Finite Group Databasebeta

← Group #11797988

Character table — Group #11797988

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57
size1122244444444444444888888888824242424242424242424242424242424363636364848484872727272
order12244334466661212121212126121212121212121212222444666688121212128888612242416161616
χ1111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111-1-1111111-1-111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ51111111-1-11111-1-1-1-111111-1-11-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1
χ61111111-1-11111-1-1-1-111111-1-11-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111-1-111-1-111
χ71111111-1-11111-1-1-1-111111-1-11-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1-1-111
χ81111111-1-11111-1-1-1-111111-1-11-1-1-1-1-1-1-1-111-1-1-1-1111111-1-111-1-11111-1-1
χ911-11-111i−i1-11-1ii−i−i-1-1-11-1i−i1ii−i−i1-11-1i−i11-1-1i−iii−i−ii−i1-11-1i−i1-1i−i
χ1011-11-111i−i1-11-1ii−i−i-1-1-11-1i−i1ii−i−i1-1-11i−i11-1-1−iiii−i−ii−i1-1-11−ii-11−ii
χ1111-11-111i−i1-11-1ii−i−i-1-1-11-1i−i1ii−i−i-111-1−ii-1-111i−i−i−iiii−i1-11-1i−i-11−ii
χ1211-11-111i−i1-11-1ii−i−i-1-1-11-1i−i1ii−i−i-11-11−ii-1-111−ii−i−iiii−i1-1-11−ii1-1i−i
χ1311-11-111−ii1-11-1−i−iii-1-1-11-1−ii1−i−iii1-11-1−ii11-1-1−ii−i−iii−ii1-11-1−ii1-1−ii
χ1411-11-111−ii1-11-1−i−iii-1-1-11-1−ii1−i−iii1-1-11−ii11-1-1i−i−i−iii−ii1-1-11i−i-11i−i
χ1511-11-111−ii1-11-1−i−iii-1-1-11-1−ii1−i−iii-111-1i−i-1-111−iiii−i−i−ii1-11-1−ii-11i−i
χ1611-11-111−ii1-11-1−i−iii-1-1-11-1−ii1−i−iii-11-11i−i-1-111i−iii−i−i−ii1-1-11i−i1-1−ii
χ17222222222222222222222222222220000000000000000-2-2-2-200000000
χ182222222-2-22222-2-2-2-222222-2-22-2-2-2-2000000000000000022-2-200000000
χ1922-22-2222i−2i2-22-22i2i−2i−2i-2-2-22-22i−2i22i2i−2i−2i0000000000000000−2i2i-2200000000
χ2022-22-222−2i2i2-22-2−2i−2i2i2i-2-2-22-2−2i2i2−2i−2i2i2i00000000000000002i−2i-2200000000
χ21444441-244-2-21-2-2-2-2-2111-2-2-2-21111100220000002200000000-1-1-1-10000
χ22444441-244-2-21-2-2-2-2-2111-2-2-2-21111100-2-2000000-2-20000000011110000
χ23444441-2-4-4-2-21-22222111-2-2221-1-1-1-10022000000-2-200000000-1-1110000
χ24444441-2-4-4-2-21-22222111-2-2221-1-1-1-100-2-2000000220000000011-1-10000
χ2544444-214411-211111-2-2-21111-2-2-2-2-2220022-1-1-1-100-1-1-1-1000000000000
χ2644444-214411-211111-2-2-21111-2-2-2-2-2-2-200-2-21111001111000000000000
χ2744444-21-4-411-21-1-1-1-1-2-2-211-1-1-222222200-2-2-1-1-1-1001111000000000000
χ2844444-21-4-411-21-1-1-1-1-2-2-211-1-1-22222-2-20022111100-1-1-1-1000000000000
χ29444-4-4440044440000-4-44-4-400-400000000000000000000000000000000
χ30444-4-4-210011-21333322-2-1-1-3-320000000000−i3i3−i3i300−i3i3−i3i3000000000000
χ31444-4-4-210011-21333322-2-1-1-3-320000000000i3−i3i3−i300i3−i3i3−i3000000000000
χ32444-4-4-210011-21-3-3-3-322-2-1-13320000000000−i3i3−i3i300i3−i3i3−i3000000000000
χ33444-4-4-210011-21-3-3-3-322-2-1-13320000000000i3−i3i3−i300−i3i3−i3i3000000000000
χ3444-44-41-24i−4i-2212−2i−2i2i2i-1-1-1-22−2i2i1ii−i−i002-20000002i−2i00000000-11−ii0000
χ3544-44-41-24i−4i-2212−2i−2i2i2i-1-1-1-22−2i2i1ii−i−i00-22000000−2i2i000000001-1i−i0000
χ3644-44-41-2−4i4i-22122i2i−2i−2i-1-1-1-222i−2i1−i−iii002-2000000−2i2i00000000-11i−i0000
χ3744-44-41-2−4i4i-22122i2i−2i−2i-1-1-1-222i−2i1−i−iii00-220000002i−2i000000001-1−ii0000
χ3844-44-4-214i−4i1-1-2-1ii−i−i2221-1i−i-2−2i−2i2i2i2-2002i−2i-1-11100−i−iii000000000000
χ3944-44-4-214i−4i1-1-2-1ii−i−i2221-1i−i-2−2i−2i2i2i-2200−2i2i11-1-100ii−i−i000000000000
χ4044-44-4-21−4i4i1-1-2-1−i−iii2221-1−ii-22i2i−2i−2i2-200−2i2i-1-11100ii−i−i000000000000
χ4144-44-4-21−4i4i1-1-2-1−i−iii2221-1−ii-22i2i−2i−2i-22002i−2i11-1-100−i−iii000000000000
χ4244-4-4444004-44-4000044-4-4400-400000000000000000000000000000000
χ4344-4-44-21001-1-2-13i3i−3i−3i-2-22-11−3i3i20000000000−i3i3i3−i3003−3−33000000000000
χ4444-4-44-21001-1-2-13i3i−3i−3i-2-22-11−3i3i20000000000i3−i3−i3i300−333−3000000000000
χ4544-4-44-21001-1-2-1−3i−3i3i3i-2-22-113i−3i20000000000−i3i3i3−i300−333−3000000000000
χ4644-4-44-21001-1-2-1−3i−3i3i3i-2-22-113i−3i20000000000i3−i3−i3i3003−3−33000000000000
χ47888-8-82-400-4-42-40000-2-224400-200000000000000000000000000000000
χ4888-8-882-400-4424000022-24-400-200000000000000000000000000000000
χ498-80002-40040-20−2ζ2−2ζ7+2ζ10+2ζ112ζ2+2ζ7−2ζ10−2ζ11−2ζ2+2ζ7+2ζ10−2ζ112ζ2−2ζ7−2ζ10+2ζ116i−6i000000−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ110000000000000000000000000000
χ508-80002-40040-20−2ζ2+2ζ7+2ζ10−2ζ112ζ2−2ζ7−2ζ10+2ζ11−2ζ2−2ζ7+2ζ10+2ζ112ζ2+2ζ7−2ζ10−2ζ11−6i6i000000−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ110000000000000000000000000000
χ518-80002-40040-202ζ2−2ζ7−2ζ10+2ζ11−2ζ2+2ζ7+2ζ10−2ζ112ζ2+2ζ7−2ζ10−2ζ11−2ζ2−2ζ7+2ζ10+2ζ11−6i6i000000ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ110000000000000000000000000000
χ528-80002-40040-202ζ2+2ζ7−2ζ10−2ζ11−2ζ2−2ζ7+2ζ10+2ζ112ζ2−2ζ7−2ζ10+2ζ11−2ζ2+2ζ7+2ζ10−2ζ116i−6i000000ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ110000000000000000000000000000
χ538-80008800-80-8000000000000000000000000000000000000000000000
χ548-8000-4200-264-6−2i32i3−2i32i3000000002i3−2i32i3−2i30000000000000000000000000000
χ558-8000-4200-264-62i3−2i32i3−2i300000000−2i32i3−2i32i30000000000000000000000000000
χ568-8000-4200-2-64623−23−232300000000−232323−230000000000000000000000000000
χ578-8000-4200-2-646−232323−230000000023−23−23230000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.