Finite Group Databasebeta

← Group #11774056

Character table — Group #11774056

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size111122224444444444444444488888888888888888888888888181818181818363636363636363636727272727272
order122222443346666666666666644121212121212121212121212121212121212121212121212444444488888888448888
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
χ9111111-1-111-1111111111111111-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-11ii−i−iii−i−i1-1i−ii−i
χ10111111-1-111-1111111111111111-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-11−i−iii−i−iii1-1−ii−ii
χ11111111-1-111-1111111111111111-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-111-1-1-1-111-111-1-11
χ12111111-1-111-1111111111111111-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-11111-1-1-11-111-1
χ13111111-1-111-111111111111111-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11ii−i−iii−i−i-11−ii−ii
χ14111111-1-111-111111111111111-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11−i−iii−i−iii-11i−ii−i
χ15111111-1-111-111111111111111-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-111-1-1-1-1111-1-111-1
χ16111111-1-111-111111111111111-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-11111-1-11-11-1-11
χ172222-2-22222-222-2-2-2-2-2-2-2-22222002222-2-2-2-200000000000000002222-2-2-200000000000000
χ182222-2-22222-222-2-2-2-2-2-2-2-22222002222-2-2-2-20000000000000000-2-2-2-222200000000000000
χ192222-2-2-2-222222-2-2-2-2-2-2-2-2222200-2-2-2-22222000000000000000022-2-222-200000000000000
χ202222-2-2-2-222222-2-2-2-2-2-2-2-2222200-2-2-2-222220000000000000000-2-222-2-2200000000000000
χ212-2-222-200220222222-2-2-2-2-2-2-2-200000000000000000000000000002i−2i2i−2i000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000
χ222-2-222-200220222222-2-2-2-2-2-2-2-200000000000000000000000000002i−2i2i−2i0002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000
χ232-2-222-200220222222-2-2-2-2-2-2-2-20000000000000000000000000000−2i2i−2i2i0002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000
χ242-2-222-200220222222-2-2-2-2-2-2-2-20000000000000000000000000000−2i2i−2i2i000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000
χ252-2-22-220022022-2-2-2-22222-2-2-2-200000000000000000000000000002i−2i−2i2i02ζ7+2ζ23−2ζ7−2ζ230000−2ζ5−2ζ132ζ5+2ζ13000000
χ262-2-22-220022022-2-2-2-22222-2-2-2-200000000000000000000000000002i−2i−2i2i0−2ζ7−2ζ232ζ7+2ζ2300002ζ5+2ζ13−2ζ5−2ζ13000000
χ272-2-22-220022022-2-2-2-22222-2-2-2-20000000000000000000000000000−2i2i2i−2i0−2ζ5−2ζ132ζ5+2ζ1300002ζ7+2ζ23−2ζ7−2ζ23000000
χ282-2-22-220022022-2-2-2-22222-2-2-2-20000000000000000000000000000−2i2i2i−2i02ζ5+2ζ13−2ζ5−2ζ130000−2ζ7−2ζ232ζ7+2ζ23000000
χ29444444441-241-211-2-211-2-21-21-24411-2-211-2-21111-2-2-2-21111-2-2-2-2000000000000000000000
χ30444444441-241-211-2-211-2-21-21-2-4-411-2-211-2-2-1-1-1-12222-1-1-1-12222000000000000000000000
χ3144444444-214-21-2-211-2-211-21-2144-2-211-2-211-2-2-2-21111-2-2-2-21111000000000000000000000
χ3244444444-214-21-2-211-2-211-21-21-4-4-2-211-2-2112222-1-1-1-12222-1-1-1-1000000000000000000000
χ33444444-4-41-2-41-211-2-211-2-21-21-24-4-1-122-1-1221111-2-2-2-2-1-1-1-12222000000000000000000000
χ34444444-4-41-2-41-211-2-211-2-21-21-2-44-1-122-1-122-1-1-1-122221111-2-2-2-2000000000000000000000
χ35444444-4-4-21-4-21-2-211-2-211-21-214-422-1-122-1-1-2-2-2-211112222-1-1-1-1000000000000000000000
χ36444444-4-4-21-4-21-2-211-2-211-21-21-4422-1-122-1-12222-1-1-1-1-2-2-2-21111000000000000000000000
χ374444-4-4441-2-41-2-1-122-1-1221-21-20011-2-2-1-12233-3-3000033-3-30000000000000000000000000
χ384444-4-4441-2-41-2-1-122-1-1221-21-20011-2-2-1-122-3-3330000-3-3330000000000000000000000000
χ394444-4-444-21-4-2122-1-122-1-1-21-2100-2-21122-1-1000033-3-3000033-3-3000000000000000000000
χ404444-4-444-21-4-2122-1-122-1-1-21-2100-2-21122-1-10000-3-3330000-3-333000000000000000000000
χ414444-4-4-4-41-241-2-1-122-1-1221-21-200-1-12211-2-233-3-30000-3-3330000000000000000000000000
χ424444-4-4-4-41-241-2-1-122-1-1221-21-200-1-12211-2-2-3-333000033-3-30000000000000000000000000
χ434444-4-4-4-4-214-2122-1-122-1-1-21-210022-1-1-2-211000033-3-30000-3-333000000000000000000000
χ444444-4-4-4-4-214-2122-1-122-1-1-21-210022-1-1-2-2110000-3-333000033-3-3000000000000000000000
χ4544-4-4004-41-20-123-3003-3001-2-12001-12-23-3003−33−30023−233−33−30023−23000000000000000000000
χ4644-4-4004-41-20-123-3003-3001-2-12001-12-23-300−33−3300−2323−33−3300−2323000000000000000000000
χ4744-4-4004-41-20-12-3300-33001-2-12001-12-2-33003−3−3323−23003−3−3323−2300000000000000000000000
χ4844-4-4004-41-20-12-3300-33001-2-12001-12-2-3300−333−3−232300−333−3−232300000000000000000000000
χ4944-4-4004-4440-4-40000000044-4-4004-4-4400000000000000000000000000000000000000000
χ5044-4-4004-4-2102-1003-3003-3-212-100-22-11003-30023−233−3−330023−233−3−33000000000000000000000
χ5144-4-4004-4-2102-1003-3003-3-212-100-22-11003-300−2323−333−300−2323−333−3000000000000000000000
χ5244-4-4004-4-2102-100-3300-33-212-100-22-1100-3323−2300−33−3323−2300−33−33000000000000000000000
χ5344-4-4004-4-2102-100-3300-33-212-100-22-1100-33−2323003−33−3−2323003−33−3000000000000000000000
χ5444-4-400-441-20-123-3003-3001-2-1200-11-22-33003−33−30023−23−33−3300−2323000000000000000000000
χ5544-4-400-441-20-123-3003-3001-2-1200-11-22-3300−33−3300−23233−33−30023−23000000000000000000000
χ5644-4-400-441-20-12-3300-33001-2-1200-11-223-3003−3−3323−2300−333−3−232300000000000000000000000
χ5744-4-400-441-20-12-3300-33001-2-1200-11-223-300−333−3−2323003−3−3323−2300000000000000000000000
χ5844-4-400-44440-4-40000000044-4-400-444-400000000000000000000000000000000000000000
χ5944-4-400-44-2102-1003-3003-3-212-1002-21-100-330023−233−3−3300−2323−333−3000000000000000000000
χ6044-4-400-44-2102-1003-3003-3-212-1002-21-100-3300−2323−333−30023−233−3−33000000000000000000000
χ6144-4-400-44-2102-100-3300-33-212-1002-21-1003-323−2300−33−33−2323003−33−3000000000000000000000
χ6244-4-400-44-2102-100-3300-33-212-1002-21-1003-3−2323003−33−323−2300−33−33000000000000000000000
χ634-44-40000440-4-400000000-4-444000000000000000000000000004i−4i0000000000000000000
χ644-44-40000440-4-400000000-4-44400000000000000000000000000−4i4i0000000000000000000
χ658-88-800002-40-246-600-6600-242-400000000000000000000000000000000000000000000000
χ668-88-800002-40-24-66006-600-242-400000000000000000000000000000000000000000000000
χ678-88-80000-4204-2006-600-664-2-4200000000000000000000000000000000000000000000000
χ688-88-80000-4204-200-66006-64-2-4200000000000000000000000000000000000000000000000
χ698-8-888-8002-402-422-4-4-2-244-24-2400000000000000000000000000000000000000000000000
χ708-8-888-800-420-42-4-42244-2-24-24-200000000000000000000000000000000000000000000000
χ718-8-88-88002-402-4-2-24422-4-4-24-2400000000000000000000000000000000000000000000000
χ728-8-88-8800-420-4244-2-2-4-4224-24-200000000000000000000000000000000000000000000000

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