Finite Group Databasebeta

← Group #11772641

Character table — Group #11772641

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size1111224444444444444444448888888812121212242424242424242424242424242424242424242424243636363672727272
order1244242334666666121212121212121266661212121288888888882424242424242424242424242424242422444444
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
χ5111111-111-111-1-111111111-1-11-1-1-11-1-1-11111-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i1-11-1ii−i−i
χ6111111-111-111-1-111111111-1-11-1-1-11-1-1-11111-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii1-11-1−i−iii
χ7111111-111-111-1-111111111-1-11-1-1-11-1-1-1-1-1-1-111ii−i−i-1-1-1-11111iiii−i−i−i−i1-11-1−i−iii
χ8111111-111-111-1-111111111-1-11-1-1-11-1-1-1-1-1-1-111−i−iii-1-1-1-11111−i−i−i−iiiii1-11-1ii−i−i
χ911-1-11-1111-1111111-1-1-1-1-1-1-1-11111-1-1-1-1ii−i−ii−ii−ii−iii−i−iii−i−iii−i−iii−i−i-111-11-11-1
χ1011-1-11-1111-1111111-1-1-1-1-1-1-1-11111-1-1-1-1ii−i−ii−i−ii−iiii−i−iii−i−i−i−iii−i−iii-111-1-11-11
χ1111-1-11-1111-1111111-1-1-1-1-1-1-1-11111-1-1-1-1−i−iii−iii−ii−i−i−iii−i−iiiii−i−iii−i−i-111-1-11-11
χ1211-1-11-1111-1111111-1-1-1-1-1-1-1-11111-1-1-1-1−i−iii−ii−ii−ii−i−iii−i−iii−i−iii−i−iii-111-11-11-1
χ1311-1-11-1-111111-1-111-1-1-1-1-1-1111-1-1-1-1111ii−i−i−ii1-1-11ii−i−i−i−iii11-1-1-1-111-1-111−iii−i
χ1411-1-11-1-111111-1-111-1-1-1-1-1-1111-1-1-1-1111ii−i−i−ii-111-1ii−i−i−i−iii-1-11111-1-1-1-111i−i−ii
χ1511-1-11-1-111111-1-111-1-1-1-1-1-1111-1-1-1-1111−i−iiii−i1-1-11−i−iiiii−i−i11-1-1-1-111-1-111i−i−ii
χ1611-1-11-1-111111-1-111-1-1-1-1-1-1111-1-1-1-1111−i−iiii−i-111-1−i−iiiii−i−i-1-11111-1-1-1-111−iii−i
χ172222222222222222222222222222222200000000000000000000000000-2-2-2-20000
χ18222222-222-222-2-222222222-2-22-2-2-22-2-2-200000000000000000000000000-22-220000
χ1922-2-22-2222-2222222-2-2-2-2-2-2-2-22222-2-2-2-2000000000000000000000000002-2-220000
χ2022-2-22-2-222222-2-222-2-2-2-2-2-2222-2-2-2-22220000000000000000000000000022-2-20000
χ2144444441-2411-2-21-2-2-21111-2-2-211-2-211-22222220000-1-1-1-1-1-1-1-10000000000000000
χ2244444441-2411-2-21-2-2-21111-2-2-211-2-211-2-2-2-2-2-2-20000111111110000000000000000
χ234444444-214-2-211-2111-2-2-2-2111-2-211-2-21000000222200000000-1-1-1-1-1-1-1-100000000
χ244444444-214-2-211-2111-2-2-2-2111-2-211-2-21000000-2-2-2-2000000001111111100000000
χ25444444-41-2-411221-2-2-2111122-2-1-12-2-1-122222-2-20000-1-1-1-111110000000000000000
χ26444444-41-2-411221-2-2-2111122-2-1-12-2-1-12-2-2-2-22200001111-1-1-1-10000000000000000
χ27444444-4-21-4-2-2-1-1-2111-2-2-2-2-1-1122-1122-10000002i2i−2i−2i00000000−i−i−i−iiiii00000000
χ28444444-4-21-4-2-2-1-1-2111-2-2-2-2-1-1122-1122-1000000−2i−2i2i2i00000000iiii−i−i−i−i00000000
χ294444-4-40440-4-400444444-4-400-4000-40000000000000000000000000000000000000
χ304444-4-40-2102233-2111-2-22233-100-3-100-30000000000000000003−33−33−33−300000000
χ314444-4-40-2102233-2111-2-22233-100-3-100-3000000000000000000−33−33−33−3300000000
χ324444-4-40-21022-3-3-2111-2-222-3-3-1003-1003000000000000000000−i3i3−i3i3i3−i3i3−i300000000
χ334444-4-40-21022-3-3-2111-2-222-3-3-1003-1003000000000000000000i3−i3i3−i3−i3i3−i3i300000000
χ3444-4-44-441-2-411-2-21-222-1-1-1-122-211-22-1-122i2i−2i−2i2i−2i0000−i−iii−i−iii0000000000000000
χ3544-4-44-441-2-411-2-21-222-1-1-1-122-211-22-1-12−2i−2i2i2i−2i2i0000ii−i−iii−i−i0000000000000000
χ3644-4-44-44-21-4-2-211-21-1-12222-1-11-2-21-122-10000002i−2i2i−2i00000000−i−iii−i−iii00000000
χ3744-4-44-44-21-4-2-211-21-1-12222-1-11-2-21-122-1000000−2i2i−2i2i00000000ii−i−iii−i−i00000000
χ3844-4-44-4-41-2411221-222-1-1-1-1-2-2-2-1-12211-22i2i−2i−2i−2i2i0000−i−iiiii−i−i0000000000000000
χ3944-4-44-4-41-2411221-222-1-1-1-1-2-2-2-1-12211-2−2i−2i2i2i2i−2i0000ii−i−i−i−iii0000000000000000
χ4044-4-44-4-4-214-2-2-1-1-21-1-1222211122-1-1-2-210000002-2-2200000000-1-11111-1-100000000
χ4144-4-44-4-4-214-2-2-1-1-21-1-1222211122-1-1-2-21000000-222-20000000011-1-1-1-11100000000
χ4244-4-4-440440-4-40044-4-4-4-44400-400040000000000000000000000000000000000000
χ4344-4-4-440-2102233-21-1-122-2-2-3-3-100-31003000000000000000000−i3i3i3−i3−i3i3i3−i300000000
χ4444-4-4-440-2102233-21-1-122-2-2-3-3-100-31003000000000000000000i3−i3−i3i3i3−i3−i3i300000000
χ4544-4-4-440-21022-3-3-21-1-122-2-233-1003100-30000000000000000003−3−33−333−300000000
χ4644-4-4-440-21022-3-3-21-1-122-2-233-1003100-3000000000000000000−333−33−3−3300000000
χ474-44i−4i0001-203-3−2i32i3-122i−2ii−i3i−3i23−230−i3i3003−302ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000000000000000
χ484-44i−4i0001-203-3−2i32i3-122i−2ii−i3i−3i23−230−i3i3003−30−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000000000000000
χ494-44i−4i0001-203-32i3−2i3-122i−2ii−i3i−3i−23230i3−i300−3302ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000000000000000
χ504-44i−4i0001-203-32i3−2i3-122i−2ii−i3i−3i−23230i3−i300−330−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000000000000000
χ514-44i−4i0004400000-4-4−4i4i4i−4i0000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000000000000000
χ524-44i−4i0004400000-4-4−4i4i4i−4i000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000000000000000
χ534-4−4i4i0001-203-3−2i32i3-12−2i2i−ii−3i3i−23230−i3i300−330−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000000000000000
χ544-4−4i4i0001-203-3−2i32i3-12−2i2i−ii−3i3i−23230−i3i300−3302ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000000000000000
χ554-4−4i4i0001-203-32i3−2i3-12−2i2i−ii−3i3i23−230i3−i3003−30−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000000000000000
χ564-4−4i4i0001-203-32i3−2i3-12−2i2i−ii−3i3i23−230i3−i3003−302ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000000000000000
χ574-4−4i4i0004400000-4-44i−4i−4i4i000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000000000000000
χ584-4−4i4i0004400000-4-44i−4i−4i4i0000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000000000000000
χ598888-8-802-40-2-2002-4-4-422-2-200400040000000000000000000000000000000000000
χ6088-8-8-8802-40-2-2002-444-2-222004000-40000000000000000000000000000000000000
χ618-88i−8i0002-40-6600-244i−4i2i−2i−6i6i00000000000000000000000000000000000000000000
χ628-88i−8i000-42000−2i32i34-2−2i2i−4i4i0023−2302i3−2i300−232300000000000000000000000000000000000
χ638-88i−8i000-420002i3−2i34-2−2i2i−4i4i00−23230−2i32i30023−2300000000000000000000000000000000000
χ648-8−8i8i0002-40-6600-24−4i4i−2i2i6i−6i00000000000000000000000000000000000000000000
χ658-8−8i8i000-42000−2i32i34-22i−2i4i−4i00−232302i3−2i30023−2300000000000000000000000000000000000
χ668-8−8i8i000-420002i3−2i34-22i−2i4i−4i0023−230−2i32i300−232300000000000000000000000000000000000

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