Finite Group Databasebeta

← Group #14298652

Character table — Group #14298652

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size112222244444444488888888888810101010101012121212121212121616161616162020202020242424242424404040404040404040404040404060606060120120120120
order12222364456661010101010121215202020203030302222662244101010103030606060604466610102020202044441212121212121212121244444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111-1-1-1-1-1-111111111111111-1-1-1-1-1111111ii−i−i-1-1ii−i−iii−i−i-1-1-1-1ii−i−i
χ61111111111111111111111111111-1-1-1-1-1-111111111111111-1-1-1-1-1111111−i−iii-1-1−i−iii−i−iii-1-1-1-1−i−iii
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1ii−i−i-1-1ii−i−iii−i−i1111−i−iii
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1−i−iii-1-1−i−iii−i−iii1111ii−i−i
χ91111111-1-1111111111-1-11-1-1-1-111111111111-1-1111111-1-1-1-1-1-111111-1-1-1-11-11-1-1-11111-1-1-1-111-1-11-11-1
χ101111111-1-1111111111-1-11-1-1-1-111111111111-1-1111111-1-1-1-1-1-111111-1-1-1-1-11-11-1-1-1-1-1-1111111-1-1-11-11
χ111111111-1-1111111111-1-11-1-1-1-1111111111-1-111-1-1-1-111-1-1-1-1-1-1111-1-111111-11-1-1-11111-1-1-1-1-1-111-11-11
χ121111111-1-1111111111-1-11-1-1-1-1111111111-1-111-1-1-1-111-1-1-1-1-1-1111-1-11111-11-11-1-1-1-1-1-11111-1-1111-11-1
χ131111111-1-1111111111-1-11-1-1-1-1111-1-1-1-1-1-111-1-1111111-1-1-1-111-1-1-111-1-1-1-1i−i−ii11ii−i−i−i−iii-1-111i−i−ii
χ141111111-1-1111111111-1-11-1-1-1-1111-1-1-1-1-1-111-1-1111111-1-1-1-111-1-1-111-1-1-1-1−iii−i11−i−iiiii−i−i-1-111−iii−i
χ151111111-1-1111111111-1-11-1-1-1-1111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-1-11111i−i−ii11ii−i−i−i−iii11-1-1−iii−i
χ161111111-1-1111111111-1-11-1-1-1-1111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-1-11111−iii−i11−i−iiiii−i−i11-1-1i−i−ii
χ1722222-1-1222-1-1-122222-1-1-12222-1-1-12222-1-100000000-1-1-1-1-1-122-1-1-10000002222-1-1-1-1-1-1-1-1-1-100000000
χ1822222-1-1222-1-1-122222-1-1-12222-1-1-12222-1-100000000-1-1-1-1-1-122-1-1-1000000-2-2-2-2-1-11111111100000000
χ1922222-1-1222-1-1-122222-1-1-12222-1-1-1-2-2-2-21100000000-1-1-1-1-1-1-2-21110000002i2i−2i−2i11−i−iii−i−iii00000000
χ2022222-1-1222-1-1-122222-1-1-12222-1-1-1-2-2-2-21100000000-1-1-1-1-1-1-2-2111000000−2i−2i2i2i11ii−i−iii−i−i00000000
χ2122222-1-1-2-22-1-1-12222211-1-2-2-2-2-1-1-12222-1-100000000-1-11111-2-2-1-1-10000002-22-211-1-1-1-1111100000000
χ2222222-1-1-2-22-1-1-12222211-1-2-2-2-2-1-1-12222-1-100000000-1-11111-2-2-1-1-1000000-22-22111111-1-1-1-100000000
χ2322222-1-1-2-22-1-1-12222211-1-2-2-2-2-1-1-1-2-2-2-21100000000-1-11111221110000002i−2i−2i2i-1-1−i−iiiii−i−i00000000
χ2422222-1-1-2-22-1-1-12222211-1-2-2-2-2-1-1-1-2-2-2-21100000000-1-1111122111000000−2i2i2i−2i-1-1ii−i−i−i−iii00000000
χ25222-2-2220022-2-22-2-22-200200002-2-222-2-222002i−2i00002-2000000-2-22002i2i−2i−2i00000000000000002i−2i0000
χ26222-2-2220022-2-22-2-22-200200002-2-222-2-22200−2i2i00002-2000000-2-2200−2i−2i2i2i0000000000000000−2i2i0000
χ27222-2-2220022-2-22-2-22-200200002-2-2-2-222-2-2002i−2i00002-200000022-2002i2i−2i−2i0000000000000000−2i2i0000
χ28222-2-2220022-2-22-2-22-200200002-2-2-2-222-2-200−2i2i00002-200000022-200−2i−2i2i2i00000000000000002i−2i0000
χ2922-22-2222i−2i2-22-22-2-2-222i−2i22i2i−2i−2i2-2-22-22-22200000000-222i2i−2i−2i2i−2i2-2-200000000002i−2i0000000000000000
χ3022-22-2222i−2i2-22-22-2-2-222i−2i22i2i−2i−2i2-2-2-22-22-2-200000000-222i2i−2i−2i−2i2i-2220000000000−2i2i0000000000000000
χ3122-22-222−2i2i2-22-22-2-2-22−2i2i2−2i−2i2i2i2-2-22-22-22200000000-22−2i−2i2i2i−2i2i2-2-20000000000−2i2i0000000000000000
χ3222-22-222−2i2i2-22-22-2-2-22−2i2i2−2i−2i2i2i2-2-2-22-22-2-200000000-22−2i−2i2i2i2i−2i-22200000000002i−2i0000000000000000
χ3322-22-2-1-12i−2i21-112-2-2-22−ii-12i2i−2i−2i-1112-22-2-1-1000000001-1−i−iii2i−2i-1110000000000−ii−i3i3−i3i33−33−300000000
χ3422-22-2-1-12i−2i21-112-2-2-22−ii-12i2i−2i−2i-1112-22-2-1-1000000001-1−i−iii2i−2i-1110000000000−iii3−i3i3−i3−33−3300000000
χ3522-22-2-1-12i−2i21-112-2-2-22−ii-12i2i−2i−2i-111-22-2211000000001-1−i−iii−2i2i1-1-10000000000i−i3−3−33i3−i3−i3i300000000
χ3622-22-2-1-12i−2i21-112-2-2-22−ii-12i2i−2i−2i-111-22-2211000000001-1−i−iii−2i2i1-1-10000000000i−i−333−3−i3i3i3−i300000000
χ3722-22-2-1-1−2i2i21-112-2-2-22i−i-1−2i−2i2i2i-1112-22-2-1-1000000001-1ii−i−i−2i2i-1110000000000i−i−i3i3−i3i3−33−3300000000
χ3822-22-2-1-1−2i2i21-112-2-2-22i−i-1−2i−2i2i2i-1112-22-2-1-1000000001-1ii−i−i−2i2i-1110000000000i−ii3−i3i3−i33−33−300000000
χ3922-22-2-1-1−2i2i21-112-2-2-22i−i-1−2i−2i2i2i-111-22-2211000000001-1ii−i−i2i−2i1-1-10000000000−ii3−3−33−i3i3i3−i300000000
χ4022-22-2-1-1−2i2i21-112-2-2-22i−i-1−2i−2i2i2i-111-22-2211000000001-1ii−i−i2i−2i1-1-10000000000−ii−333−3i3−i3−i3i300000000
χ4122-2-2222002-2-22222-2-200200002222-2-22222-2002222-2-2000000-22-2-2-20000000000000000002-2000000
χ4222-2-2222002-2-22222-2-200200002222-2-2222-2200-2-2-2-2-2-2000000-22-222000000000000000000-22000000
χ4322-2-2222002-2-22222-2-20020000222-222-2-2-22-2002222-2-20000002-22-2-2000000000000000000-22000000
χ4422-2-2222002-2-22222-2-20020000222-222-2-2-2-2200-2-2-2-2-2-20000002-22220000000000000000002-2000000
χ45444444444-1444-1-1-1-1-144-1-1-1-1-1-1-1-10000004444-1-1-1-1-1-1-1-1-1-100000-1-1-1-1-1-10000000000000000000000
χ46444444444-1444-1-1-1-1-144-1-1-1-1-1-1-1-1000000-4-4-4-41111-1-1-1-1-1-1000001111110000000000000000000000
χ474444444-4-4-1444-1-1-1-1-1-4-4-11111-1-1-100000044-4-4-1-1-1-1-1-1111100000-1-111110000000000000000000000
χ484444444-4-4-1444-1-1-1-1-1-4-4-11111-1-1-1000000-4-4441111-1-111110000011-1-1-1-10000000000000000000000
χ49444-4-44400-14-4-4-111-1100-1−i5i5−i5i5-111000000004i−4i−5−555-11−i5i5−i5i500000−55−i−iii0000000000000000000000
χ50444-4-44400-14-4-4-111-1100-1−i5i5−i5i5-11100000000−4i4i55−5−5-11−i5i5−i5i5000005−5ii−i−i0000000000000000000000
χ51444-4-44400-14-4-4-111-1100-1i5−i5i5−i5-111000000004i−4i55−5−5-11i5−i5i5−i5000005−5−i−iii0000000000000000000000
χ52444-4-44400-14-4-4-111-1100-1i5−i5i5−i5-11100000000−4i4i−5−555-11i5−i5i5−i500000−55ii−i−i0000000000000000000000
χ53444-4-4-2-2004-2224-4-44-400-20000-22244-4-4-2-200000000-2200000022-20000000000000000000000000000
χ54444-4-4-2-2004-2224-4-44-400-20000-222-4-4442200000000-22000000-2-220000000000000000000000000000
χ5544-44-4444i−4i-1-44-4-1111-14i−4i-1−i−iii-1110000000000−5−5551-1−i−iii000005−5−i5i5−i5i50000000000000000000000
χ5644-44-4444i−4i-1-44-4-1111-14i−4i-1−i−iii-111000000000055−5−51-1−i−iii00000−55i5−i5i5−i50000000000000000000000
χ5744-44-444−4i4i-1-44-4-1111-1−4i4i-1ii−i−i-1110000000000−5−5551-1ii−i−i000005−5i5−i5i5−i50000000000000000000000
χ5844-44-444−4i4i-1-44-4-1111-1−4i4i-1ii−i−i-111000000000055−5−51-1ii−i−i00000−55−i5i5−i5i50000000000000000000000
χ5944-4-444400-1-4-44-1-1-11100-1−555−5-1-1-10000004-400-1-1-1-111−555−50000011−555−50000000000000000000000
χ6044-4-444400-1-4-44-1-1-11100-1−555−5-1-1-1000000-4400111111−555−500000-1-15−5−550000000000000000000000
χ6144-4-444400-1-4-44-1-1-11100-15−5−55-1-1-10000004-400-1-1-1-1115−5−5500000115−5−550000000000000000000000
χ6244-4-444400-1-4-44-1-1-11100-15−5−55-1-1-1000000-44001111115−5−5500000-1-1−555−50000000000000000000000
χ6344-4-44-2-200422-2444-4-400-20000-2-2-24-4-44-2-200000000220000002-220000000000000000000000000000
χ6444-4-44-2-200422-2444-4-400-20000-2-2-2-444-4220000000022000000-22-20000000000000000000000000000
χ6588888-4-488-2-4-4-4-2-2-2-2-2-4-41-2-2-2-211100000000000000111111000000000000000000000000000000000
χ6688888-4-4-8-8-2-4-4-4-2-2-2-2-244122221110000000000000011-1-1-1-1000000000000000000000000000000000
χ67888-8-8-4-400-2-444-222-22001−2i52i5−2i52i51-1-1000000000000001-1i5−i5i5−i5000000000000000000000000000000000
χ68888-8-8-4-400-2-444-222-220012i5−2i52i5−2i51-1-1000000000000001-1−i5i5−i5i5000000000000000000000000000000000
χ6988-88-8-4-48i−8i-24-44-2222-2−4i4i1−2i−2i2i2i1-1-100000000000000-11ii−i−i000000000000000000000000000000000
χ7088-88-8-4-4−8i8i-24-44-2222-24i−4i12i2i−2i−2i1-1-100000000000000-11−i−iii000000000000000000000000000000000
χ7188-8-88-4-400-244-4-2-2-222001−252525−2511100000000000000-1-15−5−55000000000000000000000000000000000
χ7288-8-88-4-400-244-4-2-2-22200125−25−252511100000000000000-1-1−555−5000000000000000000000000000000000
χ738-80008-8008000-800000080000-80000000000000000000000000000000000000000000000000000000
χ748-80008-800-20002−25250000-200002−252500000000002ζ2−2ζ14+2ζ22+2ζ26−2ζ34−2ζ38+2ζ46−2ζ58−2ζ2+2ζ14−2ζ22−2ζ26+2ζ34+2ζ38−2ζ46+2ζ582ζ2+2ζ14+2ζ22−2ζ26+2ζ34−2ζ38−2ζ46−2ζ58−2ζ2−2ζ14−2ζ22+2ζ26−2ζ34+2ζ38+2ζ46+2ζ58000000000000000000000000000000000000000
χ758-80008-800-20002−25250000-200002−25250000000000−2ζ2+2ζ14−2ζ22−2ζ26+2ζ34+2ζ38−2ζ46+2ζ582ζ2−2ζ14+2ζ22+2ζ26−2ζ34−2ζ38+2ζ46−2ζ58−2ζ2−2ζ14−2ζ22+2ζ26−2ζ34+2ζ38+2ζ46+2ζ582ζ2+2ζ14+2ζ22−2ζ26+2ζ34−2ζ38−2ζ46−2ζ58000000000000000000000000000000000000000
χ768-80008-800-2000225−250000-20000225−2500000000002ζ2+2ζ14+2ζ22−2ζ26+2ζ34−2ζ38−2ζ46−2ζ58−2ζ2−2ζ14−2ζ22+2ζ26−2ζ34+2ζ38+2ζ46+2ζ58−2ζ2+2ζ14−2ζ22−2ζ26+2ζ34+2ζ38−2ζ46+2ζ582ζ2−2ζ14+2ζ22+2ζ26−2ζ34−2ζ38+2ζ46−2ζ58000000000000000000000000000000000000000
χ778-80008-800-2000225−250000-20000225−250000000000−2ζ2−2ζ14−2ζ22+2ζ26−2ζ34+2ζ38+2ζ46+2ζ582ζ2+2ζ14+2ζ22−2ζ26+2ζ34−2ζ38−2ζ46−2ζ582ζ2−2ζ14+2ζ22+2ζ26−2ζ34−2ζ38+2ζ46−2ζ58−2ζ2+2ζ14−2ζ22−2ζ26+2ζ34+2ζ38−2ζ46+2ζ58000000000000000000000000000000000000000
χ788-8000-44008000-8000000-400004000000−4i34i300000000000000000000000000000000000000000000000
χ798-8000-44008000-8000000-4000040000004i3−4i300000000000000000000000000000000000000000000000
χ8016-16000-8800-40004−4545000020000-225−2500000000000000000000000000000000000000000000000000000
χ8116-16000-8800-4000445−45000020000-2−252500000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 60 (ζ60 = 1); i = ζ15.