Finite Group Databasebeta

← Group #11776369

Character table — Group #11776369

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size11112222444444444444488888888881818181818182424242424242424242424242424242436363636363636363648484848
order12224444334666666121212121212121212121212121222444444448888242424242424242448888888812121212
χ1111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111
χ31111111111111111111111111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1
χ511111-1-1111-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-111111-1-1-1-111-1-1
χ611111-1-1111-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111111-1-1-1-1111111-1-1
χ711111-1-1111-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1-1-11-1-1-1-11111-1-111
χ811111-1-1111-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-1111111111-1-1-1-1-1-111
χ91111-111-111-1111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-11-11-1i−ii−iii−i−iii−i−i1ii−i−iii−i−i1-11-1
χ101111-111-111-1111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-11-11-1−ii−ii−i−iii−i−iii1−i−iii−i−iii1-11-1
χ111111-111-111-1111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-11-11i−ii−iii−i−iii−i−i1−i−iii−i−iii-11-11
χ121111-111-111-1111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-11-11−ii−ii−i−iii−i−iii1ii−i−iii−i−i-11-11
χ131111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11-1-11i−i−iiii−i−i−i−iii1ii−i−i−i−iii1-1-11
χ141111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11-1-11−iii−i−i−iiiii−i−i1−i−iiiii−i−i1-1-11
χ151111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-111-1i−i−iiii−i−i−i−iii1−i−iiiii−i−i-111-1
χ161111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-111-1−iii−i−i−iiiii−i−i1ii−i−i−i−iii-111-1
χ172222222222222222222222222222222-2-2-2-2-2-20000000000000000-2000000000000
χ1822222-2-2222-2222222222222-2-2-2-2-2-2-2-22222-2-20000000000000000-2000000000000
χ192222-222-222-2222222-2-2-2-2-2-222-2-2-2-222-2-222220000000000000000-2000000000000
χ202222-2-2-2-2222222222-2-2-2-2-2-2-2-22222-2-222-2-2220000000000000000-2000000000000
χ2122-2-2200-222022-2-2-2-222-2-22-2000000002-22-200000000000000000002−22−22−22−20000
χ2222-2-2200-222022-2-2-2-222-2-22-2000000002-22-20000000000000000000−22−22−22−220000
χ2322-2-2200-222022-2-2-2-222-2-22-200000000-22-2200000000000000000002−22−2−22−220000
χ2422-2-2200-222022-2-2-2-222-2-22-200000000-22-220000000000000000000−22−222−22−20000
χ2522-2-2-200222022-2-2-2-2-2-222-22000000002-2-220000000000000000000−i2i2i2−i2−i2i2i2−i20000
χ2622-2-2-200222022-2-2-2-2-2-222-22000000002-2-220000000000000000000i2−i2−i2i2i2−i2−i2i20000
χ2722-2-2-200222022-2-2-2-2-2-222-2200000000-222-20000000000000000000−i2i2i2−i2i2−i2−i2i20000
χ2822-2-2-200222022-2-2-2-2-2-222-2200000000-222-20000000000000000000i2−i2−i2i2−i2i2i2−i20000
χ29444444441-241-211-2-21111-2-21111-2-2-2-200000000002222-1-1-1-1-1-1-1-10000000000000
χ30444444441-241-211-2-21111-2-21111-2-2-2-20000000000-2-2-2-2111111110000000000000
χ3144444444-214-21-2-211-2-2-2-211-2-2-2-211110000002222000000000000000000000-1-1-1-1
χ3244444444-214-21-2-211-2-2-2-211-2-2-2-21111000000-2-2-2-20000000000000000000001111
χ3344444-4-441-2-41-211-2-21111-2-2-1-1-1-12222000000000022-2-2-1-1-1-111110000000000000
χ3444444-4-441-2-41-211-2-21111-2-2-1-1-1-122220000000000-2-2221111-1-1-1-10000000000000
χ3544444-4-44-21-4-21-2-211-2-2-2-2112222-1-1-1-100000022-2-2000000000000000000000-1-111
χ3644444-4-44-21-4-21-2-211-2-2-2-2112222-1-1-1-1000000-2-22200000000000000000000011-1-1
χ374444-444-41-2-41-211-2-2-1-1-1-12211-1-122-2-200000000002i−2i2i−2i−i−iii−i−iii0000000000000
χ384444-444-41-2-41-211-2-2-1-1-1-12211-1-122-2-20000000000−2i2i−2i2iii−i−iii−i−i0000000000000
χ394444-444-4-21-4-21-2-2112222-1-1-2-222-1-1110000002-22-2000000000000000000000-11-11
χ404444-444-4-21-4-21-2-2112222-1-1-2-222-1-111000000-22-220000000000000000000001-11-1
χ414444-4-4-4-41-241-211-2-2-1-1-1-122-1-111-2-22200000000002i−2i−2i2i−i−iiiii−i−i0000000000000
χ424444-4-4-4-41-241-211-2-2-1-1-1-122-1-111-2-2220000000000−2i2i2i−2iii−i−i−i−iii0000000000000
χ434444-4-4-4-4-214-21-2-2112222-1-122-2-211-1-10000002-2-22000000000000000000000-111-1
χ444444-4-4-4-4-214-21-2-2112222-1-122-2-211-1-1000000-222-20000000000000000000001-1-11
χ454-44-40000440-4-44-44-40000000000000000004-400000000000000000000000000000
χ464-44-40000440-4-44-44-4000000000000000000-4400000000000000000000000000000
χ474-4-4404-401-20-12-112-23i−3i3i−3i001-13i−3i002-200000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000000000000
χ484-4-4404-401-20-12-112-23i−3i3i−3i001-13i−3i002-200000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000000000000
χ494-4-4404-401-20-12-112-2−3i3i−3i3i001-1−3i3i002-200000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000000000000
χ504-4-4404-401-20-12-112-2−3i3i−3i3i001-1−3i3i002-200000000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000000000000
χ514-4-4404-40440-4-4-44-440000004-40000-4400000000000000000000000000000000000
χ524-4-440-4401-20-12-112-23i−3i3i−3i00-11−3i3i00-2200000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000000000000
χ534-4-440-4401-20-12-112-23i−3i3i−3i00-11−3i3i00-2200000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000000000000
χ544-4-440-4401-20-12-112-2−3i3i−3i3i00-113i−3i00-2200000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000000000000
χ554-4-440-4401-20-12-112-2−3i3i−3i3i00-113i−3i00-2200000000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000000000000
χ564-4-440-440440-4-4-44-44000000-4400004-400000000000000000000000000000000000
χ5788-8-8800-82-402-4-2-24422-2-2-440000000000000000000000000000000000000000000
χ5888-8-8800-8-420-4244-2-2-4-4442-20000000000000000000000000000000000000000000
χ5988-8-8-80082-402-4-2-244-2-2224-40000000000000000000000000000000000000000000
χ6088-8-8-8008-420-4244-2-244-4-4-220000000000000000000000000000000000000000000
χ618-88-800002-40-242-2-446i−6i−6i6i000000000000000000000000000000000000000000000
χ628-88-800002-40-242-2-44−6i6i6i−6i000000000000000000000000000000000000000000000
χ638-88-80000-4204-2-442-200000000006-60000000000000000000000000000000000000
χ648-88-80000-4204-2-442-20000000000-660000000000000000000000000000000000000
χ658-8-8808-80-4204-24-4-22000000-440000-2200000000000000000000000000000000000
χ668-8-880-880-4204-24-4-220000004-400002-200000000000000000000000000000000000

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