Finite Group Databasebeta

← Group #11746770

Character table — Group #11746770

Order 960.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11222222244444444444444444444558888888888888888881010101010101020202020202020206060606060606060
order122344612125688101215152020242424243030606060602210203030404040406060120120120120120120120120244661212688122424242444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−i
χ411111111111111111111111111111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii
χ511111111111-1-1111111-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11-1-1-1-11111-1-1-1-1
χ611111111111-1-1111111-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11-1-1-1-1-1-1-1-11111
χ711111111111-1-1111111-1-1-1-1111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11111ii−i−i−i−iii
χ811111111111-1-1111111-1-1-1-1111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11111−i−iiiii−i−i
χ91111-1-11-1-111i−i1-111-1-1ii−i−i11-1-1-1-1111-111ii−i−i-1-1iiii−i−i−i−i1-1-111-1-11i−i-1ii−i−i1-11-1i−ii−i
χ101111-1-11-1-111i−i1-111-1-1ii−i−i11-1-1-1-1111-111ii−i−i-1-1iiii−i−i−i−i1-1-111-1-11i−i-1ii−i−i-11-11−ii−ii
χ111111-1-11-1-111i−i1-111-1-1ii−i−i11-1-1-1-1-1-11-111ii−i−i-1-1iiii−i−i−i−i-111-1-111-1−ii1−i−iiii−i−ii-111-1
χ121111-1-11-1-111i−i1-111-1-1ii−i−i11-1-1-1-1-1-11-111ii−i−i-1-1iiii−i−i−i−i-111-1-111-1−ii1−i−iii−iii−i1-1-11
χ131111-1-11-1-111−ii1-111-1-1−i−iii11-1-1-1-1111-111−i−iii-1-1−i−i−i−iiiii1-1-111-1-11−ii-1−i−iii1-11-1−ii−ii
χ141111-1-11-1-111−ii1-111-1-1−i−iii11-1-1-1-1111-111−i−iii-1-1−i−i−i−iiiii1-1-111-1-11−ii-1−i−iii-11-11i−ii−i
χ151111-1-11-1-111−ii1-111-1-1−i−iii11-1-1-1-1-1-11-111−i−iii-1-1−i−i−i−iiiii-111-1-111-1i−i1ii−i−ii−i−ii1-1-11
χ161111-1-11-1-111−ii1-111-1-1−i−iii11-1-1-1-1-1-11-111−i−iii-1-1−i−i−i−iiiii-111-1-111-1i−i1ii−i−i−iii−i-111-1
χ17222-122-1-1-12-1222-1-1-122-1-1-1-1-1-1-1-1-1-12222-1-12222-1-1-1-1-1-1-1-1-1-1222-1-1-1-1-122-1-1-1-1-100000000
χ18222-122-1-1-12-1222-1-1-122-1-1-1-1-1-1-1-1-1-1-2-222-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-211111-2-21111100000000
χ19222-122-1-1-12-1-2-22-1-1-1221111-1-1-1-1-1-12222-1-1-2-2-2-2-1-111111111222-1-1-1-1-1-2-2-1111100000000
χ20222-122-1-1-12-1-2-22-1-1-1221111-1-1-1-1-1-1-2-222-1-1-2-2-2-2-1-111111111-2-2-211111221-1-1-1-100000000
χ21222-1-2-2-1112-12i−2i21-1-1-2-2−i−iii-1-11111222-2-1-12i2i−2i−2i11−i−i−i−iiiii2-2-2-1-111-12i−2i1−i−iii00000000
χ22222-1-2-2-1112-12i−2i21-1-1-2-2−i−iii-1-11111-2-22-2-1-12i2i−2i−2i11−i−i−i−iiiii-22211-1-11−2i2i-1ii−i−i00000000
χ23222-1-2-2-1112-1−2i2i21-1-1-2-2ii−i−i-1-11111222-2-1-1−2i−2i2i2i11iiii−i−i−i−i2-2-2-1-111-1−2i2i1ii−i−i00000000
χ24222-1-2-2-1112-1−2i2i21-1-1-2-2ii−i−i-1-11111-2-22-2-1-1−2i−2i2i2i11iiii−i−i−i−i-22211-1-112i−2i-1−i−iii00000000
χ2522-222-22-2-22-2002222-2-2000022-2-2-2-222-22-2-200002200000000-2-2222-2-2-2002000000000000
χ2622-222-22-2-22-2002222-2-2000022-2-2-2-2-2-2-22-2-20000220000000022-2-2-222200-2000000000000
χ2722-22-222222-2002-22222000022222222-2-2-2-20000-2-200000000-22-22222-200-2000000000000
χ2822-22-222222-2002-222220000222222-2-2-2-2-2-20000-2-2000000002-22-2-2-2-22002000000000000
χ2922-2-12-2-11121002-1-1-1-2-23−33−3-1-1111122-22110000-1-133−3−333−3−3-2-22-1-111100-13−33−300000000
χ3022-2-12-2-11121002-1-1-1-2-23−33−3-1-11111-2-2-22110000-1-133−3−333−3−322-211-1-1-1001−33−3300000000
χ3122-2-12-2-11121002-1-1-1-2-2−33−33-1-1111122-22110000-1-1−3−333−3−333-2-22-1-111100-1−33−3300000000
χ3222-2-12-2-11121002-1-1-1-2-2−33−33-1-11111-2-2-22110000-1-1−3−333−3−33322-211-1-1-10013−33−300000000
χ3322-2-1-22-1-1-1210021-1-122−i3i3i3−i3-1-1-1-1-1-122-2-211000011−i3−i3i3i3i3i3−i3−i3-22-2-1-1-1-11001−i3i3i3−i300000000
χ3422-2-1-22-1-1-1210021-1-122−i3i3i3−i3-1-1-1-1-1-1-2-2-2-211000011−i3−i3i3i3i3i3−i3−i32-221111-100-1i3−i3−i3i300000000
χ3522-2-1-22-1-1-1210021-1-122i3−i3−i3i3-1-1-1-1-1-122-2-211000011i3i3−i3−i3−i3−i3i3i3-22-2-1-1-1-11001i3−i3−i3i300000000
χ3622-2-1-22-1-1-1210021-1-122i3−i3−i3i3-1-1-1-1-1-1-2-2-2-211000011i3i3−i3−i3−i3−i3i3i32-221111-100-1−i3i3i3−i300000000
χ37444444444-1444-14-1-1-1-14444-1-1-1-1-1-100-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000
χ38444444444-14-4-4-14-1-1-1-1-4-4-4-4-1-1-1-1-1-100-1-1-1-11111-1-11111111100000000000000000000000
χ394444-4-44-4-4-144i−4i-1-4-1-1114i4i−4i−4i-1-1111100-11-1-1−i−iii11−i−i−i−iiiii00000000000000000000000
χ404444-4-44-4-4-14−4i4i-1-4-1-111−4i−4i4i4i-1-1111100-11-1-1ii−i−i11iiii−i−i−i−i00000000000000000000000
χ41444-244-2-2-2-1-244-1-21−i1521+i152-1-1-2-2-2-21−i1521+i1521−i1521−i1521+i1521+i15200-1-11−i1521+i152-1-1-1-11−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i15200000000000000000000000
χ42444-244-2-2-2-1-244-1-21+i1521−i152-1-1-2-2-2-21+i1521−i1521+i1521+i1521−i1521−i15200-1-11+i1521−i152-1-1-1-11+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i15200000000000000000000000
χ43444-244-2-2-2-1-2-4-4-1-21−i1521+i152-1-122221−i1521+i1521−i1521−i1521+i1521+i15200-1-11−i1521+i15211111−i1521+i152−1+i152−1−i152−1+i152−1−i152−1+i152−1−i152−1+i152−1−i15200000000000000000000000
χ44444-244-2-2-2-1-2-4-4-1-21+i1521−i152-1-122221+i1521−i1521+i1521+i1521−i1521−i15200-1-11+i1521−i15211111+i1521−i152−1−i152−1+i152−1−i152−1+i152−1−i152−1+i152−1−i152−1+i15200000000000000000000000
χ45444-2-4-4-222-1-24i−4i-121−i1521+i15211−2i−2i2i2i1−i1521+i152−1+i152−1+i152−1−i152−1−i15200-111−i1521+i152−i−iii−1+i152−1−i152ζ7+ζ11+ζ43+ζ59ζ19+ζ23+ζ31+ζ47ζ7+ζ11+ζ43+ζ59ζ19+ζ23+ζ31+ζ47−ζ7−ζ11−ζ43−ζ59−ζ19−ζ23−ζ31−ζ47−ζ7−ζ11−ζ43−ζ59−ζ19−ζ23−ζ31−ζ4700000000000000000000000
χ46444-2-4-4-222-1-24i−4i-121+i1521−i15211−2i−2i2i2i1+i1521−i152−1−i152−1−i152−1+i152−1+i15200-111+i1521−i152−i−iii−1−i152−1+i152ζ19+ζ23+ζ31+ζ47ζ7+ζ11+ζ43+ζ59ζ19+ζ23+ζ31+ζ47ζ7+ζ11+ζ43+ζ59−ζ19−ζ23−ζ31−ζ47−ζ7−ζ11−ζ43−ζ59−ζ19−ζ23−ζ31−ζ47−ζ7−ζ11−ζ43−ζ5900000000000000000000000
χ47444-2-4-4-222-1-2−4i4i-121−i1521+i152112i2i−2i−2i1−i1521+i152−1+i152−1+i152−1−i152−1−i15200-111−i1521+i152ii−i−i−1+i152−1−i152−ζ7−ζ11−ζ43−ζ59−ζ19−ζ23−ζ31−ζ47−ζ7−ζ11−ζ43−ζ59−ζ19−ζ23−ζ31−ζ47ζ7+ζ11+ζ43+ζ59ζ19+ζ23+ζ31+ζ47ζ7+ζ11+ζ43+ζ59ζ19+ζ23+ζ31+ζ4700000000000000000000000
χ48444-2-4-4-222-1-2−4i4i-121+i1521−i152112i2i−2i−2i1+i1521−i152−1−i152−1−i152−1+i152−1+i15200-111+i1521−i152ii−i−i−1−i152−1+i152−ζ19−ζ23−ζ31−ζ47−ζ7−ζ11−ζ43−ζ59−ζ19−ζ23−ζ31−ζ47−ζ7−ζ11−ζ43−ζ59ζ19+ζ23+ζ31+ζ47ζ7+ζ11+ζ43+ζ59ζ19+ζ23+ζ31+ζ47ζ7+ζ11+ζ43+ζ5900000000000000000000000
χ4944-444-44-4-4-1-400-14-1-1110000-1-11111001-111−i5i5−i5i5-1-1−i5i5i5−i5−i5i5i5−i500000000000000000000000
χ5044-444-44-4-4-1-400-14-1-1110000-1-11111001-111i5−i5i5−i5-1-1i5−i5−i5i5i5−i5−i5i500000000000000000000000
χ5144-44-44444-1-400-1-4-1-1-1-10000-1-1-1-1-1-1001111−555−511−555−55−5−5500000000000000000000000
χ5244-44-44444-1-400-1-4-1-1-1-10000-1-1-1-1-1-10011115−5−55115−5−55−555−500000000000000000000000
χ5344-4-24-4-222-1200-1-21−i1521+i1521123−2323−231−i1521+i152−1+i152−1+i152−1−i152−1−i152001-1−1+i152−1−i152i5−i5i5−i51−i1521+i152ζ7−ζ11+ζ43−ζ59ζ19−ζ23+ζ31−ζ47−ζ7+ζ11−ζ43+ζ59−ζ19+ζ23−ζ31+ζ47ζ7−ζ11+ζ43−ζ59ζ19−ζ23+ζ31−ζ47−ζ7+ζ11−ζ43+ζ59−ζ19+ζ23−ζ31+ζ4700000000000000000000000
χ5444-4-24-4-222-1200-1-21−i1521+i15211−2323−23231−i1521+i152−1+i152−1+i152−1−i152−1−i152001-1−1+i152−1−i152−i5i5−i5i51−i1521+i152−ζ7+ζ11−ζ43+ζ59−ζ19+ζ23−ζ31+ζ47ζ7−ζ11+ζ43−ζ59ζ19−ζ23+ζ31−ζ47−ζ7+ζ11−ζ43+ζ59−ζ19+ζ23−ζ31+ζ47ζ7−ζ11+ζ43−ζ59ζ19−ζ23+ζ31−ζ4700000000000000000000000
χ5544-4-24-4-222-1200-1-21+i1521−i1521123−2323−231+i1521−i152−1−i152−1−i152−1+i152−1+i152001-1−1−i152−1+i152−i5i5−i5i51+i1521−i152ζ19−ζ23+ζ31−ζ47ζ7−ζ11+ζ43−ζ59−ζ19+ζ23−ζ31+ζ47−ζ7+ζ11−ζ43+ζ59ζ19−ζ23+ζ31−ζ47ζ7−ζ11+ζ43−ζ59−ζ19+ζ23−ζ31+ζ47−ζ7+ζ11−ζ43+ζ5900000000000000000000000
χ5644-4-24-4-222-1200-1-21+i1521−i15211−2323−23231+i1521−i152−1−i152−1−i152−1+i152−1+i152001-1−1−i152−1+i152i5−i5i5−i51+i1521−i152−ζ19+ζ23−ζ31+ζ47−ζ7+ζ11−ζ43+ζ59ζ19−ζ23+ζ31−ζ47ζ7−ζ11+ζ43−ζ59−ζ19+ζ23−ζ31+ζ47−ζ7+ζ11−ζ43+ζ59ζ19−ζ23+ζ31−ζ47ζ7−ζ11+ζ43−ζ5900000000000000000000000
χ5744-4-2-44-2-2-2-1200-121−i1521+i152-1-1−2i32i32i3−2i31−i1521+i1521−i1521−i1521+i1521+i1520011−1+i152−1−i1525−5−55−1+i152−1−i152ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ4600000000000000000000000
χ5844-4-2-44-2-2-2-1200-121−i1521+i152-1-12i3−2i3−2i32i31−i1521+i1521−i1521−i1521+i1521+i1520011−1+i152−1−i152−555−5−1+i152−1−i152−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ4600000000000000000000000
χ5944-4-2-44-2-2-2-1200-121+i1521−i152-1-1−2i32i32i3−2i31+i1521−i1521+i1521+i1521−i1521−i1520011−1−i152−1+i152−555−5−1−i152−1+i152ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ5800000000000000000000000
χ6044-4-2-44-2-2-2-1200-121+i1521−i152-1-12i3−2i3−2i32i31+i1521−i1521+i1521+i1521−i1521−i1520011−1−i152−1+i1525−5−55−1−i152−1+i152−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ5800000000000000000000000
χ614-40400-4004000-4044000000-4-400004-40000000000000000000004-4000000000000000000
χ624-40400-4004000-4044000000-4-40000-44000000000000000000000-44000000000000000000
χ634-40-200223−234000-40-2-20000002223−2323−234-4000000000000000000000-2223−230000000000000000
χ644-40-200223−234000-40-2-20000002223−2323−23-440000000000000000000002-2−23230000000000000000
χ654-40-2002−23234000-40-2-200000022−2323−23234-4000000000000000000000-22−23230000000000000000
χ664-40-2002−23234000-40-2-200000022−2323−2323-440000000000000000000002-223−230000000000000000
χ678-80800-800-200020-2-2−2i52i5000022−2i52i52i5−2i50000000000000000000000000000000000000000000
χ688-80800-800-200020-2-22i5−2i50000222i5−2i5−2i52i50000000000000000000000000000000000000000000
χ698-80-400443−43-2000201−i151+i152i5−2i50000−1+i15−1−i152ζ7−2ζ11+2ζ43−2ζ59−2ζ7+2ζ11−2ζ43+2ζ592ζ19−2ζ23+2ζ31−2ζ47−2ζ19+2ζ23−2ζ31+2ζ470000000000000000000000000000000000000000000
χ708-80-400443−43-2000201+i151−i15−2i52i50000−1−i15−1+i152ζ19−2ζ23+2ζ31−2ζ47−2ζ19+2ζ23−2ζ31+2ζ472ζ7−2ζ11+2ζ43−2ζ59−2ζ7+2ζ11−2ζ43+2ζ590000000000000000000000000000000000000000000
χ718-80-4004−4343-2000201−i151+i15−2i52i50000−1+i15−1−i15−2ζ7+2ζ11−2ζ43+2ζ592ζ7−2ζ11+2ζ43−2ζ59−2ζ19+2ζ23−2ζ31+2ζ472ζ19−2ζ23+2ζ31−2ζ470000000000000000000000000000000000000000000
χ728-80-4004−4343-2000201+i151−i152i5−2i50000−1−i15−1+i15−2ζ19+2ζ23−2ζ31+2ζ472ζ19−2ζ23+2ζ31−2ζ47−2ζ7+2ζ11−2ζ43+2ζ592ζ7−2ζ11+2ζ43−2ζ590000000000000000000000000000000000000000000

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