Finite Group Databasebeta

← Group #11786662

Character table — Group #11786662

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111224444444444444444448888888812121212121212121212121218181818242424242424242424242424242424242424363672727272
order1244242334666666121212121212121266661212121288888888888822448824242424242424242424242424242424248888
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111-111-111-1-111-1-11111111-1-1-11-1-1-11111-1-1-1-111111111-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1
χ6111111-111-111-1-111-1-11111111-1-1-11-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-111
χ7111111-111-111-1-111-1-11111111-1-1-11-1-1-1-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111
χ8111111-111-111-1-111-1-11111111-1-1-11-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-111-1-1
χ911-1-11-1111-1111111-1-1-1-1-1-1-1-11111-1-1-1-1ii−i−iii−i−iii−i−i-1-111i−iii−i−iii−i−iii−i−iii−i−i1-11-11-1
χ1011-1-11-1111-1111111-1-1-1-1-1-1-1-11111-1-1-1-1ii−i−iii−i−i−i−iii-1-111−ii−i−iii−i−iiiii−i−iii−i−i1-1-11-11
χ1111-1-11-1111-1111111-1-1-1-1-1-1-1-11111-1-1-1-1−i−iii−i−iiiii−i−i-1-111i−iii−i−iii−i−i−i−iii−i−iii1-1-11-11
χ1211-1-11-1111-1111111-1-1-1-1-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−iii-1-111−ii−i−iii−i−iii−i−iii−i−iii1-11-11-1
χ1311-1-11-1-111111-1-11111-1-1-1-1-1-11-1-1-1-1111ii−i−i−i−iiiii−i−i-1-111−iiii−i−i−i−iiiii−i−i−i−iii-111-1-11
χ1411-1-11-1-111111-1-11111-1-1-1-1-1-11-1-1-1-1111ii−i−i−i−iii−i−iii-1-111i−i−i−iiiii−i−iii−i−i−i−iii-11-111-1
χ1511-1-11-1-111111-1-11111-1-1-1-1-1-11-1-1-1-1111−i−iiiii−i−iii−i−i-1-111−iiii−i−i−i−iii−i−iiiii−i−i-11-111-1
χ1611-1-11-1-111111-1-11111-1-1-1-1-1-11-1-1-1-1111−i−iiiii−i−i−i−iii-1-111i−i−i−iiiii−i−i−i−iiiii−i−i-111-1-11
χ1722222222222222222222222222222222000000000000-2-2-2-2000000000000000000-2-20000
χ18222222-222-222-2-222-2-22222222-2-2-22-2-2-2000000000000-2-2-2-2000000000000000000220000
χ192222-2-20220-2-200220022-2-222-2000-200000002-22-200002-22-2000000000000002-22-2000000
χ202222-2-20220-2-200220022-2-222-2000-20000000-22-2200002-22-200000000000000-22-22000000
χ212222-2-20220-2-200220022-2-222-2000-20002-22-200000000-22-2200000000002-22-20000000000
χ222222-2-20220-2-200220022-2-222-2000-2000-22-2200000000-22-220000000000-22-220000000000
χ2322-2-22-2222-2222222-2-2-2-2-2-2-2-22222-2-2-2-200000000000022-2-2000000000000000000-220000
χ2422-2-22-2-222222-2-22222-2-2-2-2-2-22-2-2-2-222200000000000022-2-20000000000000000002-20000
χ2522-2-2-220220-2-2002200-2-222-2-2-2000200000002i−2i−2i2i0000-222-2000000000000002i−2i−2i2i000000
χ2622-2-2-220220-2-2002200-2-222-2-2-200020000000−2i2i2i−2i0000-222-200000000000000−2i2i2i−2i000000
χ2722-2-2-220220-2-2002200-2-222-2-2-200020002i−2i−2i2i000000002-2-2200000000002i−2i−2i2i0000000000
χ2822-2-2-220220-2-2002200-2-222-2-2-20002000−2i2i2i−2i000000002-2-220000000000−2i2i2i−2i0000000000
χ2944444441-2411-2-21-2-2-21111-2-2-211-2-211-2000000002222000022-1-1-1-1-1-1-1-100000000000000
χ3044444441-2411-2-21-2-2-21111-2-2-211-2-211-200000000-2-2-2-20000-2-21111111100000000000000
χ314444444-214-2-211-2111-2-2-2-2111-2-211-2-2122222222000000000000000000-1-1-1-1-1-1-1-1000000
χ324444444-214-2-211-2111-2-2-2-2111-2-211-2-21-2-2-2-2-2-2-2-200000000000000000011111111000000
χ33444444-41-2-411221-2221111-2-2-2-1-12-2-1-120000000022220000-2-2-1-1-1-1111100000000000000
χ34444444-41-2-411221-2221111-2-2-2-1-12-2-1-1200000000-2-2-2-20000221111-1-1-1-100000000000000
χ35444444-4-21-4-2-2-1-1-21-1-1-2-2-2-211122-1122-12222-2-2-2-2000000000000000000-1-1-1-11111000000
χ36444444-4-21-4-2-2-1-1-21-1-1-2-2-2-211122-1122-1-2-2-2-222220000000000000000001111-1-1-1-1000000
χ374444-4-40-2102233-2133-2-22211-100-3-100-32-22-22-22-2000000000000000000-11-11-11-11000000
χ384444-4-40-2102233-2133-2-22211-100-3-100-3-22-22-22-220000000000000000001-11-11-11-1000000
χ394444-4-40-21022-3-3-21-3-3-2-22211-1003-10032-22-2-22-22000000000000000000-11-111-11-1000000
χ404444-4-40-21022-3-3-21-3-3-2-22211-1003-1003-22-222-22-20000000000000000001-11-1-11-11000000
χ4144-4-44-441-2-411-2-21-222-1-1-1-122-211-22-1-12000000002i2i−2i−2i00002i−2i−i−iii−i−iii00000000000000
χ4244-4-44-441-2-411-2-21-222-1-1-1-122-211-22-1-1200000000−2i−2i2i2i0000−2i2iii−i−iii−i−i00000000000000
χ4344-4-44-44-21-4-2-211-21-1-12222-1-11-2-21-122-12i2i−2i−2i2i2i−2i−2i000000000000000000−i−iii−i−iii000000
χ4444-4-44-44-21-4-2-211-21-1-12222-1-11-2-21-122-1−2i−2i2i2i−2i−2i2i2i000000000000000000ii−i−iii−i−i000000
χ4544-4-44-4-41-2411221-2-2-2-1-1-1-122-2-1-12211-2000000002i2i−2i−2i0000−2i2i−i−iiiii−i−i00000000000000
χ4644-4-44-4-41-2411221-2-2-2-1-1-1-122-2-1-12211-200000000−2i−2i2i2i00002i−2iii−i−i−i−iii00000000000000
χ4744-4-44-4-4-214-2-2-1-1-21112222-1-1122-1-1-2-212i2i−2i−2i−2i−2i2i2i000000000000000000−i−iiiii−i−i000000
χ4844-4-44-4-4-214-2-2-1-1-21112222-1-1122-1-1-2-21−2i−2i2i2i2i2i−2i−2i000000000000000000ii−i−i−i−iii000000
χ4944-4-4-440-2102233-21-3-322-2-2-1-1-100-310032i−2i−2i2i2i−2i−2i2i000000000000000000−iii−i−iii−i000000
χ5044-4-4-440-2102233-21-3-322-2-2-1-1-100-31003−2i2i2i−2i−2i2i2i−2i000000000000000000i−i−iii−i−ii000000
χ5144-4-4-440-21022-3-3-213322-2-2-1-1-1003100-32i−2i−2i2i−2i2i2i−2i000000000000000000−iii−ii−i−ii000000
χ5244-4-4-440-21022-3-3-213322-2-2-1-1-1003100-3−2i2i2i−2i2i−2i−2i2i000000000000000000i−i−ii−iii−i000000
χ534-44i−4i0001-203-3−2i32i3-1223−23i−i3i−3i2i−2i0−i3i3003−30000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ1300000000000000
χ544-44i−4i0001-203-3−2i32i3-1223−23i−i3i−3i2i−2i0−i3i3003−3000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ1300000000000000
χ554-44i−4i0001-203-32i3−2i3-12−2323i−i3i−3i2i−2i0i3−i300−330000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ1300000000000000
χ564-44i−4i0001-203-32i3−2i3-12−2323i−i3i−3i2i−2i0i3−i300−33000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ1300000000000000
χ574-44i−4i0004400000-4-4004i−4i00−4i4i00000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000000000
χ584-44i−4i0004400000-4-4004i−4i00−4i4i0000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000000000
χ594-4−4i4i0001-203-3−2i32i3-12−2323−ii−3i3i−2i2i0−i3i300−33000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ2300000000000000
χ604-4−4i4i0001-203-3−2i32i3-12−2323−ii−3i3i−2i2i0−i3i300−330000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ2300000000000000
χ614-4−4i4i0001-203-32i3−2i3-1223−23−ii−3i3i−2i2i0i3−i3003−3000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ2300000000000000
χ624-4−4i4i0001-203-32i3−2i3-1223−23−ii−3i3i−2i2i0i3−i3003−30000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ2300000000000000
χ634-4−4i4i0004400000-4-400−4i4i004i−4i0000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000000000
χ644-4−4i4i0004400000-4-400−4i4i004i−4i00000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000000000
χ658888-8-802-40-2-2002-40022-2-2-4-4400040000000000000000000000000000000000000000000
χ6688-8-8-8802-40-2-2002-400-2-222444000-40000000000000000000000000000000000000000000
χ678-88i−8i0002-40-6600-24002i−2i−6i6i4i−4i000000000000000000000000000000000000000000000000
χ688-88i−8i000-42000−2i32i34-223−23−4i4i00−2i2i02i3−2i300−232300000000000000000000000000000000000000000
χ698-88i−8i000-420002i3−2i34-2−2323−4i4i00−2i2i0−2i32i30023−2300000000000000000000000000000000000000000
χ708-8−8i8i0002-40-6600-2400−2i2i6i−6i−4i4i000000000000000000000000000000000000000000000000
χ718-8−8i8i000-42000−2i32i34-2−23234i−4i002i−2i02i3−2i30023−2300000000000000000000000000000000000000000
χ728-8−8i8i000-420002i3−2i34-223−234i−4i002i−2i0−2i32i300−232300000000000000000000000000000000000000000

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