Finite Group Databasebeta

← Group #14301360

Character table — Group #14301360

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size112222222444444558888888881010101010101016161616161616162020202020202020202020202020202024244040404040404040484848486060606060606060120120
order1223446121224561012226101215202030606024466121210203030306060602444446121212121212121212286881224242424101040404444444428
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111-1-11-1-1-1-11111-1-1-1-1-1-1-1-111
χ41111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-1-1-111111111-1-1
χ5111111111111111-1-1111111111-1-1-1-1-1-1-111111111-1-1ii−i−i-1-1iiii−i−i−i−i11-1i−i-1ii−i−i1111i−iiii−i−i−i-1-1
χ6111111111111111-1-1111111111-1-1-1-1-1-1-111111111-1-1ii−i−i-1-1iiii−i−i−i−i-1-1-1i−i-1ii−i−i-1-1-1-1−ii−i−i−iiii11
χ7111111111111111-1-1111111111-1-1-1-1-1-1-111111111-1-1−i−iii-1-1−i−i−i−iiiii11-1−ii-1−i−iii1111−ii−i−i−iiii-1-1
χ8111111111111111-1-1111111111-1-1-1-1-1-1-111111111-1-1−i−iii-1-1−i−i−i−iiiii-1-1-1−ii-1−i−iii-1-1-1-1i−iiii−i−i−i11
χ9111111111-1-1111111-11-11111111111111-1-11-1-11-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-111-1-1-1-111-111-11-1
χ10111111111-1-1111111-11-11111111111111-1-11-1-11-1-1-1-111111111111111-11-1-1-1-1-1-1-1-1-1-11111-1-11-1-11-11
χ11111111111-1-1111111-11-11111111111111-1-11-1-11-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-111-1111111-1-111-1-11-1-111-1
χ12111111111-1-1111111-11-11111111111111-1-11-1-11-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-11-111-11111-1-111-1-111-111-1-11
χ13111111111-1-11111-1-1-11-1111111-1-1-1-1-1-1-1-1-11-1-11-1-111ii−i−i-1-1iiii−i−i−i−i1-11−ii1−i−iii11-1-1−iiii−i−i−ii-11
χ14111111111-1-11111-1-1-11-1111111-1-1-1-1-1-1-1-1-11-1-11-1-111ii−i−i-1-1iiii−i−i−i−i-111−ii1−i−iii-1-111i−i−i−iiii−i1-1
χ15111111111-1-11111-1-1-11-1111111-1-1-1-1-1-1-1-1-11-1-11-1-111−i−iii-1-1−i−i−i−iiiii1-11i−i1ii−i−i11-1-1i−i−i−iiii−i-11
χ16111111111-1-11111-1-1-11-1111111-1-1-1-1-1-1-1-1-11-1-11-1-111−i−iii-1-1−i−i−i−iiiii-111i−i1ii−i−i-1-111−iiii−i−i−ii1-1
χ172222-2-22-2-200222-2220202-2-22-2-22-2-222-2-200200-2000000002-20000000000000000000000002-202-2000
χ182222-2-22-2-200222-2220202-2-22-2-22-2-222-2-200200-2000000002-2000000000000000000000000-220-22000
χ192222-2-22-2-200222-2-2-20202-2-22-2-2-222-2-22200200-200000000-220000000000000000000000002i−2i0−2i2i000
χ202222-2-22-2-200222-2-2-20202-2-22-2-2-222-2-22200200-200000000-22000000000000000000000000−2i2i02i−2i000
χ21222-122-1-1-1222-12-122-12-1-122-1-1-1222-1-1-1-122-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-100-122-1-1-1-1-100000000000000
χ22222-122-1-1-1222-12-122-12-1-122-1-1-1222-1-1-1-122-1-1-1-1-1-122-2-2-2-2-1-11111111100-1-2-2-1111100000000000000
χ23222-122-1-1-1222-12-1-2-2-12-1-122-1-1-1-2-2-2111122-1-1-1-1-1-1-2-22i2i−2i−2i11−i−i−i−iiiii0012i−2i1−i−iii00000000000000
χ24222-122-1-1-1222-12-1-2-2-12-1-122-1-1-1-2-2-2111122-1-1-1-1-1-1-2-2−2i−2i2i2i11iiii−i−i−i−i001−2i2i1ii−i−i00000000000000
χ25222-122-1-1-1-2-22-12-122121-122-1-1-1222-1-1-1-1-2-2-111-111-2-22222-1-1-1-1-1-1-1-1-1-1001-2-21111100000000000000
χ26222-122-1-1-1-2-22-12-122121-122-1-1-1222-1-1-1-1-2-2-111-111-2-2-2-2-2-2-1-111111111001221-1-1-1-100000000000000
χ27222-122-1-1-1-2-22-12-1-2-2121-122-1-1-1-2-2-21111-2-2-111-111222i2i−2i−2i11−i−i−i−iiiii00-1−2i2i-1ii−i−i00000000000000
χ28222-122-1-1-1-2-22-12-1-2-2121-122-1-1-1-2-2-21111-2-2-111-11122−2i−2i2i2i11iiii−i−i−i−i00-12i−2i-1−i−iii00000000000000
χ2922-222-2222002-22-2220-2022-2222-2-22222200-200-200000000-2-200000000000000000000002200-200-200
χ3022-222-2222002-22-2220-2022-2222-2-22222200-200-200000000-2-20000000000000000000000-2-200200200
χ3122-222-2222002-22-2-2-20-2022-222222-2-2-2-2-200-200-2000000002200000000000000000000002i−2i00−2i002i00
χ3222-222-2222002-22-2-2-20-2022-222222-2-2-2-2-200-200-200000000220000000000000000000000−2i2i002i00−2i00
χ3322-22-222-2-22-22-222222-2-22-222-2-2-22-222-2-22-2-2222-2-22-20000-220000000000200-2000000000000000000
χ3422-22-222-2-22-22-222-2-22-2-22-222-2-22-22-2-2222-2-2222-2-2-2200002-20000000000-2002000000000000000000
χ3522-22-222-2-2-222-22222-2-222-222-2-2-22-222-2-2-22-2-2-2222-220000-220000000000-2002000000000000000000
χ3622-22-222-2-2-222-222-2-2-2-222-222-2-22-22-2-222-22-2-2-22222-200002-20000000000200-2000000000000000000
χ3722-2-1-22-1112-2212-122-1-21-1-22-111-22-2-1-1112-21-1-1-1112-200001-133−3−333−3−300-10013−33−300000000000000
χ3822-2-1-22-1112-2212-122-1-21-1-22-111-22-2-1-1112-21-1-1-1112-200001-1−3−333−3−33300-1001−33−3300000000000000
χ3922-2-1-22-1112-2212-1-2-2-1-21-1-22-1112-2211-1-12-21-1-1-111-220000-11−i3−i3i3i3i3i3−i3−i300100-1−i3i3i3−i300000000000000
χ4022-2-1-22-1112-2212-1-2-2-1-21-1-22-1112-2211-1-12-21-1-1-111-220000-11i3i3−i3−i3−i3−i3i3i300100-1i3−i3−i3i300000000000000
χ4122-2-1-22-111-22212-1221-2-1-1-22-111-22-2-1-111-22111-1-1-1-2200001-133−3−333−3−300100-1−33−3300000000000000
χ4222-2-1-22-111-22212-1221-2-1-1-22-111-22-2-1-111-22111-1-1-1-2200001-1−3−333−3−33300100-13−33−300000000000000
χ4322-2-1-22-111-22212-1-2-21-2-1-1-22-1112-2211-1-1-22111-1-1-12-20000-11−i3−i3i3i3i3i3−i3−i300-1001i3−i3−i3i300000000000000
χ4422-2-1-22-111-22212-1-2-21-2-1-1-22-1112-2211-1-1-22111-1-1-12-20000-11i3i3−i3−i3−i3−i3i3i300-1001−i3i3i3−i300000000000000
χ4544444444444-14-14004-14-1-1-1-1-1-10000000-1-1-1-1-1-1-1-100000000000000004400000000-1-1-1-10000000000
χ4644444444444-14-14004-14-1-1-1-1-1-10000000-1-1-1-1-1-1-1-10000000000000000-4-40000000011110000000000
χ47444444444-4-4-14-1400-4-1-4-1-1-1-1-1-1000000011-111-11100000000000000004-400000000-1-1110000000000
χ48444444444-4-4-14-1400-4-1-4-1-1-1-1-1-1000000011-111-1110000000000000000-440000000011-1-10000000000
χ49444-2-4-4-222004-24244040-2-4-4-2224-4-4-2-22200-200200000000-2200000000000000000000000000000000
χ50444-2-4-4-222004-242-4-4040-2-4-4-222-44422-2-200-2002000000002-200000000000000000000000000000000
χ5144-44-444-4-44-4-1-4-140041-4-11-1-1110000000-111-1-1-11100000000000000000000000000−55−550000000000
χ5244-44-444-4-44-4-1-4-140041-4-11-1-1110000000-111-1-1-111000000000000000000000000005−55−50000000000
χ5344-44-444-4-4-44-1-4-1400-414-11-1-11100000001-1111-1-1-100000000000000000000000000−555−50000000000
χ5444-44-444-4-4-44-1-4-1400-414-11-1-11100000001-1111-1-1-1000000000000000000000000005−5−550000000000
χ5544-4-24-4-2-2-2004242440-40-24-4-2-2-2-4-44-2-2-2-2002002000000002200000000000000000000000000000000
χ5644-4-24-4-2-2-2004242-4-40-40-24-4-2-2-244-4222200200200000000-2-200000000000000000000000000000000
χ574-40400-4000040-404-4000400-4000004-40000000000002i−2i2i−2i002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ584-40400-4000040-404-4000400-4000004-4000000000000−2i2i−2i2i00−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ594-40400-4000040-40-44000400-400000-440000000000002-2-22002-22-2-22-22000000000000000000000000
χ604-40400-4000040-40-44000400-400000-44000000000000-222-200-22-222-22-2000000000000000000000000
χ614-40-200223−230040-404-4000-200223−23000-2223−2300000000002i−2i2i−2i00−ζ2−ζ7−ζ11−ζ14−ζ19+ζ22−ζ23−ζ26−ζ31+ζ34−ζ38−ζ43+ζ46−ζ47+ζ58−ζ59ζ2+ζ7+ζ11+ζ14+ζ19−ζ22+ζ23+ζ26+ζ31−ζ34+ζ38+ζ43−ζ46+ζ47−ζ58+ζ59ζ2−ζ7−ζ11+ζ14−ζ19−ζ22−ζ23+ζ26−ζ31−ζ34+ζ38−ζ43−ζ46−ζ47−ζ58−ζ59−ζ2+ζ7+ζ11−ζ14+ζ19+ζ22+ζ23−ζ26+ζ31+ζ34−ζ38+ζ43+ζ46+ζ47+ζ58+ζ59−ζ2−ζ7−ζ11−ζ14−ζ19+ζ22−ζ23−ζ26−ζ31+ζ34−ζ38−ζ43+ζ46−ζ47+ζ58−ζ59ζ2+ζ7+ζ11+ζ14+ζ19−ζ22+ζ23+ζ26+ζ31−ζ34+ζ38+ζ43−ζ46+ζ47−ζ58+ζ59ζ2−ζ7−ζ11+ζ14−ζ19−ζ22−ζ23+ζ26−ζ31−ζ34+ζ38−ζ43−ζ46−ζ47−ζ58−ζ59−ζ2+ζ7+ζ11−ζ14+ζ19+ζ22+ζ23−ζ26+ζ31+ζ34−ζ38+ζ43+ζ46+ζ47+ζ58+ζ59000000000000000000000000
χ624-40-200223−230040-404-4000-200223−23000-2223−230000000000−2i2i−2i2i00ζ2+ζ7+ζ11+ζ14+ζ19−ζ22+ζ23+ζ26+ζ31−ζ34+ζ38+ζ43−ζ46+ζ47−ζ58+ζ59−ζ2−ζ7−ζ11−ζ14−ζ19+ζ22−ζ23−ζ26−ζ31+ζ34−ζ38−ζ43+ζ46−ζ47+ζ58−ζ59−ζ2+ζ7+ζ11−ζ14+ζ19+ζ22+ζ23−ζ26+ζ31+ζ34−ζ38+ζ43+ζ46+ζ47+ζ58+ζ59ζ2−ζ7−ζ11+ζ14−ζ19−ζ22−ζ23+ζ26−ζ31−ζ34+ζ38−ζ43−ζ46−ζ47−ζ58−ζ59ζ2+ζ7+ζ11+ζ14+ζ19−ζ22+ζ23+ζ26+ζ31−ζ34+ζ38+ζ43−ζ46+ζ47−ζ58+ζ59−ζ2−ζ7−ζ11−ζ14−ζ19+ζ22−ζ23−ζ26−ζ31+ζ34−ζ38−ζ43+ζ46−ζ47+ζ58−ζ59−ζ2+ζ7+ζ11−ζ14+ζ19+ζ22+ζ23−ζ26+ζ31+ζ34−ζ38+ζ43+ζ46+ζ47+ζ58+ζ59ζ2−ζ7−ζ11+ζ14−ζ19−ζ22−ζ23+ζ26−ζ31−ζ34+ζ38−ζ43−ζ46−ζ47−ζ58−ζ59000000000000000000000000
χ634-40-200223−230040-40-44000-200223−230002-2−232300000000002-2-2200−1−31+3−1+31−31+3−1−31−3−1+3000000000000000000000000
χ644-40-200223−230040-40-44000-200223−230002-2−23230000000000-222-2001+3−1−31−3−1+3−1−31+3−1+31−3000000000000000000000000
χ654-40-2002−23230040-404-4000-2002−2323000-22−232300000000002i−2i2i−2i00ζ2−ζ7−ζ11+ζ14−ζ19−ζ22−ζ23+ζ26−ζ31−ζ34+ζ38−ζ43−ζ46−ζ47−ζ58−ζ59−ζ2+ζ7+ζ11−ζ14+ζ19+ζ22+ζ23−ζ26+ζ31+ζ34−ζ38+ζ43+ζ46+ζ47+ζ58+ζ59−ζ2−ζ7−ζ11−ζ14−ζ19+ζ22−ζ23−ζ26−ζ31+ζ34−ζ38−ζ43+ζ46−ζ47+ζ58−ζ59ζ2+ζ7+ζ11+ζ14+ζ19−ζ22+ζ23+ζ26+ζ31−ζ34+ζ38+ζ43−ζ46+ζ47−ζ58+ζ59ζ2−ζ7−ζ11+ζ14−ζ19−ζ22−ζ23+ζ26−ζ31−ζ34+ζ38−ζ43−ζ46−ζ47−ζ58−ζ59−ζ2+ζ7+ζ11−ζ14+ζ19+ζ22+ζ23−ζ26+ζ31+ζ34−ζ38+ζ43+ζ46+ζ47+ζ58+ζ59−ζ2−ζ7−ζ11−ζ14−ζ19+ζ22−ζ23−ζ26−ζ31+ζ34−ζ38−ζ43+ζ46−ζ47+ζ58−ζ59ζ2+ζ7+ζ11+ζ14+ζ19−ζ22+ζ23+ζ26+ζ31−ζ34+ζ38+ζ43−ζ46+ζ47−ζ58+ζ59000000000000000000000000
χ664-40-2002−23230040-404-4000-2002−2323000-22−23230000000000−2i2i−2i2i00−ζ2+ζ7+ζ11−ζ14+ζ19+ζ22+ζ23−ζ26+ζ31+ζ34−ζ38+ζ43+ζ46+ζ47+ζ58+ζ59ζ2−ζ7−ζ11+ζ14−ζ19−ζ22−ζ23+ζ26−ζ31−ζ34+ζ38−ζ43−ζ46−ζ47−ζ58−ζ59ζ2+ζ7+ζ11+ζ14+ζ19−ζ22+ζ23+ζ26+ζ31−ζ34+ζ38+ζ43−ζ46+ζ47−ζ58+ζ59−ζ2−ζ7−ζ11−ζ14−ζ19+ζ22−ζ23−ζ26−ζ31+ζ34−ζ38−ζ43+ζ46−ζ47+ζ58−ζ59−ζ2+ζ7+ζ11−ζ14+ζ19+ζ22+ζ23−ζ26+ζ31+ζ34−ζ38+ζ43+ζ46+ζ47+ζ58+ζ59ζ2−ζ7−ζ11+ζ14−ζ19−ζ22−ζ23+ζ26−ζ31−ζ34+ζ38−ζ43−ζ46−ζ47−ζ58−ζ59ζ2+ζ7+ζ11+ζ14+ζ19−ζ22+ζ23+ζ26+ζ31−ζ34+ζ38+ζ43−ζ46+ζ47−ζ58+ζ59−ζ2−ζ7−ζ11−ζ14−ζ19+ζ22−ζ23−ζ26−ζ31+ζ34−ζ38−ζ43+ζ46−ζ47+ζ58−ζ59000000000000000000000000
χ674-40-2002−23230040-40-44000-2002−23230002-223−2300000000002-2-2200−1+31−3−1−31+31−3−1+31+3−1−3000000000000000000000000
χ684-40-2002−23230040-40-44000-2002−23230002-223−230000000000-222-2001−3−1+31+3−1−3−1+31−3−1−31+3000000000000000000000000
χ698888-8-88-8-800-28-2-8000-20-222-222000000000-2002000000000000000000000000000000000000000000
χ70888-488-4-4-488-2-4-2-400-4-2-41-2-21110000000-2-21111110000000000000000000000000000000000000000
χ71888-488-4-4-4-8-8-2-4-2-4004-241-2-21110000000221-1-11-1-10000000000000000000000000000000000000000
χ72888-4-8-8-44400-2-4-24000-201221-1-10000000001−i15i15-1−i15i150000000000000000000000000000000000000000
χ73888-4-8-8-44400-2-4-24000-201221-1-10000000001i15−i15-1i15−i150000000000000000000000000000000000000000
χ7488-888-888800-2-8-2-800020-2-22-2-2-20000000002002000000000000000000000000000000000000000000
χ7588-8-48-8-4-4-400-24-24000201-22111000000000-1−i15i15-1i15−i150000000000000000000000000000000000000000
χ7688-8-48-8-4-4-400-24-24000201-22111000000000-1i15−i15-1−i15i150000000000000000000000000000000000000000
χ7788-8-4-88-4448-8-24-2-400-42412-21-1-10000000-22-1111-1-10000000000000000000000000000000000000000
χ7888-8-4-88-444-88-24-2-40042-412-21-1-100000002-2-1-1-11110000000000000000000000000000000000000000
χ7916-1601600-160000-404000000-4004000000000000000000000000000000000000000000000000000000000
χ8016-160-800883−8300-404000000200-2−23230000000000000000000000000000000000000000000000000000000
χ8116-160-8008−838300-404000000200-223−230000000000000000000000000000000000000000000000000000000

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