Finite Group Databasebeta

← Group #11774054

Character table — Group #11774054

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
χ51111111111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1
χ61111111111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i11−i−iii
χ81111111111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii11ii−i−i
χ9111111-1-111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11ii−i−iii−i−i1-1i−ii−i
χ10111111-1-111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11−i−iii−i−iii1-1−ii−ii
χ11111111-1-111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-111-1-1-1-111-111-1-11
χ12111111-1-111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-11111-1-1-11-111-1
χ13111111-1-111-111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11ii−i−iii−i−i-11−ii−ii
χ14111111-1-111-111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11−i−iii−i−iii-11i−ii−i
χ15111111-1-111-111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-1-1111-1-111-1
χ16111111-1-111-111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-11111-1-11-11-1-11
χ172222-2-22222-222-2-2-2-2-2-2-2-2222200000000002222-2-2-2-2000000002222-2-2-200000000000000
χ182222-2-22222-222-2-2-2-2-2-2-2-2222200000000002222-2-2-2-200000000-2-2-2-222200000000000000
χ192222-2-2-2-222222-2-2-2-2-2-2-2-222220000000000-2-2-2-222220000000022-2-222-200000000000000
χ202222-2-2-2-222222-2-2-2-2-2-2-2-222220000000000-2-2-2-2222200000000-2-222-2-2200000000000000
χ212-22-22-200220-2-22222-2-2-2-2-2-22200000000000000000000000000002i−2i2i−2i0002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000
χ222-22-22-200220-2-22222-2-2-2-2-2-22200000000000000000000000000002i−2i2i−2i000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000
χ232-22-22-200220-2-22222-2-2-2-2-2-2220000000000000000000000000000−2i2i−2i2i000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000
χ242-22-22-200220-2-22222-2-2-2-2-2-2220000000000000000000000000000−2i2i−2i2i0002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000
χ252-22-2-2200220-2-2-2-2-2-22222-2-22200000000000000000000000000002i−2i−2i2i02ζ7+2ζ23−2ζ7−2ζ230000−2ζ5−2ζ132ζ5+2ζ13000000
χ262-22-2-2200220-2-2-2-2-2-22222-2-22200000000000000000000000000002i−2i−2i2i0−2ζ7−2ζ232ζ7+2ζ2300002ζ5+2ζ13−2ζ5−2ζ13000000
χ272-22-2-2200220-2-2-2-2-2-22222-2-2220000000000000000000000000000−2i2i2i−2i0−2ζ5−2ζ132ζ5+2ζ1300002ζ7+2ζ23−2ζ7−2ζ23000000
χ282-22-2-2200220-2-2-2-2-2-22222-2-2220000000000000000000000000000−2i2i2i−2i02ζ5+2ζ13−2ζ5−2ζ130000−2ζ7−2ζ232ζ7+2ζ23000000
χ29444444441-241-211-2-211-2-21-21-2441111-2-2-2-211-2-211-2-21111-2-2-2-2000000000000000000000
χ30444444441-241-211-2-211-2-21-21-2-4-4-1-1-1-1222211-2-211-2-2-1-1-1-12222000000000000000000000
χ3144444444-214-21-2-211-2-211-21-2144-2-2-2-21111-2-211-2-211-2-2-2-21111000000000000000000000
χ3244444444-214-21-2-211-2-211-21-21-4-42222-1-1-1-1-2-211-2-2112222-1-1-1-1000000000000000000000
χ33444444-4-41-2-41-211-2-211-2-21-21-24-4-1-1-1-12222-1-122-1-1221111-2-2-2-2000000000000000000000
χ34444444-4-41-2-41-211-2-211-2-21-21-2-441111-2-2-2-2-1-122-1-122-1-1-1-12222000000000000000000000
χ35444444-4-4-21-4-21-2-211-2-211-21-214-42222-1-1-1-122-1-122-1-1-2-2-2-21111000000000000000000000
χ36444444-4-4-21-4-21-2-211-2-211-21-21-44-2-2-2-2111122-1-122-1-12222-1-1-1-1000000000000000000000
χ374444-4-4441-2-41-2-1-122-1-1221-21-20033-3-3000011-2-2-1-12233-3-30000000000000000000000000
χ384444-4-4441-2-41-2-1-122-1-1221-21-200-3-333000011-2-2-1-122-3-3330000000000000000000000000
χ394444-4-444-21-4-2122-1-122-1-1-21-2100000033-3-3-2-21122-1-1000033-3-3000000000000000000000
χ404444-4-444-21-4-2122-1-122-1-1-21-21000000-3-333-2-21122-1-10000-3-333000000000000000000000
χ414444-4-4-4-41-241-2-1-122-1-1221-21-20033-3-30000-1-12211-2-2-3-3330000000000000000000000000
χ424444-4-4-4-41-241-2-1-122-1-1221-21-200-3-3330000-1-12211-2-233-3-30000000000000000000000000
χ434444-4-4-4-4-214-2122-1-122-1-1-21-2100000033-3-322-1-1-2-2110000-3-333000000000000000000000
χ444444-4-4-4-4-214-2122-1-122-1-1-21-21000000-3-33322-1-1-2-211000033-3-3000000000000000000000
χ4544-4-400004404400000000-4-4-4-4000000000000000000000000004-40000000000000000000
χ4644-4-400004404400000000-4-4-4-400000000000000000000000000-440000000000000000000
χ474-4-44004i−4i1-20-123-3003-3001-2-1200−i3i3−i3i300−2i32i3i−i2i−2i3i−3i003−33−30023−23000000000000000000000
χ484-4-44004i−4i1-20-123-3003-3001-2-1200i3−i3i3−i3002i3−2i3i−i2i−2i3i−3i00−33−3300−2323000000000000000000000
χ494-4-44004i−4i1-20-12-3300-33001-2-1200−i3i3i3−i3−2i32i300i−i2i−2i−3i3i003−3−3323−2300000000000000000000000
χ504-4-44004i−4i1-20-12-3300-33001-2-1200i3−i3−i3i32i3−2i300i−i2i−2i−3i3i00−333−3−232300000000000000000000000
χ514-4-44004i−4i440-4-40000000044-4-400000000004i−4i−4i4i000000000000000000000000000000000
χ524-4-44004i−4i-2102-1003-3003-3-212-10000−2i32i3−i3i3i3−i3−2i2i−ii003i−3i0023−233−3−33000000000000000000000
χ534-4-44004i−4i-2102-1003-3003-3-212-100002i3−2i3i3−i3−i3i3−2i2i−ii003i−3i00−2323−333−3000000000000000000000
χ544-4-44004i−4i-2102-100-3300-33-212-100−2i32i300i3−i3i3−i3−2i2i−ii00−3i3i23−2300−33−33000000000000000000000
χ554-4-44004i−4i-2102-100-3300-33-212-1002i3−2i300−i3i3−i3i3−2i2i−ii00−3i3i−2323003−33−3000000000000000000000
χ564-4-4400−4i4i1-20-123-3003-3001-2-1200−i3i3−i3i300−2i32i3−ii−2i2i−3i3i00−33−3300−2323000000000000000000000
χ574-4-4400−4i4i1-20-123-3003-3001-2-1200i3−i3i3−i3002i3−2i3−ii−2i2i−3i3i003−33−30023−23000000000000000000000
χ584-4-4400−4i4i1-20-12-3300-33001-2-1200−i3i3i3−i3−2i32i300−ii−2i2i3i−3i00−333−3−232300000000000000000000000
χ594-4-4400−4i4i1-20-12-3300-33001-2-1200i3−i3−i3i32i3−2i300−ii−2i2i3i−3i003−3−3323−2300000000000000000000000
χ604-4-4400−4i4i440-4-40000000044-4-40000000000−4i4i4i−4i000000000000000000000000000000000
χ614-4-4400−4i4i-2102-1003-3003-3-212-10000−2i32i3−i3i3i3−i32i−2ii−i00−3i3i00−2323−333−3000000000000000000000
χ624-4-4400−4i4i-2102-1003-3003-3-212-100002i3−2i3i3−i3−i3i32i−2ii−i00−3i3i0023−233−3−33000000000000000000000
χ634-4-4400−4i4i-2102-100-3300-33-212-100−2i32i300i3−i3i3−i32i−2ii−i003i−3i−2323003−33−3000000000000000000000
χ644-4-4400−4i4i-2102-100-3300-33-212-1002i3−2i300−i3i3−i3i32i−2ii−i003i−3i23−2300−33−33000000000000000000000
χ6588-8-800002-402-46-600-6600-24-2400000000000000000000000000000000000000000000000
χ6688-8-800002-402-4-66006-600-24-2400000000000000000000000000000000000000000000000
χ6788-8-80000-420-42006-600-664-24-200000000000000000000000000000000000000000000000
χ6888-8-80000-420-4200-66006-64-24-200000000000000000000000000000000000000000000000
χ698-88-88-8002-40-2422-4-4-2-244-242-400000000000000000000000000000000000000000000000
χ708-88-88-800-4204-2-4-42244-2-24-2-4200000000000000000000000000000000000000000000000
χ718-88-8-88002-40-24-2-24422-4-4-242-400000000000000000000000000000000000000000000000
χ728-88-8-8800-4204-244-2-2-4-4224-2-4200000000000000000000000000000000000000000000000

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