Finite Group Databasebeta

← Group #14512584

Character table — Group #14512584

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size11244444444444446688101012161616161616161616161616161616161616202020202024242424303040404040606060606080808080808080808080
order122334566101010202020204466442121215153030303030306060606060606060488881010202022121212122888812122424242424242424
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-111111111111-1-1-1-111-1-1-1-1-1-1-1-1
χ311111111111111111111-1-11111111111111111111-1ii−i−i1111-1-1-1-1-1-1-1ii−i−i-1-1iiii−i−i−i−i
χ411111111111111111111-1-11111111111111111111-1−i−iii1111-1-1-1-1-1-1-1−i−iii-1-1−i−i−i−iiiii
χ511111-1111111-1-1-1-1111111-1-1-111111111-1-1-1-1-1-1-1-1-11-11-1-1-111111111-11-11-1-1-111-1-111-1-1
χ611111-1111111-1-1-1-1111111-1-1-111111111-1-1-1-1-1-1-1-1-1-11-11-1-111111111-1-11-11-1-1-1-111-1-111
χ711111-1111111-1-1-1-11111-1-1-1-1-111111111-1-1-1-1-1-1-1-11i−i−ii-1-111-1-1-1-1-1-11i−i−ii11ii−i−i−i−iii
χ811111-1111111-1-1-1-11111-1-1-1-1-111111111-1-1-1-1-1-1-1-11−iii−i-1-111-1-1-1-1-1-11−iii−i11−i−iiiii−i−i
χ9111−1−i32−1+i3211−1−i32−1+i32111111111−1−i32−1+i32111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i3211111111111−1−i32−1−i32−1+i32−1+i3211111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32
χ10111−1−i32−1+i3211−1−i32−1+i32111111111−1−i32−1+i32111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321-1-1-1-1111111−1−i32−1−i32−1+i32−1+i321-1-1-1-1−1−i32−1+i321+i321−i321+i321−i321+i321−i321+i321−i32
χ11111−1−i32−1+i3211−1−i32−1+i32111111111−1−i32−1+i32-1-11−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-1ii−i−i1111-1-11+i321+i321−i321−i32-1ii−i−i1+i321−i32−ζ7−ζ19−ζ31−ζ43−ζ11−ζ23−ζ47−ζ59−ζ7−ζ19−ζ31−ζ43−ζ11−ζ23−ζ47−ζ59ζ7+ζ19+ζ31+ζ43ζ11+ζ23+ζ47+ζ59ζ7+ζ19+ζ31+ζ43ζ11+ζ23+ζ47+ζ59
χ12111−1−i32−1+i3211−1−i32−1+i32111111111−1−i32−1+i32-1-11−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-1−i−iii1111-1-11+i321+i321−i321−i32-1−i−iii1+i321−i32ζ7+ζ19+ζ31+ζ43ζ11+ζ23+ζ47+ζ59ζ7+ζ19+ζ31+ζ43ζ11+ζ23+ζ47+ζ59−ζ7−ζ19−ζ31−ζ43−ζ11−ζ23−ζ47−ζ59−ζ7−ζ19−ζ31−ζ43−ζ11−ζ23−ζ47−ζ59
χ13111−1−i32−1+i32-11−1−i32−1+i32111-1-1-1-111−1−i32−1+i3211-11+i321−i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32-11-11-1-1-11111−1−i32−1−i32−1+i32−1+i32-11-11-11+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i32
χ14111−1−i32−1+i32-11−1−i32−1+i32111-1-1-1-111−1−i32−1+i3211-11+i321−i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32-1-11-11-1-11111−1−i32−1−i32−1+i32−1+i32-1-11-111+i321−i321+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i32
χ15111−1−i32−1+i32-11−1−i32−1+i32111-1-1-1-111−1−i32−1+i32-1-1-11+i321−i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i321i−i−ii-1-111-1-11+i321+i321−i321−i321i−i−ii−1−i32−1+i32−ζ7−ζ19−ζ31−ζ43−ζ11−ζ23−ζ47−ζ59ζ7+ζ19+ζ31+ζ43ζ11+ζ23+ζ47+ζ59ζ7+ζ19+ζ31+ζ43ζ11+ζ23+ζ47+ζ59−ζ7−ζ19−ζ31−ζ43−ζ11−ζ23−ζ47−ζ59
χ16111−1−i32−1+i32-11−1−i32−1+i32111-1-1-1-111−1−i32−1+i32-1-1-11+i321−i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i321−iii−i-1-111-1-11+i321+i321−i321−i321−iii−i−1−i32−1+i32ζ7+ζ19+ζ31+ζ43ζ11+ζ23+ζ47+ζ59−ζ7−ζ19−ζ31−ζ43−ζ11−ζ23−ζ47−ζ59−ζ7−ζ19−ζ31−ζ43−ζ11−ζ23−ζ47−ζ59ζ7+ζ19+ζ31+ζ43ζ11+ζ23+ζ47+ζ59
χ17111−1+i32−1−i3211−1+i32−1−i32111111111−1+i32−1−i32111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i3211111111111−1+i32−1+i32−1−i32−1−i3211111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32
χ18111−1+i32−1−i3211−1+i32−1−i32111111111−1+i32−1−i32111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321-1-1-1-1111111−1+i32−1+i32−1−i32−1−i321-1-1-1-1−1+i32−1−i321−i321+i321−i321+i321−i321+i321−i321+i32
χ19111−1+i32−1−i3211−1+i32−1−i32111111111−1+i32−1−i32-1-11−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-1ii−i−i1111-1-11−i321−i321+i321+i32-1ii−i−i1−i321+i32−ζ11−ζ23−ζ47−ζ59−ζ7−ζ19−ζ31−ζ43−ζ11−ζ23−ζ47−ζ59−ζ7−ζ19−ζ31−ζ43ζ11+ζ23+ζ47+ζ59ζ7+ζ19+ζ31+ζ43ζ11+ζ23+ζ47+ζ59ζ7+ζ19+ζ31+ζ43
χ20111−1+i32−1−i3211−1+i32−1−i32111111111−1+i32−1−i32-1-11−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-1−i−iii1111-1-11−i321−i321+i321+i32-1−i−iii1−i321+i32ζ11+ζ23+ζ47+ζ59ζ7+ζ19+ζ31+ζ43ζ11+ζ23+ζ47+ζ59ζ7+ζ19+ζ31+ζ43−ζ11−ζ23−ζ47−ζ59−ζ7−ζ19−ζ31−ζ43−ζ11−ζ23−ζ47−ζ59−ζ7−ζ19−ζ31−ζ43
χ21111−1+i32−1−i32-11−1+i32−1−i32111-1-1-1-111−1+i32−1−i3211-11−i321+i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32-11-11-1-1-11111−1+i32−1+i32−1−i32−1−i32-11-11-11−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i321−i321+i32
χ22111−1+i32−1−i32-11−1+i32−1−i32111-1-1-1-111−1+i32−1−i3211-11−i321+i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32-1-11-11-1-11111−1+i32−1+i32−1−i32−1−i32-1-11-111−i321+i321−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i32
χ23111−1+i32−1−i32-11−1+i32−1−i32111-1-1-1-111−1+i32−1−i32-1-1-11−i321+i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i321i−i−ii-1-111-1-11−i321−i321+i321+i321i−i−ii−1+i32−1−i32−ζ11−ζ23−ζ47−ζ59−ζ7−ζ19−ζ31−ζ43ζ11+ζ23+ζ47+ζ59ζ7+ζ19+ζ31+ζ43ζ11+ζ23+ζ47+ζ59ζ7+ζ19+ζ31+ζ43−ζ11−ζ23−ζ47−ζ59−ζ7−ζ19−ζ31−ζ43
χ24111−1+i32−1−i32-11−1+i32−1−i32111-1-1-1-111−1+i32−1−i32-1-1-11−i321+i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i321−iii−i-1-111-1-11−i321−i321+i321+i321−iii−i−1+i32−1−i32ζ11+ζ23+ζ47+ζ59ζ7+ζ19+ζ31+ζ43−ζ11−ζ23−ζ47−ζ59−ζ7−ζ19−ζ31−ζ43−ζ11−ζ23−ζ47−ζ59−ζ7−ζ19−ζ31−ζ43ζ11+ζ23+ζ47+ζ59ζ7+ζ19+ζ31+ζ43
χ2522-2220222-2-2200002-2-2-22-200022-2-2-2-2220000000000000002-22-22-22-2000000000000000
χ2622-2220222-2-2200002-2-2-2-2200022-2-2-2-2220000000000000002-2-22-22-22000000000000000
χ2722-2−1−i3−1+i302−1−i3−1+i3-2-2200002-21+i31−i32-2000−1−i3−1+i31+i31+i31−i31−i3−1−i3−1+i30000000000000002-22-2−1−i31+i3−1+i31−i3000000000000000
χ2822-2−1−i3−1+i302−1−i3−1+i3-2-2200002-21+i31−i3-22000−1−i3−1+i31+i31+i31−i31−i3−1−i3−1+i30000000000000002-2-221+i3−1−i31−i3−1+i3000000000000000
χ2922-2−1+i3−1−i302−1+i3−1−i3-2-2200002-21−i31+i32-2000−1+i3−1−i31−i31−i31+i31+i3−1+i3−1−i30000000000000002-22-2−1+i31−i3−1−i31+i3000000000000000
χ3022-2−1+i3−1−i302−1+i3−1−i3-2-2200002-21−i31+i3-22000−1+i3−1−i31−i31−i31+i31+i3−1+i3−1−i30000000000000002-2-221−i3−1+i31+i3−1−i3000000000000000
χ313330033003333333-1-10033-100000000000000000033333-1-1-1-1-1-10000-1-1-1-1-10000000000
χ323330033003333333-1-10033-10000000000000000003-3-3-3-3-1-1-1-1-1-10000-111110000000000
χ333330033003333333-1-100-3-3-1000000000000000000-33i3i−3i−3i-1-1-1-11100001−i−iii0000000000
χ343330033003333333-1-100-3-3-1000000000000000000-3−3i−3i3i3i-1-1-1-11100001ii−i−i0000000000
χ3533300-3300333-3-3-3-3-1-100331000000000000000000-33-33-311-1-1-1-100001-11-110000000000
χ3633300-3300333-3-3-3-3-1-100331000000000000000000-3-33-3311-1-1-1-1000011-11-10000000000
χ3733300-3300333-3-3-3-3-1-100-3-3100000000000000000033i−3i−3i3i11-1-1110000-1−iii−i0000000000
χ3833300-3300333-3-3-3-3-1-100-3-310000000000000000003−3i3i3i−3i11-1-1110000-1i−i−ii0000000000
χ39444444-144-1-1-1-1-1-1-1444400444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000-1-1-1-1000000000000000000000
χ4044444-4-144-1-1-11111444400-4-4-4-1-1-1-1-1-1-1-1111111110000011-1-1000000000000000000000
χ41444−2−2i3−2+2i34-1−2−2i3−2+2i3-1-1-1-1-1-1-144−2−2i3−2+2i3004−2−2i3−2+2i31+i321−i321+i321+i321−i321−i321+i321−i321+i321+i321+i321+i321−i321−i321−i321−i3200000-1-1-1-1000000000000000000000
χ42444−2−2i3−2+2i3-4-1−2−2i3−2+2i3-1-1-1111144−2−2i3−2+2i300-42+2i32−2i31+i321−i321+i321+i321−i321−i321+i321−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i320000011-1-1000000000000000000000
χ43444−2+2i3−2−2i34-1−2+2i3−2−2i3-1-1-1-1-1-1-144−2+2i3−2−2i3004−2+2i3−2−2i31−i321+i321−i321−i321+i321+i321−i321+i321−i321−i321−i321−i321+i321+i321+i321+i3200000-1-1-1-1000000000000000000000
χ44444−2+2i3−2−2i3-4-1−2+2i3−2−2i3-1-1-1111144−2+2i3−2−2i300-42−2i32+2i31−i321+i321−i321−i321+i321+i321−i321+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i320000011-1-1000000000000000000000
χ4544-4440-14411-1−5−5554-4-4-400000-1-11111-1-1−5−555−5−55500000−55-11000000000000000000000
χ4644-4440-14411-155−5−54-4-4-400000-1-11111-1-155−5−555−5−5000005−5-11000000000000000000000
χ4744-4−2−2i3−2+2i30-1−2−2i3−2+2i311-1−5−5554-42+2i32−2i3000001+i321−i32−1−i32−1−i32−1+i32−1+i321+i321−i32ζ22−ζ34−ζ46+ζ58ζ22−ζ34−ζ46+ζ58−ζ22+ζ34+ζ46−ζ58−ζ22+ζ34+ζ46−ζ58ζ2−ζ14−ζ26+ζ38ζ2−ζ14−ζ26+ζ38−ζ2+ζ14+ζ26−ζ38−ζ2+ζ14+ζ26−ζ3800000−55-11000000000000000000000
χ4844-4−2−2i3−2+2i30-1−2−2i3−2+2i311-155−5−54-42+2i32−2i3000001+i321−i32−1−i32−1−i32−1+i32−1+i321+i321−i32−ζ22+ζ34+ζ46−ζ58−ζ22+ζ34+ζ46−ζ58ζ22−ζ34−ζ46+ζ58ζ22−ζ34−ζ46+ζ58−ζ2+ζ14+ζ26−ζ38−ζ2+ζ14+ζ26−ζ38ζ2−ζ14−ζ26+ζ38ζ2−ζ14−ζ26+ζ38000005−5-11000000000000000000000
χ4944-4−2+2i3−2−2i30-1−2+2i3−2−2i311-1−5−5554-42−2i32+2i3000001−i321+i32−1+i32−1+i32−1−i32−1−i321−i321+i32ζ2−ζ14−ζ26+ζ38ζ2−ζ14−ζ26+ζ38−ζ2+ζ14+ζ26−ζ38−ζ2+ζ14+ζ26−ζ38ζ22−ζ34−ζ46+ζ58ζ22−ζ34−ζ46+ζ58−ζ22+ζ34+ζ46−ζ58−ζ22+ζ34+ζ46−ζ5800000−55-11000000000000000000000
χ5044-4−2+2i3−2−2i30-1−2+2i3−2−2i311-155−5−54-42−2i32+2i3000001−i321+i32−1+i32−1+i32−1−i32−1−i321−i321+i32−ζ2+ζ14+ζ26−ζ38−ζ2+ζ14+ζ26−ζ38ζ2−ζ14−ζ26+ζ38ζ2−ζ14−ζ26+ζ38−ζ22+ζ34+ζ46−ζ58−ζ22+ζ34+ζ46−ζ58ζ22−ζ34−ζ46+ζ58ζ22−ζ34−ζ46+ζ58000005−5-11000000000000000000000
χ5166-6000600-6-660000-22006-600000000000000000000000000-22-220000000000000000000
χ5266-6000600-6-660000-2200-6600000000000000000000000000-222-20000000000000000000
χ538-80-4-4084400-80000000000000-4-400004400000000000000000000000000000000000000
χ548-80-4-40-244−252522ζ7+2ζ11−2ζ19−2ζ23+2ζ31−2ζ43+2ζ47−2ζ59−2ζ7−2ζ11+2ζ19+2ζ23−2ζ31+2ζ43−2ζ47+2ζ592ζ7−2ζ11+2ζ19−2ζ23−2ζ31−2ζ43+2ζ47+2ζ59−2ζ7+2ζ11−2ζ19+2ζ23+2ζ31+2ζ43−2ζ47−2ζ5900000000011−55−55-1-1ζ7+ζ11−ζ19−ζ23+ζ31−ζ43+ζ47−ζ59−ζ7−ζ11+ζ19+ζ23−ζ31+ζ43−ζ47+ζ59ζ7−ζ11+ζ19−ζ23−ζ31−ζ43+ζ47+ζ59−ζ7+ζ11−ζ19+ζ23+ζ31+ζ43−ζ47−ζ59ζ7+ζ11−ζ19−ζ23+ζ31−ζ43+ζ47−ζ59−ζ7−ζ11+ζ19+ζ23−ζ31+ζ43−ζ47+ζ59ζ7−ζ11+ζ19−ζ23−ζ31−ζ43+ζ47+ζ59−ζ7+ζ11−ζ19+ζ23+ζ31+ζ43−ζ47−ζ59000000000000000000000000000000
χ558-80-4-40-244−25252−2ζ7−2ζ11+2ζ19+2ζ23−2ζ31+2ζ43−2ζ47+2ζ592ζ7+2ζ11−2ζ19−2ζ23+2ζ31−2ζ43+2ζ47−2ζ59−2ζ7+2ζ11−2ζ19+2ζ23+2ζ31+2ζ43−2ζ47−2ζ592ζ7−2ζ11+2ζ19−2ζ23−2ζ31−2ζ43+2ζ47+2ζ5900000000011−55−55-1-1−ζ7−ζ11+ζ19+ζ23−ζ31+ζ43−ζ47+ζ59ζ7+ζ11−ζ19−ζ23+ζ31−ζ43+ζ47−ζ59−ζ7+ζ11−ζ19+ζ23+ζ31+ζ43−ζ47−ζ59ζ7−ζ11+ζ19−ζ23−ζ31−ζ43+ζ47+ζ59−ζ7−ζ11+ζ19+ζ23−ζ31+ζ43−ζ47+ζ59ζ7+ζ11−ζ19−ζ23+ζ31−ζ43+ζ47−ζ59−ζ7+ζ11−ζ19+ζ23+ζ31+ζ43−ζ47−ζ59ζ7−ζ11+ζ19−ζ23−ζ31−ζ43+ζ47+ζ59000000000000000000000000000000
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Here ζ is a primitive root of unity of order 60 (ζ60 = 1); i = ζ15.