii11-1-1-1-11−i−iii−i−iii1-11-1−ii
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-1-11111-111-1-1-1-111i−i−iii−i
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-1-11111-1-1-11111-1-1−iii−ii−i
χ172222-2-22222-22222222222222200-2-2-2-2-2-2-2-200000000000000002222-2-2-200000000000000
χ182222-2-22222-22222222222222200-2-2-2-2-2-2-2-20000000000000000-2-2-2-222200000000000000
χ192222-2-2-2-2222222222-2-2-2-2-2-2-2-200-2-2-2-22222000000000000000022-2-222-200000000000000
χ202222-2-2-2-2222222222-2-2-2-2-2-2-2-200-2-2-2-222220000000000000000-2-222-2-2200000000000000
χ2122-2-2002i−2i22022-2-2-2-22i2i2i2i−2i−2i−2i−2i000000000000000000000000002-22i−2i0001+i−1−i1−i−1+i1+i−1−i1−i−1+i000000
χ2222-2-2002i−2i22022-2-2-2-22i2i2i2i−2i−2i−2i−2i000000000000000000000000002-22i−2i000−1−i1+i−1+i1−i−1−i1+i−1+i1−i000000
χ2322-2-2002i−2i22022-2-2-2-22i2i2i2i−2i−2i−2i−2i00000000000000000000000000-22−2i2i0001−i−1+i−1−i1+i−1+i1−i1+i−1−i000000
χ2422-2-2002i−2i22022-2-2-2-22i2i2i2i−2i−2i−2i−2i00000000000000000000000000-22−2i2i000−1+i1−i1+i−1−i1−i−1+i−1−i1+i000000
χ2522-2-200−2i2i22022-2-2-2-2−2i−2i−2i−2i2i2i2i2i000000000000000000000000002-2−2i2i0001−i−1+i1+i−1−i1−i−1+i1+i−1−i000000
χ2622-2-200−2i2i22022-2-2-2-2−2i−2i−2i−2i2i2i2i2i000000000000000000000000002-2−2i2i000−1+i1−i−1−i1+i−1+i1−i−1−i1+i000000
χ2722-2-200−2i2i22022-2-2-2-2−2i−2i−2i−2i2i2i2i2i00000000000000000000000000-222i−2i0001+i−1−i−1+i1−i−1−i1+i1−i−1+i000000
χ2822-2-200−2i2i22022-2-2-2-2−2i−2i−2i−2i2i2i2i2i00000000000000000000000000-222i−2i000−1−i1+i1−i−1+i1+i−1−i−1+i1−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
χ454-44-40000440-4-44-44-4000000000000000000000000000000000000004i−4i000000000000000
χ464-44-40000440-4-44-44-400000000000000000000000000000000000000−4i4i000000000000000
χ474-4-444i−4i001-20-12-112-23-3003-30000i−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
χ484-4-444i−4i001-20-12-112-23-3003-30000i−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
χ494-4-444i−4i001-20-12-112-2-3300-330000i−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
χ504-4-444i−4i001-20-12-112-2-3300-330000i−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
χ514-4-444i−4i00440-4-4-44-4400000000004i−4i−4i4i00000000000000000000000000000000000000000
χ524-4-444i−4i00-2102-12-2-11003-3003-300−2i2i−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
χ534-4-444i−4i00-2102-12-2-11003-3003-300−2i2i−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
χ544-4-444i−4i00-2102-12-2-1100-3300-3300−2i2i−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
χ554-4-444i−4i00-2102-12-2-1100-3300-3300−2i2i−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
χ564-4-44−4i4i001-20-12-112-23-3003-30000−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
χ574-4-44−4i4i001-20-12-112-23-3003-30000−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
χ584-4-44−4i4i001-20-12-112-2-3300-330000−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
χ594-4-44−4i4i001-20-12-112-2-3300-330000−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
χ604-4-44−4i4i00440-4-4-44-440000000000−4i4i4i−4i00000000000000000000000000000000000000000
χ614-4-44−4i4i00-2102-12-2-11003-3003-3002i−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
χ624-4-44−4i4i00-2102-12-2-11003-3003-3002i−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
χ634-4-44−4i4i00-2102-12-2-1100-3300-33002i−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
χ644-4-44−4i4i00-2102-12-2-1100-3300-33002i−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
χ6588-8-8008i−8i2-402-4-2-2442i2i−4i−4i−2i−2i4i4i00000000000000000000000000000000000000000000000
χ6688-8-8008i−8i-420-4244-2-2−4i−4i2i2i4i4i−2i−2i00000000000000000000000000000000000000000000000
χ6788-8-800−8i8i2-402-4-2-244−2i−2i4i4i2i2i−4i−4i00000000000000000000000000000000000000000000000
χ6888-8-800−8i8i-420-4244-2-24i4i−2i−2i−4i−4i2i2i00000000000000000000000000000000000000000000000
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 12 (ζ12 = 1); i = ζ3.