Finite Group Databasebeta

← Group #11776366

Character table — Group #11776366

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size111122224444444444444444488888888121212121212121218181818181824242424242424242424242424242424242424243672727272
order12222244334666666666612121212661212121212128888888844444444441212121212121212242424242424242448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1
χ4111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111
χ5111111-1-111-11111111111-1-1-1-111-1-1-1-1-1-1iiii−i−i−i−i-1-1-111-111-1-11111-1-1-1-1iiii−i−i−i−i1ii−i−i
χ6111111-1-111-11111111111-1-1-1-111-1-1-1-1-1-1iiii−i−i−i−i-1-1-111-1-1-111-1-1-1-11111iiii−i−i−i−i1−i−iii
χ7111111-1-111-11111111111-1-1-1-111-1-1-1-1-1-1−i−i−i−iiiii-1-1-111-111-1-11111-1-1-1-1−i−i−i−iiiii1−i−iii
χ8111111-1-111-11111111111-1-1-1-111-1-1-1-1-1-1−i−i−i−iiiii-1-1-111-1-1-111-1-1-1-11111−i−i−i−iiiii1ii−i−i
χ91111-1-11111-1111-1-1-1-11111111-1-111-1-1-1-111-1-111-1-11-1-1-1-111-11-111-1-111-1-111-1-111-1-111-11-1
χ101111-1-11111-1111-1-1-1-11111111-1-111-1-1-1-111-1-111-1-11-1-1-1-11-11-11-1-111-1-11111-1-111-1-11-11-11
χ111111-1-11111-1111-1-1-1-11111111-1-111-1-1-1-1-1-111-1-1111-1-1-1-111-11-111-1-111-1-1-1-111-1-1111-11-11
χ121111-1-11111-1111-1-1-1-11111111-1-111-1-1-1-1-1-111-1-1111-1-1-1-11-11-11-1-111-1-111-1-111-1-11111-11-1
χ131111-1-1-1-1111111-1-1-1-1111-1-1-1-1-1-1-1-11111ii−i−i−i−iii-111-1-1-11-1-1111-1-1-1-111ii−i−i−i−iii1i−i−ii
χ141111-1-1-1-1111111-1-1-1-1111-1-1-1-1-1-1-1-11111ii−i−i−i−iii-111-1-1-1-111-1-1-11111-1-1ii−i−i−i−iii1−iii−i
χ151111-1-1-1-1111111-1-1-1-1111-1-1-1-1-1-1-1-11111−i−iiiii−i−i-111-1-1-11-1-1111-1-1-1-111−i−iiiii−i−i1−iii−i
χ161111-1-1-1-1111111-1-1-1-1111-1-1-1-1-1-1-1-11111−i−iiiii−i−i-111-1-1-1-111-1-1-11111-1-1−i−iiiii−i−i1i−i−ii
χ1722222222222222222222222222222222200000000-2-2-2-2-2-200000000000000000000-20000
χ18222222-2-222-22222222222-2-2-2-222-2-2-2-2-2-200000000222-2-2200000000000000000000-20000
χ192222-2-22222-2222-2-2-2-22222222-2-222-2-2-2-200000000-22222-200000000000000000000-20000
χ202222-2-2-2-2222222-2-2-2-2222-2-2-2-2-2-2-2-22222000000002-2-222200000000000000000000-20000
χ212-22-22-20022022-222-2-2-2-2-200002-20000002−22−22−22−222-200-20000000000002−22−22−22−200000
χ222-22-22-20022022-222-2-2-2-2-200002-2000000−i2i2−i2i2i2−i2i2−i2-2-22002000000000000−i2i2−i2i2i2−i2i2−i200000
χ232-22-22-20022022-222-2-2-2-2-200002-2000000i2−i2i2−i2−i2i2−i2i2-2-22002000000000000i2−i2i2−i2−i2i2−i2i200000
χ242-22-22-20022022-222-2-2-2-2-200002-2000000−22−22−22−2222-200-2000000000000−22−22−22−2200000
χ252-22-2-220022022-2-2-222-2-2-20000-220000002−2−222−2−222-2200-20000000000002−2−222−2−2200000
χ262-22-2-220022022-2-2-222-2-2-20000-22000000−i2i2i2−i2i2−i2−i2i2-22-2002000000000000−i2i2i2−i2i2−i2−i2i200000
χ272-22-2-220022022-2-2-222-2-2-20000-22000000i2−i2−i2i2−i2i2i2−i2-22-2002000000000000i2−i2−i2i2−i2i2i2−i200000
χ282-22-2-220022022-2-2-222-2-2-20000-22000000−222−2−222−22-2200-2000000000000−222−2−222−200000
χ29444444441-241-21-2-2-2-21-2-2111111-2-211-2-222222222000000000000000000-1-1-1-1-1-1-1-100000
χ30444444441-241-21-2-2-2-21-2-2111111-2-211-2-2-2-2-2-2-2-2-2-20000000000000000001111111100000
χ3144444444-214-21-21111-211-2-2-2-2-2-211-2-211000000000000002222-1-1-1-1-1-1-1-10000000000000
χ3244444444-214-21-21111-211-2-2-2-2-2-211-2-21100000000000000-2-2-2-2111111110000000000000
χ33444444-4-41-2-41-21-2-2-2-21-2-2-1-1-1-11122-1-1222i2i2i2i−2i−2i−2i−2i000000000000000000−i−i−i−iiiii00000
χ34444444-4-41-2-41-21-2-2-2-21-2-2-1-1-1-11122-1-122−2i−2i−2i−2i2i2i2i2i000000000000000000iiii−i−i−i−i00000
χ35444444-4-4-21-4-21-21111-2112222-2-2-1-122-1-10000000000000022-2-2-1-1-1-111110000000000000
χ36444444-4-4-21-4-21-21111-2112222-2-2-1-122-1-100000000000000-2-2221111-1-1-1-10000000000000
χ374444-4-4441-2-41-2122221-2-21111-1-1-2-2-1-12222-2-222-2-2000000000000000000-1-111-1-11100000
χ384444-4-4441-2-41-2122221-2-21111-1-1-2-2-1-122-2-222-2-22200000000000000000011-1-111-1-100000
χ394444-4-444-21-4-21-2-1-1-1-1-211-2-2-2-2221122-1-1000000000000002-22-2-1-111-1-1110000000000000
χ404444-4-444-21-4-21-2-1-1-1-1-211-2-2-2-2221122-1-100000000000000-22-2211-1-111-1-10000000000000
χ414444-4-4-4-41-241-2122221-2-2-1-1-1-1-1-12211-2-22i2i−2i−2i−2i−2i2i2i000000000000000000−i−iiiii−i−i00000
χ424444-4-4-4-41-241-2122221-2-2-1-1-1-1-1-12211-2-2−2i−2i2i2i2i2i−2i−2i000000000000000000ii−i−i−i−iii00000
χ434444-4-4-4-4-214-21-2-1-1-1-1-211222222-1-1-2-211000000000000002-2-22-1-11111-1-10000000000000
χ444444-4-4-4-4-214-21-2-1-1-1-1-211222222-1-1-2-21100000000000000-222-211-1-1-1-1110000000000000
χ4544-4-4004-4440-4-4-4000044-444-4-4004-40000000000000000000000000000000000000000000
χ4644-4-4004-4-2102-123-33-3-21-1-2-222001-1003-30000000000000000003−33−33−33−30000000000000
χ4744-4-4004-4-2102-123-33-3-21-1-2-222001-1003-3000000000000000000−33−33−33−330000000000000
χ4844-4-4004-4-2102-12-33-33-21-1-2-222001-100-330000000000000000003−3−333−3−330000000000000
χ4944-4-4004-4-2102-12-33-33-21-1-2-222001-100-33000000000000000000−333−3−333−30000000000000
χ5044-4-400-44440-4-4-4000044-4-4-44400-440000000000000000000000000000000000000000000
χ5144-4-400-44-2102-123-33-3-21-122-2-200-1100-330000000000000000003−33−3−33−330000000000000
χ5244-4-400-44-2102-123-33-3-21-122-2-200-1100-33000000000000000000−33−333−33−30000000000000
χ5344-4-400-44-2102-12-33-33-21-122-2-200-11003-30000000000000000003−3−33−333−30000000000000
χ5444-4-400-44-2102-12-33-33-21-122-2-200-11003-3000000000000000000−333−33−3−330000000000000
χ554-44-44-4001-201-2-1-2-222-1223i−3i3i−3i1-1003i−3i002ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13000000000000000000−ζ7−ζ23ζ7+ζ23−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ζ5+ζ13−ζ5−ζ1300000
χ564-44-44-4001-201-2-1-2-222-1223i−3i3i−3i1-1003i−3i00−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13000000000000000000ζ7+ζ23−ζ7−ζ23ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−ζ5−ζ13ζ5+ζ1300000
χ574-44-44-4001-201-2-1-2-222-122−3i3i−3i3i1-100−3i3i00−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23000000000000000000ζ5+ζ13−ζ5−ζ13ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−ζ7−ζ23ζ7+ζ2300000
χ584-44-44-4001-201-2-1-2-222-122−3i3i−3i3i1-100−3i3i002ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23000000000000000000−ζ5−ζ13ζ5+ζ13−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23ζ7+ζ23−ζ7−ζ2300000
χ594-44-4-44001-201-2-122-2-2-1223i−3i3i−3i-1100−3i3i002ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13000000000000000000−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ1300000
χ604-44-4-44001-201-2-122-2-2-1223i−3i3i−3i-1100−3i3i00−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ13000000000000000000ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ1300000
χ614-44-4-44001-201-2-122-2-2-122−3i3i−3i3i-11003i−3i00−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ23000000000000000000ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ2300000
χ624-44-4-44001-201-2-122-2-2-122−3i3i−3i3i-11003i−3i002ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23000000000000000000−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ2300000
χ634-4-440000440-4-440000-4-44000000000000000000000004-400000000000000000000000000
χ644-4-440000440-4-440000-4-4400000000000000000000000-4400000000000000000000000000
χ6588-8-8008-82-40-24-200002-4422-2-200-440000000000000000000000000000000000000000000
χ6688-8-800-882-40-24-200002-44-2-222004-40000000000000000000000000000000000000000000
χ678-88-88-800-420-42422-2-24-2-20000-44000000000000000000000000000000000000000000000
χ688-88-8-8800-420-424-2-2224-2-200004-4000000000000000000000000000000000000000000000
χ698-8-8800002-40-2420000-24-46i−6i−6i6i00000000000000000000000000000000000000000000000
χ708-8-8800002-40-2420000-24-4−6i6i6i−6i00000000000000000000000000000000000000000000000
χ718-8-880000-4204-2-46-6-664-22000000000000000000000000000000000000000000000000000
χ728-8-880000-4204-2-4-666-64-22000000000000000000000000000000000000000000000000000

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