Finite Group Databasebeta

← Group #11772579

Character table — Group #11772579

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size1111224444444444444444448888888812121212242424242424242424242424242424242424242424243636363672727272
order1244242334666666121212121212121266661212121288884444881212121212121212242424242424242422444444
χ1111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ311111111111111111111111111111111-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
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
χ5111111-111-11111-1-111-1-111111-1-1-11-1-1-11111ii−i−i-1-1iiii−i−i−i−i1111-1-1-1-11-11-1ii−i−i
χ6111111-111-11111-1-111-1-111111-1-1-11-1-1-11111−i−iii-1-1−i−i−i−iiiii1111-1-1-1-11-11-1−i−iii
χ7111111-111-11111-1-111-1-111111-1-1-11-1-1-1-1-1-1-1ii−i−i11iiii−i−i−i−i-1-1-1-111111-11-1−i−iii
χ8111111-111-11111-1-111-1-111111-1-1-11-1-1-1-1-1-1-1−i−iii11−i−i−i−iiiii-1-1-1-111111-11-1ii−i−i
χ911-1-11-1111-1111111-1-1-1-1-1-1-1-11111-1-1-1-1ii−i−i1-11-1i−i11-1-111-1-1ii−i−iii−i−i1-1-11i−ii−i
χ1011-1-11-1111-1111111-1-1-1-1-1-1-1-11111-1-1-1-1ii−i−i-11-11i−i-1-111-1-111ii−i−iii−i−i1-1-11−ii−ii
χ1111-1-11-1111-1111111-1-1-1-1-1-1-1-11111-1-1-1-1−i−iii1-11-1−ii11-1-111-1-1−i−iii−i−iii1-1-11−ii−ii
χ1211-1-11-1111-1111111-1-1-1-1-1-1-1-11111-1-1-1-1−i−iii-11-11−ii-1-111-1-111−i−iii−i−iii1-1-11i−ii−i
χ1311-1-11-1-11111111-1-1-1-111-1-1-1-11-1-1-1-1111ii−i−ii−i−ii−iiii−i−i−i−iiiii−i−i−i−iii11-1-1-111-1
χ1411-1-11-1-11111111-1-1-1-111-1-1-1-11-1-1-1-1111ii−i−i−iii−i−ii−i−iiiii−i−iii−i−i−i−iii11-1-11-1-11
χ1511-1-11-1-11111111-1-1-1-111-1-1-1-11-1-1-1-1111−i−iiii−i−iii−iii−i−i−i−iii−i−iiiii−i−i11-1-11-1-11
χ1611-1-11-1-11111111-1-1-1-111-1-1-1-11-1-1-1-1111−i−iii−iii−ii−i−i−iiiii−i−i−i−iiiii−i−i11-1-1-111-1
χ172222222222222222222222222222222200000000000000000000000000-2-2-2-20000
χ18222222-222-22222-2-222-2-222222-2-2-22-2-2-200000000000000000000000000-22-220000
χ1922-2-22-2222-2222222-2-2-2-2-2-2-2-22222-2-2-2-200000000000000000000000000-222-20000
χ2022-2-22-2-22222222-2-2-2-222-2-2-2-22-2-2-2-222200000000000000000000000000-2-2220000
χ2144444441-24111-2-2-2-2-2-2-21111-211-2-211-2222200002200000000-1-1-1-1-1-1-1-100000000
χ2244444441-24111-2-2-2-2-2-2-21111-211-2-211-2-2-2-2-20000-2-2000000001111111100000000
χ234444444-214-2-2-21111111-2-2-2-21-2-211-2-210000222200-1-1-1-1-1-1-1-10000000000000000
χ244444444-214-2-2-21111111-2-2-2-21-2-211-2-210000-2-2-2-200111111110000000000000000
χ25444444-41-2-4111-222-2-2221111-2-1-12-2-1-1222220000-2-200000000-1-1-1-1111100000000
χ26444444-41-2-4111-222-2-2221111-2-1-12-2-1-12-2-2-2-2000022000000001111-1-1-1-100000000
χ27444444-4-21-4-2-2-21-1-111-1-1-2-2-2-2122-1122-100002i2i−2i−2i00−i−i−i−iiiii0000000000000000
χ28444444-4-21-4-2-2-21-1-111-1-1-2-2-2-2122-1122-10000−2i−2i2i2i00iiii−i−i−i−i0000000000000000
χ294444-4-40440-4-44400440044-4-4-4000-40000000000000000000000000000000000000
χ304444-4-40-21022-21331133-2-222-100-3-100-300000000003−33−33−33−30000000000000000
χ314444-4-40-21022-21331133-2-222-100-3-100-30000000000−33−33−33−330000000000000000
χ324444-4-40-21022-21-3-311-3-3-2-222-1003-10030000000000−i3i3−i3i3i3−i3i3−i30000000000000000
χ334444-4-40-21022-21-3-311-3-3-2-222-1003-10030000000000i3−i3i3−i3−i3i3−i3i30000000000000000
χ3444-4-44-441-2-4111-2-2-22222-1-1-1-1-211-22-1-122i2i−2i−2i00002i−2i00000000−i−iii−i−iii00000000
χ3544-4-44-441-2-4111-2-2-22222-1-1-1-1-211-22-1-12−2i−2i2i2i0000−2i2i00000000ii−i−iii−i−i00000000
χ3644-4-44-44-21-4-2-2-2111-1-1-1-122221-2-21-122-100002-22-200-1-111-1-1110000000000000000
χ3744-4-44-44-21-4-2-2-2111-1-1-1-122221-2-21-122-10000-22-220011-1-111-1-10000000000000000
χ3844-4-44-4-41-24111-22222-2-2-1-1-1-1-2-1-12211-22i2i−2i−2i0000−2i2i00000000−i−iiiii−i−i00000000
χ3944-4-44-4-41-24111-22222-2-2-1-1-1-1-2-1-12211-2−2i−2i2i2i00002i−2i00000000ii−i−i−i−iii00000000
χ4044-4-44-4-4-214-2-2-21-1-1-1-1112222122-1-1-2-2100002i−2i−2i2i00−i−iiiii−i−i0000000000000000
χ4144-4-44-4-4-214-2-2-21-1-1-1-1112222122-1-1-2-210000−2i2i2i−2i00ii−i−i−i−iii0000000000000000
χ4244-4-4-440440-4-44400-4-400-4-444-400040000000000000000000000000000000000000
χ4344-4-4-440-21022-2133-1-1-3-322-2-2-100-3100300000000003−3−333−3−330000000000000000
χ4444-4-4-440-21022-2133-1-1-3-322-2-2-100-310030000000000−333−3−333−30000000000000000
χ4544-4-4-440-21022-21-3-3-1-13322-2-2-1003100-30000000000−i3i3i3−i3i3−i3−i3i30000000000000000
χ4644-4-4-440-21022-21-3-3-1-13322-2-2-1003100-30000000000i3−i3−i3i3−i3i3i3−i30000000000000000
χ474-44i−4i0001-203-3-12−2i32i32i−2i23−23i−i3i−3i0−i3i3003−302ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000000000ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ1300000000
χ484-44i−4i0001-203-3-12−2i32i32i−2i23−23i−i3i−3i0−i3i3003−30−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000000000−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ1300000000
χ494-44i−4i0001-203-3-122i3−2i32i−2i−2323i−i3i−3i0i3−i300−3302ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000000000ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ1300000000
χ504-44i−4i0001-203-3-122i3−2i32i−2i−2323i−i3i−3i0i3−i300−330−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000000000−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ1300000000
χ514-44i−4i00044000-4-400−4i4i004i−4i00000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000
χ524-44i−4i00044000-4-400−4i4i004i−4i0000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000
χ534-4−4i4i0001-203-3-12−2i32i3−2i2i−2323−ii−3i3i0−i3i300−330−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000000000−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ2300000000
χ544-4−4i4i0001-203-3-12−2i32i3−2i2i−2323−ii−3i3i0−i3i300−3302ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000000000ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ2300000000
χ554-4−4i4i0001-203-3-122i3−2i3−2i2i23−23−ii−3i3i0i3−i3003−30−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000000000−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ2300000000
χ564-4−4i4i0001-203-3-122i3−2i3−2i2i23−23−ii−3i3i0i3−i3003−302ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000000000ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ2300000000
χ574-4−4i4i00044000-4-4004i−4i00−4i4i0000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000
χ584-4−4i4i00044000-4-4004i−4i00−4i4i00000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000
χ598888-8-802-40-2-22-400-4-40022-2-2400040000000000000000000000000000000000000
χ6088-8-8-8802-40-2-22-4004400-2-2224000-40000000000000000000000000000000000000
χ618-88i−8i0002-40-66-24004i−4i002i−2i−6i6i000000000000000000000000000000000000000000
χ628-88i−8i000-420004-2−2i32i3−2i2i23−23−4i4i0002i3−2i300−232300000000000000000000000000000000000
χ638-88i−8i000-420004-22i3−2i3−2i2i−2323−4i4i000−2i32i30023−2300000000000000000000000000000000000
χ648-8−8i8i0002-40-66-2400−4i4i00−2i2i6i−6i000000000000000000000000000000000000000000
χ658-8−8i8i000-420004-2−2i32i32i−2i−23234i−4i0002i3−2i30023−2300000000000000000000000000000000000
χ668-8−8i8i000-420004-22i3−2i32i−2i23−234i−4i000−2i32i300−232300000000000000000000000000000000000

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