Finite Group Databasebeta

← Group #11797942

Character table — Group #11797942

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57
size1122244444444444444888888888824242424242424242424242424242424363636364848484872727272
order122443344666612121212121261212121212121212122444448812121212121212128888612242416161616
χ1111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ311111111111111111111111111111-1-11111-1-1111111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ51111111-1-11111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1
χ61111111-1-11111-1-1-1-1111111-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-11111-1-1-1-111
χ71111111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-111-1-111-1-111
χ81111111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-11111-1-1
χ911-11-111i−i-111-1ii−i−i-1-1-111-1i−iii−i−i1-11-1i−ii−i11-1-1ii−i−ii−i1-11-1i−i1-1i−i
χ1011-11-111i−i-111-1ii−i−i-1-1-111-1i−iii−i−i1-1-11−iii−i-1-111−i−iiii−i1-11-1i−i-11−ii
χ1111-11-111i−i-111-1ii−i−i-1-1-111-1i−iii−i−i-111-1i−i−ii11-1-1ii−i−ii−i1-1-11−ii-11−ii
χ1211-11-111i−i-111-1ii−i−i-1-1-111-1i−iii−i−i-11-11−ii−ii-1-111−i−iiii−i1-1-11−ii1-1i−i
χ1311-11-111−ii-111-1−i−iii-1-1-111-1−ii−i−iii1-11-1−ii−ii11-1-1−i−iii−ii1-11-1−ii1-1−ii
χ1411-11-111−ii-111-1−i−iii-1-1-111-1−ii−i−iii1-1-11i−i−ii-1-111ii−i−i−ii1-11-1−ii-11i−i
χ1511-11-111−ii-111-1−i−iii-1-1-111-1−ii−i−iii-111-1−iii−i11-1-1−i−iii−ii1-1-11i−i-11i−i
χ1611-11-111−ii-111-1−i−iii-1-1-111-1−ii−i−iii-11-11i−ii−i-1-111ii−i−i−ii1-1-11i−i1-1−ii
χ17222222222222222222222222222220000000000000000-2-2-2-200000000
χ182222222-2-22222-2-2-2-2222222-2-2-2-2-2-2000000000000000022-2-200000000
χ1922-22-2222i−2i-222-22i2i−2i−2i-2-2-222-22i−2i2i2i−2i−2i0000000000000000−2i2i-2200000000
χ2022-22-222−2i2i-222-2−2i−2i2i2i-2-2-222-2−2i2i−2i−2i2i2i00000000000000002i−2i-2200000000
χ21444441-2441-2111111-2-2-2-21111-2-2-2-200222200-1-1-1-1-1-1-1-1000000000000
χ22444441-2441-2111111-2-2-2-21111-2-2-2-200-2-2-2-20011111111000000000000
χ23444441-2-4-41-211-1-1-1-1-2-2-2-211-1-122220022-2-200-1-1-1-11111000000000000
χ24444441-2-4-41-211-1-1-1-1-2-2-2-211-1-1222200-2-222001111-1-1-1-1000000000000
χ2544444-2144-21-2-2-2-2-2-21111-2-2-2-2111122000022000000000000-1-1-1-10000
χ2644444-2144-21-2-2-2-2-2-21111-2-2-2-21111-2-20000-2-200000000000011110000
χ2744444-21-4-4-21-2-222221111-2-222-1-1-1-1220000-2-2000000000000-1-1110000
χ2844444-21-4-4-21-2-222221111-2-222-1-1-1-1-2-200002200000000000011-1-10000
χ29444-4-41-2001-211333322-22-1-1-3-3000000000000−i3i3−i3i3−i3i3−i3i3000000000000
χ30444-4-41-2001-211333322-22-1-1-3-3000000000000i3−i3i3−i3i3−i3i3−i3000000000000
χ31444-4-41-2001-211-3-3-3-322-22-1-133000000000000−i3i3−i3i3i3−i3i3−i3000000000000
χ32444-4-41-2001-211-3-3-3-322-22-1-133000000000000i3−i3i3−i3−i3i3−i3i3000000000000
χ33444-4-4440044440000-4-44-4-4-40000000000000000000000000000000000
χ3444-44-41-24i−4i-1-21-1ii−i−i222-21-1i−i−2i−2i2i2i002-22i−2i00-1-111−i−iii000000000000
χ3544-44-41-24i−4i-1-21-1ii−i−i222-21-1i−i−2i−2i2i2i00-22−2i2i0011-1-1ii−i−i000000000000
χ3644-44-41-2−4i4i-1-21-1−i−iii222-21-1−ii2i2i−2i−2i002-2−2i2i00-1-111ii−i−i000000000000
χ3744-44-41-2−4i4i-1-21-1−i−iii222-21-1−ii2i2i−2i−2i00-222i−2i0011-1-1−i−iii000000000000
χ3844-44-4-214i−4i21-22−2i−2i2i2i-1-1-11-22−2i2iii−i−i2-200002i−2i000000000000-11−ii0000
χ3944-44-4-214i−4i21-22−2i−2i2i2i-1-1-11-22−2i2iii−i−i-220000−2i2i0000000000001-1i−i0000
χ4044-44-4-21−4i4i21-222i2i−2i−2i-1-1-11-222i−2i−i−iii2-20000−2i2i000000000000-11i−i0000
χ4144-44-4-21−4i4i21-222i2i−2i−2i-1-1-11-222i−2i−i−iii-2200002i−2i0000000000001-1−ii0000
χ4244-4-441-200-1-21-13i3i−3i−3i-2-222-11−3i3i000000000000−i3i3i3−i33−3−33000000000000
χ4344-4-441-200-1-21-13i3i−3i−3i-2-222-11−3i3i000000000000i3−i3−i3i3−333−3000000000000
χ4444-4-441-200-1-21-1−3i−3i3i3i-2-222-113i−3i000000000000−i3i3i3−i3−333−3000000000000
χ4544-4-441-200-1-21-1−3i−3i3i3i-2-222-113i−3i000000000000i3−i3−i3i33−3−33000000000000
χ4644-4-444400-444-4000044-4-4-440000000000000000000000000000000000
χ47888-8-8-4200-42-4-40000-2-22-2440000000000000000000000000000000000
χ4888-8-88-420042-44000022-2-24-40000000000000000000000000000000000
χ498-80002-40064-2-623−2323−230000000023−2323−230000000000000000000000000000
χ508-80002-40064-2-6−2323−232300000000−2323−23230000000000000000000000000000
χ518-80002-400-64-26−2i32i32i3−2i300000000−2i32i32i3−2i30000000000000000000000000000
χ528-80002-400-64-262i3−2i3−2i32i3000000002i3−2i3−2i32i30000000000000000000000000000
χ538-800088000-8-8000000000000000000000000000000000000000000000
χ548-8000-42000-240−2ζ2−2ζ7+2ζ10+2ζ112ζ2+2ζ7−2ζ10−2ζ112ζ2−2ζ7−2ζ10+2ζ11−2ζ2+2ζ7+2ζ10−2ζ116i−6i000000ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ110000000000000000000000000000
χ558-8000-42000-240−2ζ2+2ζ7+2ζ10−2ζ112ζ2−2ζ7−2ζ10+2ζ112ζ2+2ζ7−2ζ10−2ζ11−2ζ2−2ζ7+2ζ10+2ζ11−6i6i000000ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ110000000000000000000000000000
χ568-8000-42000-2402ζ2−2ζ7−2ζ10+2ζ11−2ζ2+2ζ7+2ζ10−2ζ11−2ζ2−2ζ7+2ζ10+2ζ112ζ2+2ζ7−2ζ10−2ζ11−6i6i000000−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ110000000000000000000000000000
χ578-8000-42000-2402ζ2+2ζ7−2ζ10−2ζ11−2ζ2−2ζ7+2ζ10+2ζ11−2ζ2+2ζ7+2ζ10−2ζ112ζ2−2ζ7−2ζ10+2ζ116i−6i000000−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ110000000000000000000000000000

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