Finite Group Databasebeta

← Group #11771420

Character table — Group #11771420

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size1111224444444444444444448888888812121212242424242424242424242424242424242424242424243636363672727272
order124424336666881212121212122424242461224242424242422446688121216161616242424244848484848484848248816161616
χ1111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1
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
χ5111111111111-1-1111111-1-1-1-111-1-1-1-1-1-1111111-1-111ii−i−i-1-1-1-1iiii−i−i−i−i11-1-1ii−i−i
χ6111111111111-1-1111111-1-1-1-111-1-1-1-1-1-1111111-1-111−i−iii-1-1-1-1−i−i−i−iiiii11-1-1−i−iii
χ7111111111111-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1ii−i−i1111iiii−i−i−i−i11-1-1−i−iii
χ8111111111111-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1−i−iii1111−i−i−i−iiiii11-1-1ii−i−i
χ911-1-11-1111111i−i-1-1-1-1-1-1ii−i−i1-1iii−i−i−i11-1-111i−i-1-1ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ii−i−iζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ131-1i−iζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13
χ1011-1-11-1111111i−i-1-1-1-1-1-1ii−i−i1-1iii−i−i−i11-1-111i−i-1-1−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ii−i−i−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ131-1i−i−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13
χ1111-1-11-1111111i−i-1-1-1-1-1-1ii−i−i1-1iii−i−i−i-1-111-1-1−ii11ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−i−iiiζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ131-1i−i−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13
χ1211-1-11-1111111i−i-1-1-1-1-1-1ii−i−i1-1iii−i−i−i-1-111-1-1−ii11−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−i−iii−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ131-1i−iζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13
χ1311-1-11-1111111−ii-1-1-1-1-1-1−i−iii1-1−i−i−iiii11-1-111−ii-1-1−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−i−iii−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ231-1−ii−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23
χ1411-1-11-1111111−ii-1-1-1-1-1-1−i−iii1-1−i−i−iiii11-1-111−ii-1-1ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−i−iiiζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ231-1−iiζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23
χ1511-1-11-1111111−ii-1-1-1-1-1-1−i−iii1-1−i−i−iiii-1-111-1-1i−i11−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23ii−i−i−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ231-1−iiζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23
χ1611-1-11-1111111−ii-1-1-1-1-1-1−i−iii1-1−i−i−iiii-1-111-1-1i−i11ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ii−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
χ18222222222222-2-2222222-2-2-2-222-2-2-2-2-2-200000000000000000000000000-2-2220000
χ1922-2-22-22222222i−2i-2-2-2-2-2-22i2i−2i−2i2-22i2i2i−2i−2i−2i00000000000000000000000000-22−2i2i0000
χ2022-2-22-2222222−2i2i-2-2-2-2-2-2−2i−2i2i2i2-2−2i−2i−2i2i2i2i00000000000000000000000000-222i−2i0000
χ214444441-2-2-21-24411-2-2-2-21111111-2-21-2-2000000000022220000-1-1-1-1-1-1-1-100000000
χ224444441-2-2-21-24411-2-2-2-21111111-2-21-2-20000000000-2-2-2-200001111111100000000
χ234444441-2-2-21-2-4-411-2-2-2-2-1-1-1-111-122-12200000000002i2i−2i−2i0000−i−i−i−iiiii00000000
χ244444441-2-2-21-2-4-411-2-2-2-2-1-1-1-111-122-1220000000000−2i−2i2i2i0000iiii−i−i−i−i00000000
χ25444444-2111-2144-2-21111-2-2-2-2-2-2-211-2112222-1-122-1-10000-1-1-1-10000000000000000
χ26444444-2111-2144-2-21111-2-2-2-2-2-2-211-211-2-2-2-211-2-211000011110000000000000000
χ27444444-2111-21-4-4-2-211112222-2-22-1-12-1-12222-1-1-2-2-1-1000011110000000000000000
χ28444444-2111-21-4-4-2-211112222-2-22-1-12-1-1-2-2-2-21122110000-1-1-1-10000000000000000
χ294444-4-41-2221-20011-2-2223333-1-1-300-3000000000000000000003−33−33−33−300000000
χ304444-4-41-2221-20011-2-2223333-1-1-300-300000000000000000000−33−33−33−3300000000
χ314444-4-41-2221-20011-2-222-3-3-3-3-1-1300300000000000000000000−i3i3−i3i3i3−i3i3−i300000000
χ324444-4-41-2221-20011-2-222-3-3-3-3-1-1300300000000000000000000i3−i3i3−i3−i3i3−i3i300000000
χ334444-4-444-4-444004444-4-40000-4-40000000000000000000000000000000000000000
χ3444-4-44-41-2-2-21-24i−4i-1-12222ii−i−i1-1i−2i−2i−i2i2i00000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ1300000000
χ3544-4-44-41-2-2-21-24i−4i-1-12222ii−i−i1-1i−2i−2i−i2i2i0000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ1300000000
χ3644-4-44-41-2-2-21-2−4i4i-1-12222−i−iii1-1−i2i2ii−2i−2i0000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ2300000000
χ3744-4-44-41-2-2-21-2−4i4i-1-12222−i−iii1-1−i2i2ii−2i−2i00000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ2300000000
χ3844-4-44-4-2111-214i−4i22-1-1-1-1−2i−2i2i2i-22−2iii2i−i−i22-2-2-1-12i−2i110000−i−iii0000000000000000
χ3944-4-44-4-2111-214i−4i22-1-1-1-1−2i−2i2i2i-22−2iii2i−i−i-2-22211−2i2i-1-10000ii−i−i0000000000000000
χ4044-4-44-4-2111-21−4i4i22-1-1-1-12i2i−2i−2i-222i−i−i−2iii22-2-2-1-1−2i2i110000ii−i−i0000000000000000
χ4144-4-44-4-2111-21−4i4i22-1-1-1-12i2i−2i−2i-222i−i−i−2iii-2-222112i−2i-1-10000−i−iii0000000000000000
χ4244-4-4-441-2221-200-1-122-2-23i3i−3i−3i-11−3i003i00000000000000000000ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ2300000000
χ4344-4-4-441-2221-200-1-122-2-23i3i−3i−3i-11−3i003i00000000000000000000−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ2300000000
χ4444-4-4-441-2221-200-1-122-2-2−3i−3i3i3i-113i00−3i00000000000000000000−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ1300000000
χ4544-4-4-441-2221-200-1-122-2-2−3i−3i3i3i-113i00−3i00000000000000000000ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ1300000000
χ4644-4-4-4444-4-44400-4-4-4-4440000-440000000000000000000000000000000000000000
χ474-44i−4i004400-4-4004i−4i4i−4i000000000000002-22i−2i2-2002i−2i000000000000000000000000
χ484-44i−4i004400-4-4004i−4i4i−4i00000000000000-22−2i2i-2200−2i2i000000000000000000000000
χ494-44i−4i00-213-32-100−2i2ii−i3i−3i−2ζ7+2ζ232ζ7−2ζ232ζ5−2ζ13−2ζ5+2ζ13000−ζ7+ζ23ζ7−ζ230ζ5−ζ13−ζ5+ζ132-22i−2i-1100−ii0000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000000000000000
χ504-44i−4i00-213-32-100−2i2ii−i3i−3i−2ζ7+2ζ232ζ7−2ζ232ζ5−2ζ13−2ζ5+2ζ13000−ζ7+ζ23ζ7−ζ230ζ5−ζ13−ζ5+ζ13-22−2i2i1-100i−i0000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000000000000000
χ514-44i−4i00-213-32-100−2i2ii−i3i−3i2ζ7−2ζ23−2ζ7+2ζ23−2ζ5+2ζ132ζ5−2ζ13000ζ7−ζ23−ζ7+ζ230−ζ5+ζ13ζ5−ζ132-22i−2i-1100−ii0000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000000000000000
χ524-44i−4i00-213-32-100−2i2ii−i3i−3i2ζ7−2ζ23−2ζ7+2ζ23−2ζ5+2ζ132ζ5−2ζ13000ζ7−ζ23−ζ7+ζ230−ζ5+ζ13ζ5−ζ13-22−2i2i1-100i−i0000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000000000000000
χ534-4−4i4i004400-4-400−4i4i−4i4i000000000000002-2−2i2i2-200−2i2i000000000000000000000000
χ544-4−4i4i004400-4-400−4i4i−4i4i00000000000000-222i−2i-22002i−2i000000000000000000000000
χ554-4−4i4i00-213-32-1002i−2i−ii−3i3i2ζ5−2ζ13−2ζ5+2ζ13−2ζ7+2ζ232ζ7−2ζ23000ζ5−ζ13−ζ5+ζ130−ζ7+ζ23ζ7−ζ232-2−2i2i-1100i−i0000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000000000000000
χ564-4−4i4i00-213-32-1002i−2i−ii−3i3i2ζ5−2ζ13−2ζ5+2ζ13−2ζ7+2ζ232ζ7−2ζ23000ζ5−ζ13−ζ5+ζ130−ζ7+ζ23ζ7−ζ23-222i−2i1-100−ii0000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000000000000000
χ574-4−4i4i00-213-32-1002i−2i−ii−3i3i−2ζ5+2ζ132ζ5−2ζ132ζ7−2ζ23−2ζ7+2ζ23000−ζ5+ζ13ζ5−ζ130ζ7−ζ23−ζ7+ζ232-2−2i2i-1100i−i0000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000000000000000
χ584-4−4i4i00-213-32-1002i−2i−ii−3i3i−2ζ5+2ζ132ζ5−2ζ132ζ7−2ζ23−2ζ7+2ζ23000−ζ5+ζ13ζ5−ζ130ζ7−ζ23−ζ7+ζ23-222i−2i1-100−ii0000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000000000000000
χ598888-8-8-42-2-2-4200-4-422-2-20000440000000000000000000000000000000000000000
χ6088-8-8-88-42-2-2-420044-2-22200004-40000000000000000000000000000000000000000
χ618-88i−8i002-400-24002i−2i−4i4i00−2ζ7+2ζ232ζ7−2ζ232ζ5−2ζ13−2ζ5+2ζ130002ζ7−2ζ23−2ζ7+2ζ230−2ζ5+2ζ132ζ5−2ζ130000000000000000000000000000000000
χ628-88i−8i002-400-24002i−2i−4i4i002ζ7−2ζ23−2ζ7+2ζ23−2ζ5+2ζ132ζ5−2ζ13000−2ζ7+2ζ232ζ7−2ζ2302ζ5−2ζ13−2ζ5+2ζ130000000000000000000000000000000000
χ638-88i−8i00-42-664-200−4i4i2i−2i−6i6i0000000000000000000000000000000000000000000000
χ648-8−8i8i002-400-2400−2i2i4i−4i002ζ5−2ζ13−2ζ5+2ζ13−2ζ7+2ζ232ζ7−2ζ23000−2ζ5+2ζ132ζ5−2ζ1302ζ7−2ζ23−2ζ7+2ζ230000000000000000000000000000000000
χ658-8−8i8i002-400-2400−2i2i4i−4i00−2ζ5+2ζ132ζ5−2ζ132ζ7−2ζ23−2ζ7+2ζ230002ζ5−2ζ13−2ζ5+2ζ130−2ζ7+2ζ232ζ7−2ζ230000000000000000000000000000000000
χ668-8−8i8i00-42-664-2004i−4i−2i2i6i−6i0000000000000000000000000000000000000000000000

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