Finite Group Databasebeta

← Group #11787415

Character table — Group #11787415

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11111111444444444444444444888888881212121212121212181818181818181824242424242424242424242424242424242424243636363636363636
order1222444433666666881212121212121212242424242424242422448888224488882466668812121212242424242424242444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ61111111111111111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-11111-1-11111-1-1-1-11111-1-1-1-1
χ71111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1
χ81111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-11111
χ91111-1-1-1-111111111i−i-1-1-1-1-1-1-1-1ii−i−iii−i−i11-1-1ii−i−i-1-111ii−i−i1-11111i−i-1-1-1-1ii−i−iii−i−iii−i−i11-1-1
χ101111-1-1-1-111111111i−i-1-1-1-1-1-1-1-1ii−i−iii−i−i11-1-1ii−i−i-1-111ii−i−i-1111-1-1−ii-1-111−i−iiiii−i−i−i−iii-1-111
χ111111-1-1-1-111111111i−i-1-1-1-1-1-1-1-1ii−i−iii−i−i-1-111−i−iii-1-111ii−i−i1-1-1-111i−i11-1-1ii−i−i−i−iii−i−iii-1-111
χ121111-1-1-1-111111111i−i-1-1-1-1-1-1-1-1ii−i−iii−i−i-1-111−i−iii-1-111ii−i−i-11-1-1-1-1−ii1111−i−iii−i−iiiii−i−i11-1-1
χ131111-1-1-1-111111111−ii-1-1-1-1-1-1-1-1−i−iii−i−iii11-1-1−i−iii-1-111−i−iii1-11111−ii-1-1-1-1−i−iii−i−iii−i−iii11-1-1
χ141111-1-1-1-111111111−ii-1-1-1-1-1-1-1-1−i−iii−i−iii11-1-1−i−iii-1-111−i−iii-1111-1-1i−i-1-111ii−i−i−i−iiiii−i−i-1-111
χ151111-1-1-1-111111111−ii-1-1-1-1-1-1-1-1−i−iii−i−iii-1-111ii−i−i-1-111−i−iii1-1-1-111−ii11-1-1−i−iiiii−i−iii−i−i-1-111
χ161111-1-1-1-111111111−ii-1-1-1-1-1-1-1-1−i−iii−i−iii-1-111ii−i−i-1-111−i−iii-11-1-1-1-1i−i1111ii−i−iii−i−i−i−iii11-1-1
χ17222222222222222222222222222222222200000000-2-2-2-2-2-2-2-20000000000000000000000000000
χ182222222222222222-2-222222222-2-2-2-2-2-2-2-200000000-2-2-2-222220000000000000000000000000000
χ192222-2-2-2-2222222222i−2i-2-2-2-2-2-2-2-22i2i−2i−2i2i2i−2i−2i0000000022-2-2−2i−2i2i2i0000000000000000000000000000
χ202222-2-2-2-222222222−2i2i-2-2-2-2-2-2-2-2−2i−2i2i2i−2i−2i2i2i0000000022-2-22i2i−2i−2i0000000000000000000000000000
χ2122-2-22i−2i2i−2i2222-2-2-2-2002i−2i2i−2i2i−2i2i−2i00000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000000000001−i−1+i1+i−1−i2−2−i2i2
χ2222-2-22i−2i2i−2i2222-2-2-2-2002i−2i2i−2i2i−2i2i−2i00000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000000000000000−1+i1−i−1−i1+i−22i2−i2
χ2322-2-22i−2i2i−2i2222-2-2-2-2002i−2i2i−2i2i−2i2i−2i000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000000000001−i−1+i1+i−1−i−22i2−i2
χ2422-2-22i−2i2i−2i2222-2-2-2-2002i−2i2i−2i2i−2i2i−2i000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000000000000000−1+i1−i−1−i1+i2−2−i2i2
χ2522-2-2−2i2i−2i2i2222-2-2-2-200−2i2i−2i2i−2i2i−2i2i000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000000000001+i−1−i1−i−1+i2−2i2−i2
χ2622-2-2−2i2i−2i2i2222-2-2-2-200−2i2i−2i2i−2i2i−2i2i000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000000000000000−1−i1+i−1+i1−i−22−i2i2
χ2722-2-2−2i2i−2i2i2222-2-2-2-200−2i2i−2i2i−2i2i−2i2i00000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000000000001+i−1−i1−i−1+i−22−i2i2
χ2822-2-2−2i2i−2i2i2222-2-2-2-200−2i2i−2i2i−2i2i−2i2i00000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000000000000000−1−i1+i−1+i1−i2−2i2−i2
χ292-2-2222-2-222-2-2-2-2220022-2-222-2-20000000000002i−2i2i−2i2-22-2000000000000000000002i−2i2i−2i00000000
χ302-2-2222-2-222-2-2-2-2220022-2-222-2-2000000000000−2i2i−2i2i2-22-200000000000000000000−2i2i−2i2i00000000
χ312-2-2222-2-222-2-2-2-2220022-2-222-2-2000000002-22-20000-22-220000002-200002-2000000000000000000
χ322-2-2222-2-222-2-2-2-2220022-2-222-2-200000000-22-220000-22-22000000-220000-22000000000000000000
χ332-2-22-2-22222-2-2-2-22200-2-222-2-2220000000000002-2-22-222-2000000000000000000002-2-2200000000
χ342-2-22-2-22222-2-2-2-22200-2-222-2-222000000000000-222-2-222-200000000000000000000-222-200000000
χ352-2-22-2-22222-2-2-2-22200-2-222-2-222000000002-2-2200002-2-220000002-20000-22000000000000000000
χ362-2-22-2-22222-2-2-2-22200-2-222-2-22200000000-222-200002-2-22000000-2200002-2000000000000000000
χ37444444441-21-21-21-24411-2-2-2-211-2-2-2-21111222222220000000000-1-10000-1-1000000-1-1-1-100000000
χ38444444441-21-21-21-24411-2-2-2-211-2-2-2-21111-2-2-2-2-2-2-2-2000000000011000011000000111100000000
χ39444444441-21-21-21-2-4-411-2-2-2-2112222-1-1-1-12222-2-2-2-20000000000-1-10000-1-1000000111100000000
χ40444444441-21-21-21-2-4-411-2-2-2-2112222-1-1-1-1-2-2-2-22222000000000011000011000000-1-1-1-100000000
χ4144444444-21-21-21-2144-2-21111-2-21111-2-2-2-200000000000000002200-1-12200-1-1-1-1-1-1000000000000
χ4244444444-21-21-21-2144-2-21111-2-21111-2-2-2-20000000000000000-2-20011-2-200111111000000000000
χ4344444444-21-21-21-21-4-4-2-21111-2-2-1-1-1-1222200000000000000002200-1-1-2-200-1-11111000000000000
χ4444444444-21-21-21-21-4-4-2-21111-2-2-1-1-1-122220000000000000000-2-20011220011-1-1-1-1000000000000
χ454444-4-4-4-41-21-21-21-24i−4i-1-12222-1-1−2i−2i2i2iii−i−i22-2-22i2i−2i−2i0000000000-1-1000011000000−i−iii00000000
χ464444-4-4-4-41-21-21-21-24i−4i-1-12222-1-1−2i−2i2i2iii−i−i-2-222−2i−2i2i2i0000000000110000-1-1000000ii−i−i00000000
χ474444-4-4-4-41-21-21-21-2−4i4i-1-12222-1-12i2i−2i−2i−i−iii22-2-2−2i−2i2i2i0000000000-1-1000011000000ii−i−i00000000
χ484444-4-4-4-41-21-21-21-2−4i4i-1-12222-1-12i2i−2i−2i−i−iii-2-2222i2i−2i−2i0000000000110000-1-1000000−i−iii00000000
χ494444-4-4-4-4-21-21-21-214i−4i22-1-1-1-122ii−i−i−2i−2i2i2i00000000000000002-200-1-12i−2i0011−i−iii000000000000
χ504444-4-4-4-4-21-21-21-214i−4i22-1-1-1-122ii−i−i−2i−2i2i2i0000000000000000-220011−2i2i00-1-1ii−i−i000000000000
χ514444-4-4-4-4-21-21-21-21−4i4i22-1-1-1-122−i−iii2i2i−2i−2i00000000000000002-200-1-1−2i2i0011ii−i−i000000000000
χ524444-4-4-4-4-21-21-21-21−4i4i22-1-1-1-122−i−iii2i2i−2i−2i0000000000000000-2200112i−2i00-1-1−i−iii000000000000
χ534-44-44i−4i−4i4i44-4-444-4-4004i−4i−4i4i4i−4i−4i4i0000000000000000000000000000000000000000000000000000
χ544-44-44i−4i−4i4i-212-1-212-100−2i2i−iii−i2i−2i−3ζ5−3ζ133ζ5+3ζ133ζ7+3ζ23−3ζ7−3ζ23000000000000000000000000−i3i300003−3ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000000000
χ554-44-44i−4i−4i4i-212-1-212-100−2i2i−iii−i2i−2i−3ζ5−3ζ133ζ5+3ζ133ζ7+3ζ23−3ζ7−3ζ23000000000000000000000000i3−i30000−33−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000000000
χ564-44-44i−4i−4i4i-212-1-212-100−2i2i−iii−i2i−2i3ζ5+3ζ13−3ζ5−3ζ13−3ζ7−3ζ233ζ7+3ζ23000000000000000000000000−i3i300003−3−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000000000
χ574-44-44i−4i−4i4i-212-1-212-100−2i2i−iii−i2i−2i3ζ5+3ζ13−3ζ5−3ζ13−3ζ7−3ζ233ζ7+3ζ23000000000000000000000000i3−i30000−33ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000000000
χ584-44-4−4i4i4i−4i44-4-444-4-400−4i4i4i−4i−4i4i4i−4i0000000000000000000000000000000000000000000000000000
χ594-44-4−4i4i4i−4i-212-1-212-1002i−2ii−i−ii−2i2i3ζ7+3ζ23−3ζ7−3ζ23−3ζ5−3ζ133ζ5+3ζ13000000000000000000000000−i3i30000−33ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000000000
χ604-44-4−4i4i4i−4i-212-1-212-1002i−2ii−i−ii−2i2i3ζ7+3ζ23−3ζ7−3ζ23−3ζ5−3ζ133ζ5+3ζ13000000000000000000000000i3−i300003−3−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000000000
χ614-44-4−4i4i4i−4i-212-1-212-1002i−2ii−i−ii−2i2i−3ζ7−3ζ233ζ7+3ζ233ζ5+3ζ13−3ζ5−3ζ13000000000000000000000000−i3i30000−33−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000000000
χ624-44-4−4i4i4i−4i-212-1-212-1002i−2ii−i−ii−2i2i−3ζ7−3ζ233ζ7+3ζ233ζ5+3ζ13−3ζ5−3ζ13000000000000000000000000i3−i300003−3ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000000000
χ634-4-4444-4-41-2-12-121-2001122-2-2-1-100003i−3i3i−3i2-22-22i−2i2i−2i0000000000-110000-11000000−ii−ii00000000
χ644-4-4444-4-41-2-12-121-2001122-2-2-1-100003i−3i3i−3i-22-22−2i2i−2i2i00000000001-100001-1000000i−ii−i00000000
χ654-4-4444-4-41-2-12-121-2001122-2-2-1-10000−3i3i−3i3i2-22-2−2i2i−2i2i0000000000-110000-11000000i−ii−i00000000
χ664-4-4444-4-41-2-12-121-2001122-2-2-1-10000−3i3i−3i3i-22-222i−2i2i−2i00000000001-100001-1000000−ii−ii00000000
χ674-4-44-4-4441-2-12-121-200-1-1-2-2221100003-3-332-2-222-2-220000000000-1100001-1000000-111-100000000
χ684-4-44-4-4441-2-12-121-200-1-1-2-2221100003-3-33-222-2-222-200000000001-10000-110000001-1-1100000000
χ694-4-44-4-4441-2-12-121-200-1-1-2-222110000-333-32-2-22-222-20000000000-1100001-10000001-1-1100000000
χ704-4-44-4-4441-2-12-121-200-1-1-2-222110000-333-3-222-22-2-2200000000001-10000-11000000-111-100000000
χ7188-8-88i−8i8i−8i2-42-4-24-24002i−2i−4i4i−4i4i2i−2i0000000000000000000000000000000000000000000000000000
χ7288-8-88i−8i8i−8i-42-424-24-200−4i4i2i−2i2i−2i−4i4i0000000000000000000000000000000000000000000000000000
χ7388-8-8−8i8i−8i8i2-42-4-24-2400−2i2i4i−4i4i−4i−2i2i0000000000000000000000000000000000000000000000000000
χ7488-8-8−8i8i−8i8i-42-424-24-2004i−4i−2i2i−2i2i4i−4i0000000000000000000000000000000000000000000000000000
χ758-88-88i−8i−8i8i2-4-242-4-24002i−2i4i−4i−4i4i−2i2i0000000000000000000000000000000000000000000000000000
χ768-88-8−8i8i8i−8i2-4-242-4-2400−2i2i−4i4i4i−4i2i−2i0000000000000000000000000000000000000000000000000000
χ778-8-8888-8-8-424-24-2-4200-4-4-2-222440000000000000000000000000000000000000000000000000000
χ788-8-88-8-888-424-24-2-42004422-2-2-4-40000000000000000000000000000000000000000000000000000

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