Finite Group Databasebeta

← Group #90958

Character table — Group #90958

Order 480.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57
size112222222222222224444444444444444444444121212121212121212122020202020206060
order122344556661010202020201010121215152020303030303030606060606060606088404040404040404022666688
χ1111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1
χ4111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ51111-1-11111111-1-1-1-111-1-111-1-1111111-1-1-1-1-1-1-1-1i−iiiii−i−i−i−i1-111-1-1i−i
χ61111-1-11111111-1-1-1-111-1-111-1-1111111-1-1-1-1-1-1-1-1i−iiiii−i−i−i−i-11-1-111−ii
χ71111-1-11111111-1-1-1-111-1-111-1-1111111-1-1-1-1-1-1-1-1−ii−i−i−i−iiiii1-111-1-1−ii
χ81111-1-11111111-1-1-1-111-1-111-1-1111111-1-1-1-1-1-1-1-1−ii−i−i−i−iiiii-11-1-111i−i
χ9222222−1−52−1+52222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+5222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+5222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5200000000
χ10222222−1−52−1+52222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+5222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52-2-21+521+521−521−521+521+521−521−5200000000
χ11222222−1+52−1−52222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−5222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−5222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5200000000
χ12222222−1+52−1−52222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−5222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52-2-21−521−521+521+521−521−521+521+5200000000
χ132222-2-2−1−52−1+52222−1−52−1+521+521+521−521−52−1−52−1+52-2-2−1−52−1+521+521−52−1−52−1−52−1+52−1+52−1−52−1+521+521+521+521+521−521−521−521−522i−2i−ζ11−ζ19−ζ31−ζ59−ζ11−ζ19−ζ31−ζ59−ζ7−ζ23−ζ43−ζ47−ζ7−ζ23−ζ43−ζ47ζ11+ζ19+ζ31+ζ59ζ11+ζ19+ζ31+ζ59ζ7+ζ23+ζ43+ζ47ζ7+ζ23+ζ43+ζ4700000000
χ142222-2-2−1−52−1+52222−1−52−1+521+521+521−521−52−1−52−1+52-2-2−1−52−1+521+521−52−1−52−1−52−1+52−1+52−1−52−1+521+521+521+521+521−521−521−521−52−2i2iζ11+ζ19+ζ31+ζ59ζ11+ζ19+ζ31+ζ59ζ7+ζ23+ζ43+ζ47ζ7+ζ23+ζ43+ζ47−ζ11−ζ19−ζ31−ζ59−ζ11−ζ19−ζ31−ζ59−ζ7−ζ23−ζ43−ζ47−ζ7−ζ23−ζ43−ζ4700000000
χ152222-2-2−1+52−1−52222−1+52−1−521−521−521+521+52−1+52−1−52-2-2−1+52−1−521−521+52−1+52−1+52−1−52−1−52−1+52−1−521−521−521−521−521+521+521+521+522i−2i−ζ7−ζ23−ζ43−ζ47−ζ7−ζ23−ζ43−ζ47−ζ11−ζ19−ζ31−ζ59−ζ11−ζ19−ζ31−ζ59ζ7+ζ23+ζ43+ζ47ζ7+ζ23+ζ43+ζ47ζ11+ζ19+ζ31+ζ59ζ11+ζ19+ζ31+ζ5900000000
χ162222-2-2−1+52−1−52222−1+52−1−521−521−521+521+52−1+52−1−52-2-2−1+52−1−521−521+52−1+52−1+52−1−52−1−52−1+52−1−521−521−521−521−521+521+521+521+52−2i2iζ7+ζ23+ζ43+ζ47ζ7+ζ23+ζ43+ζ47ζ11+ζ19+ζ31+ζ59ζ11+ζ19+ζ31+ζ59−ζ7−ζ23−ζ43−ζ47−ζ7−ζ23−ζ43−ζ47−ζ11−ζ19−ζ31−ζ59−ζ11−ζ19−ζ31−ζ5900000000
χ17222-12222-1-1-122222222-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000022-1-1-1-100
χ18222-12222-1-1-122222222-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000-2-2111100
χ19222-1-2-222-1-1-122-2-2-2-22211-1-1-2-2-1-1-1-1-1-11111111100000000002-2-1-11100
χ20222-1-2-222-1-1-122-2-2-2-22211-1-1-2-2-1-1-1-1-1-1111111110000000000-2211-1-100
χ2122-222-222-2-22222222-2-22-222-2-2-2-2-2-22222-2-222-2-2000000000000000000
χ2222-222-2−1−52−1+52-2-22−1−52−1+52−1−52−1−52−1+52−1+521+521−522-2−1−52−1+521+521−521+521+521−521−52−1−52−1+52−1−52−1−521+521+52−1+52−1+521−521−5200−ζ14+ζ26−ζ34+ζ46ζ14−ζ26+ζ34−ζ46ζ2+ζ22−ζ38−ζ58−ζ2−ζ22+ζ38+ζ58−ζ14+ζ26−ζ34+ζ46ζ14−ζ26+ζ34−ζ46ζ2+ζ22−ζ38−ζ58−ζ2−ζ22+ζ38+ζ5800000000
χ2322-222-2−1−52−1+52-2-22−1−52−1+52−1−52−1−52−1+52−1+521+521−522-2−1−52−1+521+521−521+521+521−521−52−1−52−1+52−1−52−1−521+521+52−1+52−1+521−521−5200ζ14−ζ26+ζ34−ζ46−ζ14+ζ26−ζ34+ζ46−ζ2−ζ22+ζ38+ζ58ζ2+ζ22−ζ38−ζ58ζ14−ζ26+ζ34−ζ46−ζ14+ζ26−ζ34+ζ46−ζ2−ζ22+ζ38+ζ58ζ2+ζ22−ζ38−ζ5800000000
χ2422-222-2−1+52−1−52-2-22−1+52−1−52−1+52−1+52−1−52−1−521−521+522-2−1+52−1−521−521+521−521−521+521+52−1+52−1−52−1+52−1+521−521−52−1−52−1−521+521+5200ζ2+ζ22−ζ38−ζ58−ζ2−ζ22+ζ38+ζ58ζ14−ζ26+ζ34−ζ46−ζ14+ζ26−ζ34+ζ46ζ2+ζ22−ζ38−ζ58−ζ2−ζ22+ζ38+ζ58ζ14−ζ26+ζ34−ζ46−ζ14+ζ26−ζ34+ζ4600000000
χ2522-222-2−1+52−1−52-2-22−1+52−1−52−1+52−1+52−1−52−1−521−521+522-2−1+52−1−521−521+521−521−521+521+52−1+52−1−52−1+52−1+521−521−52−1−52−1−521+521+5200−ζ2−ζ22+ζ38+ζ58ζ2+ζ22−ζ38−ζ58−ζ14+ζ26−ζ34+ζ46ζ14−ζ26+ζ34−ζ46−ζ2−ζ22+ζ38+ζ58ζ2+ζ22−ζ38−ζ58−ζ14+ζ26−ζ34+ζ46ζ14−ζ26+ζ34−ζ4600000000
χ2622-22-2222-2-2222-2-2-2-2-2-2-222222-2-2-2-222-2-222-2-222000000000000000000
χ2722-22-22−1−52−1+52-2-22−1−52−1+521+521+521−521−521+521−52-22−1−52−1+52−1−52−1+521+521+521−521−52−1−52−1+521+521+52−1−52−1−521−521−52−1+52−1+5200−ζ11+ζ19−ζ31+ζ59ζ11−ζ19+ζ31−ζ59−ζ7+ζ23+ζ43−ζ47ζ7−ζ23−ζ43+ζ47ζ11−ζ19+ζ31−ζ59−ζ11+ζ19−ζ31+ζ59ζ7−ζ23−ζ43+ζ47−ζ7+ζ23+ζ43−ζ4700000000
χ2822-22-22−1−52−1+52-2-22−1−52−1+521+521+521−521−521+521−52-22−1−52−1+52−1−52−1+521+521+521−521−52−1−52−1+521+521+52−1−52−1−521−521−52−1+52−1+5200ζ11−ζ19+ζ31−ζ59−ζ11+ζ19−ζ31+ζ59ζ7−ζ23−ζ43+ζ47−ζ7+ζ23+ζ43−ζ47−ζ11+ζ19−ζ31+ζ59ζ11−ζ19+ζ31−ζ59−ζ7+ζ23+ζ43−ζ47ζ7−ζ23−ζ43+ζ4700000000
χ2922-22-22−1+52−1−52-2-22−1+52−1−521−521−521+521+521−521+52-22−1+52−1−52−1+52−1−521−521−521+521+52−1+52−1−521−521−52−1+52−1+521+521+52−1−52−1−5200ζ7−ζ23−ζ43+ζ47−ζ7+ζ23+ζ43−ζ47−ζ11+ζ19−ζ31+ζ59ζ11−ζ19+ζ31−ζ59−ζ7+ζ23+ζ43−ζ47ζ7−ζ23−ζ43+ζ47ζ11−ζ19+ζ31−ζ59−ζ11+ζ19−ζ31+ζ5900000000
χ3022-22-22−1+52−1−52-2-22−1+52−1−521−521−521+521+521−521+52-22−1+52−1−52−1+52−1−521−521−521+521+52−1+52−1−521−521−52−1+52−1+521+521+52−1−52−1−5200−ζ7+ζ23+ζ43−ζ47ζ7−ζ23−ζ43+ζ47ζ11−ζ19+ζ31−ζ59−ζ11+ζ19−ζ31+ζ59ζ7−ζ23−ζ43+ζ47−ζ7+ζ23+ζ43−ζ47−ζ11+ζ19−ζ31+ζ59ζ11−ζ19+ζ31−ζ5900000000
χ3122-2-12-22211-1222222-2-2-11-1-1-2-21111-1-1-1-111-1-111000000000000−i3i3−i3i300
χ3222-2-12-22211-1222222-2-2-11-1-1-2-21111-1-1-1-111-1-111000000000000i3−i3i3−i300
χ3322-2-1-222211-122-2-2-2-2-2-21-1-1-1221111-1-111-1-111-1-1000000000000−i3i3i3−i300
χ3422-2-1-222211-122-2-2-2-2-2-21-1-1-1221111-1-111-1-111-1-1000000000000i3−i3−i3i300
χ35444-244−1−5−1+5-2-2-2−1−5−1+5−1−5−1−5−1+5−1+5−1−5−1+5-2-21+521−52−1−5−1+51+521+521−521−521+521−521+521+521+521+521−521−521−521−52000000000000000000
χ36444-244−1+5−1−5-2-2-2−1+5−1−5−1+5−1+5−1−5−1−5−1+5−1−5-2-21−521+52−1+5−1−51−521−521+521+521−521+521−521−521−521−521+521+521+521+52000000000000000000
χ37444-2-4-4−1−5−1+5-2-2-2−1−5−1+51+51+51−51−5−1−5−1+5221+521−521+51−51+521+521−521−521+521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52000000000000000000
χ38444-2-4-4−1+5−1−5-2-2-2−1+5−1−51−51−51+51+5−1+5−1−5221−521+521−51+51−521−521+521+521−521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52000000000000000000
χ3944-4-24-4−1−5−1+522-2−1−5−1+5−1−5−1−5−1+5−1+51+51−5-221+521−521+51−5−1−52−1−52−1+52−1+521+521−521+521+52−1−52−1−521−521−52−1+52−1+52000000000000000000
χ4044-4-24-4−1+5−1−522-2−1+5−1−5−1+5−1+5−1−5−1−51−51+5-221−521+521−51+5−1+52−1+52−1−52−1−521−521+521−521−52−1+52−1+521+521+52−1−52−1−52000000000000000000
χ4144-4-2-44−1−5−1+522-2−1−5−1+51+51+51−51−51+51−52-21+521−52−1−5−1+5−1−52−1−52−1+52−1+521+521−52−1−52−1−521+521+52−1+52−1+521−521−52000000000000000000
χ4244-4-2-44−1+5−1−522-2−1+5−1−51−51−51+51+51−51+52-21−521+52−1+5−1−5−1+52−1+52−1−52−1−521−521+52−1+52−1+521−521−52−1−52−1−521+521+52000000000000000000
χ434-404004400-4-4-40000000044000000-4-400000000000000000000000000
χ444-40400−1−5−1+500-41+51−5−2ζ11+2ζ19−2ζ31+2ζ592ζ11−2ζ19+2ζ31−2ζ592ζ7−2ζ23−2ζ43+2ζ47−2ζ7+2ζ23+2ζ43−2ζ470000−1−5−1+50000001+51−5−2ζ11+2ζ19−2ζ31+2ζ592ζ11−2ζ19+2ζ31−2ζ59002ζ7−2ζ23−2ζ43+2ζ47−2ζ7+2ζ23+2ζ43−2ζ4700000000000000000000
χ454-40400−1−5−1+500-41+51−52ζ11−2ζ19+2ζ31−2ζ59−2ζ11+2ζ19−2ζ31+2ζ59−2ζ7+2ζ23+2ζ43−2ζ472ζ7−2ζ23−2ζ43+2ζ470000−1−5−1+50000001+51−52ζ11−2ζ19+2ζ31−2ζ59−2ζ11+2ζ19−2ζ31+2ζ5900−2ζ7+2ζ23+2ζ43−2ζ472ζ7−2ζ23−2ζ43+2ζ4700000000000000000000
χ464-40400−1+5−1−500-41−51+52ζ7−2ζ23−2ζ43+2ζ47−2ζ7+2ζ23+2ζ43−2ζ472ζ11−2ζ19+2ζ31−2ζ59−2ζ11+2ζ19−2ζ31+2ζ590000−1+5−1−50000001−51+52ζ7−2ζ23−2ζ43+2ζ47−2ζ7+2ζ23+2ζ43−2ζ47002ζ11−2ζ19+2ζ31−2ζ59−2ζ11+2ζ19−2ζ31+2ζ5900000000000000000000
χ474-40400−1+5−1−500-41−51+5−2ζ7+2ζ23+2ζ43−2ζ472ζ7−2ζ23−2ζ43+2ζ47−2ζ11+2ζ19−2ζ31+2ζ592ζ11−2ζ19+2ζ31−2ζ590000−1+5−1−50000001−51+5−2ζ7+2ζ23+2ζ43−2ζ472ζ7−2ζ23−2ζ43+2ζ4700−2ζ11+2ζ19−2ζ31+2ζ592ζ11−2ζ19+2ζ31−2ζ5900000000000000000000
χ484-40-20044−2i32i32-4-400000000-2-200−2i32i3−2i32i32200000000000000000000000000
χ494-40-200442i3−2i32-4-400000000-2-2002i3−2i32i3−2i32200000000000000000000000000
χ504-40-200−1−5−1+5−2i32i321+51−5−2ζ11+2ζ19−2ζ31+2ζ592ζ11−2ζ19+2ζ31−2ζ592ζ7−2ζ23−2ζ43+2ζ47−2ζ7+2ζ23+2ζ43−2ζ4700001+521−5200ζ14+ζ26−ζ34−ζ46−ζ14−ζ26+ζ34+ζ46ζ2−ζ22+ζ38−ζ58−ζ2+ζ22−ζ38+ζ58−1−52−1+52ζ11−ζ19+ζ31−ζ59−ζ11+ζ19−ζ31+ζ59ζ11+ζ19−ζ31−ζ59−ζ11−ζ19+ζ31+ζ59−ζ7+ζ23+ζ43−ζ47ζ7−ζ23−ζ43+ζ47−ζ7−ζ23+ζ43+ζ47ζ7+ζ23−ζ43−ζ47000000000000000000
χ514-40-200−1−5−1+5−2i32i321+51−52ζ11−2ζ19+2ζ31−2ζ59−2ζ11+2ζ19−2ζ31+2ζ59−2ζ7+2ζ23+2ζ43−2ζ472ζ7−2ζ23−2ζ43+2ζ4700001+521−5200ζ14+ζ26−ζ34−ζ46−ζ14−ζ26+ζ34+ζ46ζ2−ζ22+ζ38−ζ58−ζ2+ζ22−ζ38+ζ58−1−52−1+52−ζ11+ζ19−ζ31+ζ59ζ11−ζ19+ζ31−ζ59−ζ11−ζ19+ζ31+ζ59ζ11+ζ19−ζ31−ζ59ζ7−ζ23−ζ43+ζ47−ζ7+ζ23+ζ43−ζ47ζ7+ζ23−ζ43−ζ47−ζ7−ζ23+ζ43+ζ47000000000000000000
χ524-40-200−1−5−1+52i3−2i321+51−5−2ζ11+2ζ19−2ζ31+2ζ592ζ11−2ζ19+2ζ31−2ζ592ζ7−2ζ23−2ζ43+2ζ47−2ζ7+2ζ23+2ζ43−2ζ4700001+521−5200−ζ14−ζ26+ζ34+ζ46ζ14+ζ26−ζ34−ζ46−ζ2+ζ22−ζ38+ζ58ζ2−ζ22+ζ38−ζ58−1−52−1+52ζ11−ζ19+ζ31−ζ59−ζ11+ζ19−ζ31+ζ59−ζ11−ζ19+ζ31+ζ59ζ11+ζ19−ζ31−ζ59−ζ7+ζ23+ζ43−ζ47ζ7−ζ23−ζ43+ζ47ζ7+ζ23−ζ43−ζ47−ζ7−ζ23+ζ43+ζ47000000000000000000
χ534-40-200−1−5−1+52i3−2i321+51−52ζ11−2ζ19+2ζ31−2ζ59−2ζ11+2ζ19−2ζ31+2ζ59−2ζ7+2ζ23+2ζ43−2ζ472ζ7−2ζ23−2ζ43+2ζ4700001+521−5200−ζ14−ζ26+ζ34+ζ46ζ14+ζ26−ζ34−ζ46−ζ2+ζ22−ζ38+ζ58ζ2−ζ22+ζ38−ζ58−1−52−1+52−ζ11+ζ19−ζ31+ζ59ζ11−ζ19+ζ31−ζ59ζ11+ζ19−ζ31−ζ59−ζ11−ζ19+ζ31+ζ59ζ7−ζ23−ζ43+ζ47−ζ7+ζ23+ζ43−ζ47−ζ7−ζ23+ζ43+ζ47ζ7+ζ23−ζ43−ζ47000000000000000000
χ544-40-200−1+5−1−5−2i32i321−51+52ζ7−2ζ23−2ζ43+2ζ47−2ζ7+2ζ23+2ζ43−2ζ472ζ11−2ζ19+2ζ31−2ζ59−2ζ11+2ζ19−2ζ31+2ζ5900001−521+5200ζ2−ζ22+ζ38−ζ58−ζ2+ζ22−ζ38+ζ58ζ14+ζ26−ζ34−ζ46−ζ14−ζ26+ζ34+ζ46−1+52−1−52−ζ7+ζ23+ζ43−ζ47ζ7−ζ23−ζ43+ζ47ζ7+ζ23−ζ43−ζ47−ζ7−ζ23+ζ43+ζ47−ζ11+ζ19−ζ31+ζ59ζ11−ζ19+ζ31−ζ59ζ11+ζ19−ζ31−ζ59−ζ11−ζ19+ζ31+ζ59000000000000000000
χ554-40-200−1+5−1−5−2i32i321−51+5−2ζ7+2ζ23+2ζ43−2ζ472ζ7−2ζ23−2ζ43+2ζ47−2ζ11+2ζ19−2ζ31+2ζ592ζ11−2ζ19+2ζ31−2ζ5900001−521+5200ζ2−ζ22+ζ38−ζ58−ζ2+ζ22−ζ38+ζ58ζ14+ζ26−ζ34−ζ46−ζ14−ζ26+ζ34+ζ46−1+52−1−52ζ7−ζ23−ζ43+ζ47−ζ7+ζ23+ζ43−ζ47−ζ7−ζ23+ζ43+ζ47ζ7+ζ23−ζ43−ζ47ζ11−ζ19+ζ31−ζ59−ζ11+ζ19−ζ31+ζ59−ζ11−ζ19+ζ31+ζ59ζ11+ζ19−ζ31−ζ59000000000000000000
χ564-40-200−1+5−1−52i3−2i321−51+52ζ7−2ζ23−2ζ43+2ζ47−2ζ7+2ζ23+2ζ43−2ζ472ζ11−2ζ19+2ζ31−2ζ59−2ζ11+2ζ19−2ζ31+2ζ5900001−521+5200−ζ2+ζ22−ζ38+ζ58ζ2−ζ22+ζ38−ζ58−ζ14−ζ26+ζ34+ζ46ζ14+ζ26−ζ34−ζ46−1+52−1−52−ζ7+ζ23+ζ43−ζ47ζ7−ζ23−ζ43+ζ47−ζ7−ζ23+ζ43+ζ47ζ7+ζ23−ζ43−ζ47−ζ11+ζ19−ζ31+ζ59ζ11−ζ19+ζ31−ζ59−ζ11−ζ19+ζ31+ζ59ζ11+ζ19−ζ31−ζ59000000000000000000
χ574-40-200−1+5−1−52i3−2i321−51+5−2ζ7+2ζ23+2ζ43−2ζ472ζ7−2ζ23−2ζ43+2ζ47−2ζ11+2ζ19−2ζ31+2ζ592ζ11−2ζ19+2ζ31−2ζ5900001−521+5200−ζ2+ζ22−ζ38+ζ58ζ2−ζ22+ζ38−ζ58−ζ14−ζ26+ζ34+ζ46ζ14+ζ26−ζ34−ζ46−1+52−1−52ζ7−ζ23−ζ43+ζ47−ζ7+ζ23+ζ43−ζ47ζ7+ζ23−ζ43−ζ47−ζ7−ζ23+ζ43+ζ47ζ11−ζ19+ζ31−ζ59−ζ11+ζ19−ζ31+ζ59ζ11+ζ19−ζ31−ζ59−ζ11−ζ19+ζ31+ζ59000000000000000000

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