Finite Group Databasebeta

← Group #11771470

Character table — Group #11771470

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size1111224444444444444444448888888812121212242424242424242424242424242424242424242424243636363672727272
order12222233446666666666121212126612121212121244444488881212121212121212242424242424242444448888
χ1111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111-1-11111111111-1-1-1-111-1-1-1-1-1-11111-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i11-1-1ii−i−i
χ611111111-1-11111111111-1-1-1-111-1-1-1-1-1-11111-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii11-1-1−i−iii
χ711111111-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111ii−i−i-1-1-1-11111iiii−i−i−i−i11-1-1−i−iii
χ811111111-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111−i−iii-1-1-1-11111−i−i−i−iiiii11-1-1ii−i−i
χ91-11-1-1111i−i111-1-1-1-1-11-1ii−i−i1-1iii−i−i−i11-1-1i−iζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ1311-1-1ii−i−iζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ131-1i−iζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13
χ101-11-1-1111i−i111-1-1-1-1-11-1ii−i−i1-1iii−i−i−i11-1-1i−i−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ1311-1-1ii−i−i−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ131-1i−i−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13
χ111-11-1-1111i−i111-1-1-1-1-11-1ii−i−i1-1iii−i−i−i-1-111−iiζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13-1-111−i−iiiζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ131-1i−i−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13
χ121-11-1-1111i−i111-1-1-1-1-11-1ii−i−i1-1iii−i−i−i-1-111−ii−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13-1-111−i−iii−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ131-1i−iζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13
χ131-11-1-1111−ii111-1-1-1-1-11-1−i−iii1-1−i−i−iiii11-1-1−ii−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ2311-1-1−i−iii−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ231-1−ii−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23
χ141-11-1-1111−ii111-1-1-1-1-11-1−i−iii1-1−i−i−iiii11-1-1−iiζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ2311-1-1−i−iiiζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ231-1−iiζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23
χ151-11-1-1111−ii111-1-1-1-1-11-1−i−iii1-1−i−i−iiii-1-111i−i−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23-1-111ii−i−i−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ231-1−iiζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23
χ161-11-1-1111−ii111-1-1-1-1-11-1−i−iii1-1−i−i−iiii-1-111i−iζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23-1-111ii−i−iζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ231-1−ii−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23
χ172222222222222222222222222222222200000000000000000000000000-2-2-2-20000
χ1822222222-2-22222222222-2-2-2-222-2-2-2-2-2-200000000000000000000000000-2-2220000
χ192-22-2-22222i−2i222-2-2-2-2-22-22i2i−2i−2i2-22i2i2i−2i−2i−2i00000000000000000000000000-22−2i2i0000
χ202-22-2-2222−2i2i222-2-2-2-2-22-2−2i−2i2i2i2-2−2i−2i−2i2i2i2i00000000000000000000000000-222i−2i0000
χ214444441-24411-211-21-211-2-2-2-2-2-211-211-22222220000-1-1-1-1-1-1-1-10000000000000000
χ224444441-24411-211-21-211-2-2-2-2-2-211-211-2-2-2-2-2-2-20000111111110000000000000000
χ234444441-2-4-411-211-21-2112222-2-2-1-12-1-122222-2-20000-1-1-1-111110000000000000000
χ244444441-2-4-411-211-21-2112222-2-2-1-12-1-12-2-2-2-22200001111-1-1-1-10000000000000000
χ25444444-2144-2-21-2-21-21-2-2111111-2-21-2-21000000222200000000-1-1-1-1-1-1-1-100000000
χ26444444-2144-2-21-2-21-21-2-2111111-2-21-2-21000000-2-2-2-2000000001111111100000000
χ27444444-21-4-4-2-21-2-21-21-2-2-1-1-1-11122-122-10000002i2i−2i−2i00000000−i−i−i−iiiii00000000
χ28444444-21-4-4-2-21-2-21-21-2-2-1-1-1-11122-122-1000000−2i−2i2i2i00000000iiii−i−i−i−i00000000
χ294444-4-444004-44-4-4444-440000-4-40000000000000000000000000000000000000000
χ304444-4-4-2100-221221-212-23333-1-100-300-30000000000000000003−33−33−33−300000000
χ314444-4-4-2100-221221-212-23333-1-100-300-3000000000000000000−33−33−33−3300000000
χ324444-4-4-2100-221221-212-2-3-3-3-3-1-1003003000000000000000000−i3i3−i3i3i3−i3i3−i300000000
χ334444-4-4-2100-221221-212-2-3-3-3-3-1-1003003000000000000000000i3−i3i3−i3−i3i3−i3i300000000
χ3444-4-4001-200-1-323-3-2-123123−2323−23003−303−302i−2i2i−2i000000i−ii−i−i3i3−i3i30000000000000000
χ3544-4-4001-200-1-323-3-2-123123−2323−23003−303−30−2i2i−2i2i000000−ii−iii3−i3i3−i30000000000000000
χ3644-4-4001-200-1-323-3-2-1231−2323−232300−330−3302i−2i2i−2i000000i−ii−ii3−i3i3−i30000000000000000
χ3744-4-4001-200-1-323-3-2-1231−2323−232300−330−330−2i2i−2i2i000000−ii−ii−i3i3−i3i30000000000000000
χ3844-4-4004400-40-4004-4-4040000000000002i−2i2i−2i000000−2i2i−2i2i00000000000000000000
χ3944-4-4004400-40-4004-4-404000000000000−2i2i−2i2i0000002i−2i2i−2i00000000000000000000
χ404-44-44-444004-4444-4-4-4-4-40000-440000000000000000000000000000000000000000
χ414-44-44-4-2100-221-2-2-12-1223i3i−3i−3i-1100−3i003i000000000000000000ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ2300000000
χ424-44-44-4-2100-221-2-2-12-1223i3i−3i−3i-1100−3i003i000000000000000000−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ2300000000
χ434-44-44-4-2100-221-2-2-12-122−3i−3i3i3i-11003i00−3i000000000000000000−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ1300000000
χ444-44-44-4-2100-221-2-2-12-122−3i−3i3i3i-11003i00−3i000000000000000000ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ1300000000
χ454-44-4-441-24i−4i11-2-1-12-121-1−2i−2i2i2i-22ii−2i−i−i2i22-2-22i−2i0000-1-111−i−iii0000000000000000
χ464-44-4-441-24i−4i11-2-1-12-121-1−2i−2i2i2i-22ii−2i−i−i2i-2-222−2i2i000011-1-1ii−i−i0000000000000000
χ474-44-4-441-2−4i4i11-2-1-12-121-12i2i−2i−2i-22−i−i2iii−2i22-2-2−2i2i0000-1-111ii−i−i0000000000000000
χ484-44-4-441-2−4i4i11-2-1-12-121-12i2i−2i−2i-22−i−i2iii−2i-2-2222i−2i000011-1-1−i−iii0000000000000000
χ494-44-4-44-214i−4i-2-2122-12-1-22ii−i−i1-1−2i−2ii2i2i−i0000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ1300000000
χ504-44-4-44-214i−4i-2-2122-12-1-22ii−i−i1-1−2i−2ii2i2i−i000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ1300000000
χ514-44-4-44-21−4i4i-2-2122-12-1-22−i−iii1-12i2i−i−2i−2ii000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ2300000000
χ524-44-4-44-21−4i4i-2-2122-12-1-22−i−iii1-12i2i−i−2i−2ii0000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ2300000000
χ534-4-44001-200-1-32-3321-23-1−2i32i32i3−2i300−i3i30i3−i302i−2i−2i2i000000i−i−ii−333−30000000000000000
χ544-4-44001-200-1-32-3321-23-1−2i32i32i3−2i300−i3i30i3−i30−2i2i2i−2i000000−iii−i3−3−330000000000000000
χ554-4-44001-200-1-32-3321-23-12i3−2i3−2i32i300i3−i30−i3i302i−2i−2i2i000000i−i−ii3−3−330000000000000000
χ564-4-44001-200-1-32-3321-23-12i3−2i3−2i32i300i3−i30−i3i30−2i2i2i−2i000000−iii−i−333−30000000000000000
χ574-4-44004400-40-400-4440-40000000000002i−2i−2i2i000000−2i2i2i−2i00000000000000000000
χ584-4-44004400-40-400-4440-4000000000000−2i2i2i−2i0000002i−2i−2i2i00000000000000000000
χ598888-8-82-4002-2-4-2-2-42-4-220000440000000000000000000000000000000000000000
χ6088-8-8002-400-264-66-4-24-620000000000000000000000000000000000000000000000
χ6188-8-800-420040-20024-20-423−2323−2300−23230−232300000000000000000000000000000000000
χ6288-8-800-420040-20024-20-4−2323−23230023−23023−2300000000000000000000000000000000000
χ638-88-88-82-4002-2-4224-24-2-200004-40000000000000000000000000000000000000000
χ648-8-88002-400-2646-642-4-6-20000000000000000000000000000000000000000000000
χ658-8-8800-420040-200-2-4204−2i32i32i3−2i3002i3−2i30−2i32i300000000000000000000000000000000000
χ668-8-8800-420040-200-2-42042i3−2i3−2i32i300−2i32i302i3−2i300000000000000000000000000000000000

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