Finite Group Databasebeta

← Group #11772575

Character table — Group #11772575

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size1111224444444444444444448888888888888888888888888836363636363636367272727272727272
order1244242334666666121212121212121266668812121212242424242424242424242424242424242244888844444444
χ1111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1iiii−i−i−i−i
χ411111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii
χ51111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1
χ61111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111
χ71111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−i−i−iii
χ81111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−iiiii−i−i
χ911-1-11-1111-1111111-1-1-1-1-1-1-1-11111i−i-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1-11-1ii−i−i1-1i−i1-1i−i
χ1011-1-11-1111-1111111-1-1-1-1-1-1-1-11111i−i-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1-11-1ii−i−i-11−ii-11−ii
χ1111-1-11-1111-1111111-1-1-1-1-1-1-1-11111i−i-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-11-11−i−iiii−i-11−ii1-1
χ1211-1-11-1111-1111111-1-1-1-1-1-1-1-11111i−i-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-11-11−i−iii−ii1-1i−i-11
χ1311-1-11-1111-1111111-1-1-1-1-1-1-1-11111−ii-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1-11-1−i−iii1-1−ii1-1−ii
χ1411-1-11-1111-1111111-1-1-1-1-1-1-1-11111−ii-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1-11-1−i−iii-11i−i-11i−i
χ1511-1-11-1111-1111111-1-1-1-1-1-1-1-11111−ii-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-11-11ii−i−ii−i1-1−ii-11
χ1611-1-11-1111-1111111-1-1-1-1-1-1-1-11111−ii-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-11-11ii−i−i−ii-11i−i1-1
χ17222222-222-222222222222222-2-2-2-200-2-2-2-200000000000000002-2-22000000000000
χ18222222-222-222222222222222-2-2-2-200-2-2-2-20000000000000000-222-2000000000000
χ1922-2-22-2-2222222222-2-2-2-2-2-2-2-2-2-2-2-2002222000000000000000022-2-2000000000000
χ2022-2-22-2-2222222222-2-2-2-2-2-2-2-2-2-2-2-20022220000000000000000-2-222000000000000
χ2144444441-2411-2-21-211-2-211-2-211-2-24411-2-21111-2-2-2-21111-2-2-2-20000000000000000
χ2244444441-2411-2-21-211-2-211-2-211-2-2-4-411-2-2-1-1-1-12222-1-1-1-122220000000000000000
χ234444444-214-2-211-21-2-211-2-211-2-21144-2-211-2-2-2-21111-2-2-2-211110000000000000000
χ244444444-214-2-211-21-2-211-2-211-2-211-4-4-2-2112222-1-1-1-12222-1-1-1-10000000000000000
χ25444444-41-2-411-2-21-211-2-211-2-2-1-12200-1-12233-3-3000033-3-300000000000000000000
χ26444444-41-2-411-2-21-211-2-211-2-2-1-12200-1-122-3-3330000-3-33300000000000000000000
χ27444444-4-21-4-2-211-21-2-211-2-21122-1-10022-1-1000033-3-3000033-3-30000000000000000
χ28444444-4-21-4-2-211-21-2-211-2-21122-1-10022-1-10000-3-3330000-3-3330000000000000000
χ294444-4-401-20-1-1221-211-2-2-1-1223-300003-3003−33−30023−233−33−30023−230000000000000000
χ304444-4-401-20-1-1221-211-2-2-1-1223-300003-300−33−3300−2323−33−3300−23230000000000000000
χ314444-4-401-20-1-1221-211-2-2-1-122-330000-33003−3−3323−23003−3−3323−23000000000000000000
χ324444-4-401-20-1-1221-211-2-2-1-122-330000-3300−333−3−232300−333−3−2323000000000000000000
χ334444-4-40440-4-4-4-4444444-4-4-4-4000000000000000000000000000000000000000000
χ344444-4-40-21022-1-1-21-2-21122-1-1003-300003-30023−233−3−330023−233−3−330000000000000000
χ354444-4-40-21022-1-1-21-2-21122-1-1003-300003-300−2323−333−300−2323−333−30000000000000000
χ364444-4-40-21022-1-1-21-2-21122-1-100-330000-3323−2300−33−3323−2300−33−330000000000000000
χ374444-4-40-21022-1-1-21-2-21122-1-100-330000-33−2323003−33−3−2323003−33−30000000000000000
χ3844-4-44-441-2-411-2-21-2-1-122-1-12211-2-24i−4i-1-122iiii−2i−2i−2i−2i−i−i−i−i2i2i2i2i0000000000000000
χ3944-4-44-441-2-411-2-21-2-1-122-1-12211-2-2−4i4i-1-122−i−i−i−i2i2i2i2iiiii−2i−2i−2i−2i0000000000000000
χ4044-4-44-44-21-4-2-211-2122-1-122-1-1-2-2114i−4i22-1-1−2i−2i−2i−2iiiii2i2i2i2i−i−i−i−i0000000000000000
χ4144-4-44-44-21-4-2-211-2122-1-122-1-1-2-211−4i4i22-1-12i2i2i2i−i−i−i−i−2i−2i−2i−2iiiii0000000000000000
χ4244-4-44-4-41-2411-2-21-2-1-122-1-122-1-1220011-2-23i3i−3i−3i0000−3i−3i3i3i00000000000000000000
χ4344-4-44-4-41-2411-2-21-2-1-122-1-122-1-1220011-2-2−3i−3i3i3i00003i3i−3i−3i00000000000000000000
χ4444-4-44-4-4-214-2-211-2122-1-122-1-122-1-100-2-21100003i3i−3i−3i0000−3i−3i3i3i0000000000000000
χ4544-4-44-4-4-214-2-211-2122-1-122-1-122-1-100-2-2110000−3i−3i3i3i00003i3i−3i−3i0000000000000000
χ4644-4-4-4401-20-1-1221-2-1-12211-2-23-30000-3300−i3i3−i3i300−2i32i3i3−i3i3−i3002i3−2i30000000000000000
χ4744-4-4-4401-20-1-1221-2-1-12211-2-23-30000-3300i3−i3i3−i3002i3−2i3−i3i3−i3i300−2i32i30000000000000000
χ4844-4-4-4401-20-1-1221-2-1-12211-2-2-3300003-300−i3i3i3−i3−2i32i300i3−i3−i3i32i3−2i3000000000000000000
χ4944-4-4-4401-20-1-1221-2-1-12211-2-2-3300003-300i3−i3−i3i32i3−2i300−i3i3i3−i3−2i32i3000000000000000000
χ5044-4-4-440440-4-4-4-444-4-4-4-44444000000000000000000000000000000000000000000
χ5144-4-4-440-21022-1-1-2122-1-1-2-211003-30000-3300−2i32i3−i3i3i3−i3002i3−2i3i3−i3−i3i30000000000000000
χ5244-4-4-440-21022-1-1-2122-1-1-2-211003-30000-33002i3−2i3i3−i3−i3i300−2i32i3−i3i3i3−i30000000000000000
χ5344-4-4-440-21022-1-1-2122-1-1-2-21100-3300003-3−2i32i300i3−i3i3−i32i3−2i300−i3i3−i3i30000000000000000
χ5444-4-4-440-21022-1-1-2122-1-1-2-21100-3300003-32i3−2i300−i3i3−i3i3−2i32i300i3−i3i3−i30000000000000000
χ554-44i−4i0004400000-4-44i−4i4i−4i00000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000
χ564-44i−4i0004400000-4-44i−4i4i−4i0000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000
χ574-4−4i4i0004400000-4-4−4i4i−4i4i0000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000
χ584-4−4i4i0004400000-4-4−4i4i−4i4i00000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000
χ598-88i−8i0002-406-600-242i−2i−4i4i6i−6i00000000000000000000000000000000000000000000
χ608-88i−8i0002-40-6600-242i−2i−4i4i−6i6i00000000000000000000000000000000000000000000
χ618-88i−8i000-420006-64-2−4i4i2i−2i006i−6i000000000000000000000000000000000000000000
χ628-88i−8i000-42000-664-2−4i4i2i−2i00−6i6i000000000000000000000000000000000000000000
χ638-8−8i8i0002-406-600-24−2i2i4i−4i−6i6i00000000000000000000000000000000000000000000
χ648-8−8i8i0002-40-6600-24−2i2i4i−4i6i−6i00000000000000000000000000000000000000000000
χ658-8−8i8i000-420006-64-24i−4i−2i2i00−6i6i000000000000000000000000000000000000000000
χ668-8−8i8i000-42000-664-24i−4i−2i2i006i−6i000000000000000000000000000000000000000000

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