Finite Group Databasebeta

← Group #11771203

Character table — Group #11771203

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11111111444444444444444444888888888888888888888888881818181818181818363636363636363636363636363636367272
order12224444334466666612121212121212128812121212121212122424242424242424242424242424242422444444444444448888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ31111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1
χ41111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1
χ511111111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1
χ611111111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1
χ711111111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii11
χ811111111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i11
χ91111-1-1-1-1111-1111111-1-1-1-1-1-1-1-1i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-111-1-111-1-1ii−i−iii−i−ii−i
χ101111-1-1-1-1111-1111111-1-1-1-1-1-1-1-1i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1-1-111-1-111−i−iii−i−iiii−i
χ111111-1-1-1-1111-1111111-1-1-1-1-1-1-1-1i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111ii−i−i−i−iii-1-11111-1-1−ii
χ121111-1-1-1-1111-1111111-1-1-1-1-1-1-1-1i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111−i−iiiii−i−i11-1-1-1-111−ii
χ131111-1-1-1-1111-1111111-1-1-1-1-1-1-1-1−ii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-111-1-111-1-1−i−iii−i−iii−ii
χ141111-1-1-1-1111-1111111-1-1-1-1-1-1-1-1−ii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1-1-111-1-111ii−i−iii−i−i−ii
χ151111-1-1-1-1111-1111111-1-1-1-1-1-1-1-1−ii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111ii−i−i−i−iii11-1-1-1-111i−i
χ161111-1-1-1-1111-1111111-1-1-1-1-1-1-1-1−ii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111−i−iiiii−i−i-1-11111-1-1i−i
χ172222222222-2-22222222222222200-2-2-2-2-2-2-2-2000000000000000022-2-222-2-2000000000000000000
χ182222222222-2-22222222222222200-2-2-2-2-2-2-2-20000000000000000-2-222-2-222000000000000000000
χ192222-2-2-2-222-22222222-2-2-2-2-2-2-2-200-2-2-2-22222000000000000000022-2-2-2-222000000000000000000
χ202222-2-2-2-222-22222222-2-2-2-2-2-2-2-200-2-2-2-222220000000000000000-2-22222-2-2000000000000000000
χ2122-2-222-2-2220022-2-2-2-22222-2-2-2-2000000000000000000000000002-2002-200000000002−22−22−22−200
χ2222-2-222-2-2220022-2-2-2-22222-2-2-2-2000000000000000000000000002-2002-20000000000−22−22−22−2200
χ2322-2-222-2-2220022-2-2-2-22222-2-2-2-200000000000000000000000000-2200-220000000000−i2i2−i2i2i2−i2i2−i200
χ2422-2-222-2-2220022-2-2-2-22222-2-2-2-200000000000000000000000000-2200-220000000000i2−i2i2−i2−i2i2−i2i200
χ2522-2-2-2-222220022-2-2-2-2-2-2-2-22222000000000000000000000000002-200-220000000000−i2i2i2−i2−i2i2i2−i200
χ2622-2-2-2-222220022-2-2-2-2-2-2-2-22222000000000000000000000000002-200-220000000000i2−i2−i2i2i2−i2−i2i200
χ2722-2-2-2-222220022-2-2-2-2-2-2-2-2222200000000000000000000000000-22002-200000000002−2−22−222−200
χ2822-2-2-2-222220022-2-2-2-2-2-2-2-2222200000000000000000000000000-22002-20000000000−222−22−2−2200
χ292-22-22i−2i2i−2i2200-2-222-2-22i2i−2i−2i2i2i−2i−2i00000000000000000000000000002i−2i002-21+i−1−i1−i−1+i1−i−1+i1+i−1−i0000000000
χ302-22-22i−2i2i−2i2200-2-222-2-22i2i−2i−2i2i2i−2i−2i00000000000000000000000000002i−2i002-2−1−i1+i−1+i1−i−1+i1−i−1−i1+i0000000000
χ312-22-22i−2i2i−2i2200-2-222-2-22i2i−2i−2i2i2i−2i−2i0000000000000000000000000000−2i2i00-221−i−1+i−1−i1+i1+i−1−i−1+i1−i0000000000
χ322-22-22i−2i2i−2i2200-2-222-2-22i2i−2i−2i2i2i−2i−2i0000000000000000000000000000−2i2i00-22−1+i1−i1+i−1−i−1−i1+i1−i−1+i0000000000
χ332-22-2−2i2i−2i2i2200-2-222-2-2−2i−2i2i2i−2i−2i2i2i00000000000000000000000000002i−2i00-221+i−1−i−1+i1−i1−i−1+i−1−i1+i0000000000
χ342-22-2−2i2i−2i2i2200-2-222-2-2−2i−2i2i2i−2i−2i2i2i00000000000000000000000000002i−2i00-22−1−i1+i1−i−1+i−1+i1−i1+i−1−i0000000000
χ352-22-2−2i2i−2i2i2200-2-222-2-2−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000−2i2i002-21−i−1+i1+i−1−i1+i−1−i1−i−1+i0000000000
χ362-22-2−2i2i−2i2i2200-2-222-2-2−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000−2i2i002-2−1+i1−i−1−i1+i−1−i1+i−1+i1−i0000000000
χ37444444441-2441-21-21-21-21-21-21-24411-2-211-2-21111-2-2-2-21111-2-2-2-200000000000000000000000000
χ38444444441-2441-21-21-21-21-21-21-2-4-411-2-211-2-2-1-1-1-12222-1-1-1-1222200000000000000000000000000
χ39444444441-2-4-41-21-21-21-21-21-21-200-1-122-1-12233-3-3000033-3-3000000000000000000000000000000
χ40444444441-2-4-41-21-21-21-21-21-21-200-1-122-1-122-3-3330000-3-333000000000000000000000000000000
χ4144444444-2144-21-21-21-21-21-21-2144-2-211-2-211-2-2-2-21111-2-2-2-2111100000000000000000000000000
χ4244444444-2144-21-21-21-21-21-21-21-4-4-2-211-2-2112222-1-1-1-12222-1-1-1-100000000000000000000000000
χ4344444444-21-4-4-21-21-21-21-21-21-210022-1-122-1-1000033-3-3000033-3-300000000000000000000000000
χ4444444444-21-4-4-21-21-21-21-21-21-210022-1-122-1-10000-3-3330000-3-33300000000000000000000000000
χ454444-4-4-4-41-24-41-21-21-2-12-12-12-124i−4i11-2-2-1-122iiii−2i−2i−2i−2i−i−i−i−i2i2i2i2i00000000000000000000000000
χ464444-4-4-4-41-24-41-21-21-2-12-12-12-12−4i4i11-2-2-1-122−i−i−i−i2i2i2i2iiiii−2i−2i−2i−2i00000000000000000000000000
χ474444-4-4-4-41-2-441-21-21-2-12-12-12-1200-1-12211-2-23i3i−3i−3i0000−3i−3i3i3i000000000000000000000000000000
χ484444-4-4-4-41-2-441-21-21-2-12-12-12-1200-1-12211-2-2−3i−3i3i3i00003i3i−3i−3i000000000000000000000000000000
χ494444-4-4-4-4-214-4-21-21-212-12-12-12-14i−4i-2-21122-1-1−2i−2i−2i−2iiiii2i2i2i2i−i−i−i−i00000000000000000000000000
χ504444-4-4-4-4-214-4-21-21-212-12-12-12-1−4i4i-2-21122-1-12i2i2i2i−i−i−i−i−2i−2i−2i−2iiiii00000000000000000000000000
χ514444-4-4-4-4-21-44-21-21-212-12-12-12-10022-1-1-2-21100003i3i−3i−3i0000−3i−3i3i3i00000000000000000000000000
χ524444-4-4-4-4-21-44-21-21-212-12-12-12-10022-1-1-2-2110000−3i−3i3i3i00003i3i−3i−3i00000000000000000000000000
χ534-4-444i−4i−4i4i1-200-12-121-2i−2i−i2i−i2ii−2i003-3003i−3i00ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13002ζ5−2ζ13−2ζ5+2ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ2300−2ζ7+2ζ232ζ7−2ζ2300000000000000000000000000
χ544-4-444i−4i−4i4i1-200-12-121-2i−2i−i2i−i2ii−2i003-3003i−3i00−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ1300−2ζ5+2ζ132ζ5−2ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23002ζ7−2ζ23−2ζ7+2ζ2300000000000000000000000000
χ554-4-444i−4i−4i4i1-200-12-121-2i−2i−i2i−i2ii−2i00-3300−3i3i00ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ132ζ5−2ζ13−2ζ5+2ζ1300−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−2ζ7+2ζ232ζ7−2ζ230000000000000000000000000000
χ564-4-444i−4i−4i4i1-200-12-121-2i−2i−i2i−i2ii−2i00-3300−3i3i00−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−2ζ5+2ζ132ζ5−2ζ1300ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ232ζ7−2ζ23−2ζ7+2ζ230000000000000000000000000000
χ574-4-444i−4i−4i4i4400-4-4-4-4444i4i−4i−4i−4i−4i4i4i0000000000000000000000000000000000000000000000000000
χ584-4-444i−4i−4i4i-21002-12-1-21−2ii2i−i2i−i−2ii00003-3003i−3i002ζ5−2ζ13−2ζ5+2ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ1300−2ζ7+2ζ232ζ7−2ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ2300000000000000000000000000
χ594-4-444i−4i−4i4i-21002-12-1-21−2ii2i−i2i−i−2ii00003-3003i−3i00−2ζ5+2ζ132ζ5−2ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13002ζ7−2ζ23−2ζ7+2ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ2300000000000000000000000000
χ604-4-444i−4i−4i4i-21002-12-1-21−2ii2i−i2i−i−2ii0000-3300−3i3i2ζ5−2ζ13−2ζ5+2ζ1300−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−2ζ7+2ζ232ζ7−2ζ2300ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ2300000000000000000000000000
χ614-4-444i−4i−4i4i-21002-12-1-21−2ii2i−i2i−i−2ii0000-3300−3i3i−2ζ5+2ζ132ζ5−2ζ1300ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ132ζ7−2ζ23−2ζ7+2ζ2300−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ2300000000000000000000000000
χ624-4-44−4i4i4i−4i1-200-12-121-2−i2ii−2ii−2i−i2i003-300−3i3i00−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ2300−2ζ7+2ζ232ζ7−2ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13002ζ5−2ζ13−2ζ5+2ζ1300000000000000000000000000
χ634-4-44−4i4i4i−4i1-200-12-121-2−i2ii−2ii−2i−i2i003-300−3i3i00ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23002ζ7−2ζ23−2ζ7+2ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ1300−2ζ5+2ζ132ζ5−2ζ1300000000000000000000000000
χ644-4-44−4i4i4i−4i1-200-12-121-2−i2ii−2ii−2i−i2i00-33003i−3i00−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−2ζ7+2ζ232ζ7−2ζ2300ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ132ζ5−2ζ13−2ζ5+2ζ130000000000000000000000000000
χ654-4-44−4i4i4i−4i1-200-12-121-2−i2ii−2ii−2i−i2i00-33003i−3i00ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ232ζ7−2ζ23−2ζ7+2ζ2300−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−2ζ5+2ζ132ζ5−2ζ130000000000000000000000000000
χ664-4-44−4i4i4i−4i4400-4-4-4-444−4i−4i4i4i4i4i−4i−4i0000000000000000000000000000000000000000000000000000
χ674-4-44−4i4i4i−4i-21002-12-1-212i−i−2ii−2ii2i−i00003-300−3i3i00−2ζ7+2ζ232ζ7−2ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23002ζ5−2ζ13−2ζ5+2ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ1300000000000000000000000000
χ684-4-44−4i4i4i−4i-21002-12-1-212i−i−2ii−2ii2i−i00003-300−3i3i002ζ7−2ζ23−2ζ7+2ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ2300−2ζ5+2ζ132ζ5−2ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ1300000000000000000000000000
χ694-4-44−4i4i4i−4i-21002-12-1-212i−i−2ii−2ii2i−i0000-33003i−3i−2ζ7+2ζ232ζ7−2ζ2300ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ232ζ5−2ζ13−2ζ5+2ζ1300−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ1300000000000000000000000000
χ704-4-44−4i4i4i−4i-21002-12-1-212i−i−2ii−2ii2i−i0000-33003i−3i2ζ7−2ζ23−2ζ7+2ζ2300−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−2ζ5+2ζ132ζ5−2ζ1300ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ1300000000000000000000000000
χ7188-8-888-8-82-4002-4-24-242-42-4-24-240000000000000000000000000000000000000000000000000000
χ7288-8-888-8-8-4200-424-24-2-42-424-24-20000000000000000000000000000000000000000000000000000
χ7388-8-8-8-8882-4002-4-24-24-24-242-42-40000000000000000000000000000000000000000000000000000
χ7488-8-8-8-888-4200-424-24-24-24-2-42-420000000000000000000000000000000000000000000000000000
χ758-88-88i−8i8i−8i2-400-242-4-242i−4i−2i4i2i−4i−2i4i0000000000000000000000000000000000000000000000000000
χ768-88-88i−8i8i−8i-42004-2-424-2−4i2i4i−2i−4i2i4i−2i0000000000000000000000000000000000000000000000000000
χ778-88-8−8i8i−8i8i2-400-242-4-24−2i4i2i−4i−2i4i2i−4i0000000000000000000000000000000000000000000000000000
χ788-88-8−8i8i−8i8i-42004-2-424-24i−2i−4i2i4i−2i−4i2i0000000000000000000000000000000000000000000000000000

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