Finite Group Databasebeta

← Group #90997

Character table — Group #90997

Order 480.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57
size112222222222222224444444444444444444444121212121212121212122020202020206060
order12222355666101010101010661010101015153030303030303030303030303030442020202020202020441212121224
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
χ5111-1-11111-1-111-1-1-1-11-111-1-111111111-1-1-1-1-1-1-1-1i−iiiii−i−i−i−ii−iii−i−i1-1
χ6111-1-11111-1-111-1-1-1-11-111-1-111111111-1-1-1-1-1-1-1-1i−iiiii−i−i−i−i−ii−i−iii-11
χ7111-1-11111-1-111-1-1-1-11-111-1-111111111-1-1-1-1-1-1-1-1−ii−i−i−i−iiiiii−iii−i−i-11
χ8111-1-11111-1-111-1-1-1-11-111-1-111111111-1-1-1-1-1-1-1-1−ii−i−i−i−iiiii−ii−i−iii1-1
χ9222222−1−52−1+52222−1−52−1+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+52−1+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+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+52−1+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+52−1−52−1−5222−1+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+52−1−52−1−52−1−52−1−5222−1+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+52−1−52−1−5222−1+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+52−1−52−1−52−1−52−1−52-2-21−521−521+521+521−521−521+521+5200000000
χ1322222-122-1-1-1222222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000022-1-1-1-100
χ1422222-122-1-1-1222222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000-2-2111100
χ15222-2-22−1−52−1+522-2-2−1−52−1+521+521+521−521−522-2−1−52−1+521+521−52−1−52−1+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
χ16222-2-22−1−52−1+522-2-2−1−52−1+521+521+521−521−522-2−1−52−1+521+521−52−1−52−1+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
χ17222-2-22−1+52−1−522-2-2−1+52−1−521−521−521+521+522-2−1+52−1−521−521+52−1+52−1−52−1+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
χ18222-2-22−1+52−1−522-2-2−1+52−1−521−521−521+521+522-2−1+52−1−521−521+52−1+52−1−52−1+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
χ19222-2-2-122-11122-2-2-2-2-1122-2-2-1-1-1-1-1-1-1-11111111100000000002i−2i−i−iii00
χ20222-2-2-122-11122-2-2-2-2-1122-2-2-1-1-1-1-1-1-1-1111111110000000000−2i2iii−i−i00
χ2122-22-22222-2-2222222-22-2-2-2-2222-2-22-2-222-2-222-2-2000000000000000000
χ2222-22-22−1−52−1+522-2-2−1−52−1+52−1−52−1−52−1+52−1+52-221+521−521+521−52−1−52−1+52−1−521+521+52−1+521−521−52−1−52−1−521+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
χ2322-22-22−1−52−1+522-2-2−1−52−1+52−1−52−1−52−1+52−1+52-221+521−521+521−52−1−52−1+52−1−521+521+52−1+521−521−52−1−52−1−521+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
χ2422-22-22−1+52−1−522-2-2−1+52−1−52−1+52−1+52−1−52−1−52-221−521+521−521+52−1+52−1−52−1+521−521−52−1−521+521+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
χ2522-22-22−1+52−1−522-2-2−1+52−1−52−1+52−1+52−1−52−1−52-221−521+521−521+52−1+52−1−52−1+521−521−52−1−521+521+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
χ2622-22-2-122-1112222221-1-2-2-2-2-1-1-111-111-1-111-1-1110000000000003−33−300
χ2722-22-2-122-1112222221-1-2-2-2-2-1-1-111-111-1-111-1-111000000000000−33−3300
χ2822-2-2222222222-2-2-2-2-2-2-2-222222-2-22-2-2-2-222-2-222000000000000000000
χ2922-2-222−1−52−1+52222−1−52−1+521+521+521−521−52-2-21+521−52−1−52−1+52−1−52−1+52−1−521+521+52−1+521−521−521+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
χ3022-2-222−1−52−1+52222−1−52−1+521+521+521−521−52-2-21+521−52−1−52−1+52−1−52−1+52−1−521+521+52−1+521−521−521+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
χ3122-2-222−1+52−1−52222−1+52−1−521−521−521+521+52-2-21−521+52−1+52−1−52−1+52−1−52−1+521−521−52−1−521+521+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
χ3222-2-222−1+52−1−52222−1+52−1−521−521−521+521+52-2-21−521+52−1+52−1−52−1+52−1−52−1+521−521−52−1−521+521+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
χ3322-2-22-122-1-1-122-2-2-2-211-2-222-1-1-111-11111-1-111-1-1000000000000−i3i3i3−i300
χ3422-2-22-122-1-1-122-2-2-2-211-2-222-1-1-111-11111-1-111-1-1000000000000i3−i3−i3i300
χ3544444-2−1−5−1+5-2-2-2−1−5−1+5−1−5−1−5−1+5−1+5-2-2−1−5−1+5−1−5−1+51+521−521+521+521+521−521−521−521+521+521+521+521−521−521−521−52000000000000000000
χ3644444-2−1+5−1−5-2-2-2−1+5−1−5−1+5−1+5−1−5−1−5-2-2−1+5−1−5−1+5−1−51−521+521−521−521−521+521+521+521−521−521−521−521+521+521+521+52000000000000000000
χ37444-4-4-2−1−5−1+5-222−1−5−1+51+51+51−51−5-22−1−5−1+51+51−51+521−521+521+521+521−521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52000000000000000000
χ38444-4-4-2−1+5−1−5-222−1+5−1−51−51−51+51+5-22−1+5−1−51−51+51−521+521−521−521−521+521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52000000000000000000
χ3944-44-4-2−1−5−1+5-222−1−5−1+5−1−5−1−5−1+5−1+52-21+51−51+51−51+521−521+52−1−52−1−521−52−1+52−1+521+521+52−1−52−1−521−521−52−1+52−1+52000000000000000000
χ4044-44-4-2−1+5−1−5-222−1+5−1−5−1+5−1+5−1−5−1−52-21−51+51−51+51−521+521−52−1+52−1+521+52−1−52−1−521−521−52−1+52−1+521+521+52−1−52−1−52000000000000000000
χ4144-4-44-2−1−5−1+5-2-2-2−1−5−1+51+51+51−51−5221+51−5−1−5−1+51+521−521+52−1−52−1−521−52−1+52−1+52−1−52−1−521+521+52−1+52−1+521−521−52000000000000000000
χ4244-4-44-2−1+5−1−5-2-2-2−1+5−1−51−51−51+51+5221−51+5−1+5−1−51−521+521−52−1+52−1+521+52−1−52−1−52−1+52−1+521−521−52−1−52−1−521+521+52000000000000000000
χ434-4000444-400-4-4000000000044-400-40000000000000000000000000000
χ444-40004−1−5−1+5-4001+51−5−2ζ14+2ζ26−2ζ34+2ζ462ζ14−2ζ26+2ζ34−2ζ462ζ2+2ζ22−2ζ38−2ζ58−2ζ2−2ζ22+2ζ38+2ζ58000000−1−5−1+51+5001−500−2ζ14+2ζ26−2ζ34+2ζ462ζ14−2ζ26+2ζ34−2ζ46002ζ2+2ζ22−2ζ38−2ζ58−2ζ2−2ζ22+2ζ38+2ζ5800000000000000000000
χ454-40004−1−5−1+5-4001+51−52ζ14−2ζ26+2ζ34−2ζ46−2ζ14+2ζ26−2ζ34+2ζ46−2ζ2−2ζ22+2ζ38+2ζ582ζ2+2ζ22−2ζ38−2ζ58000000−1−5−1+51+5001−5002ζ14−2ζ26+2ζ34−2ζ46−2ζ14+2ζ26−2ζ34+2ζ4600−2ζ2−2ζ22+2ζ38+2ζ582ζ2+2ζ22−2ζ38−2ζ5800000000000000000000
χ464-40004−1+5−1−5-4001−51+52ζ2+2ζ22−2ζ38−2ζ58−2ζ2−2ζ22+2ζ38+2ζ582ζ14−2ζ26+2ζ34−2ζ46−2ζ14+2ζ26−2ζ34+2ζ46000000−1+5−1−51−5001+5002ζ2+2ζ22−2ζ38−2ζ58−2ζ2−2ζ22+2ζ38+2ζ58002ζ14−2ζ26+2ζ34−2ζ46−2ζ14+2ζ26−2ζ34+2ζ4600000000000000000000
χ474-40004−1+5−1−5-4001−51+5−2ζ2−2ζ22+2ζ38+2ζ582ζ2+2ζ22−2ζ38−2ζ58−2ζ14+2ζ26−2ζ34+2ζ462ζ14−2ζ26+2ζ34−2ζ46000000−1+5−1−51−5001+500−2ζ2−2ζ22+2ζ38+2ζ582ζ2+2ζ22−2ζ38−2ζ5800−2ζ14+2ζ26−2ζ34+2ζ462ζ14−2ζ26+2ζ34−2ζ4600000000000000000000
χ484-4000-2442−2i32i3-4-40000000000-2-220020000−2i32i300−2i32i3000000000000000000
χ494-4000-24422i3−2i3-4-40000000000-2-2200200002i3−2i3002i3−2i3000000000000000000
χ504-4000-2−1−5−1+52−2i32i31+51−5−2ζ14+2ζ26−2ζ34+2ζ462ζ14−2ζ26+2ζ34−2ζ462ζ2+2ζ22−2ζ38−2ζ58−2ζ2−2ζ22+2ζ38+2ζ580000001+521−52−1−52ζ14−ζ26−ζ34+ζ46−ζ14+ζ26+ζ34−ζ46−1+52−ζ2+ζ22+ζ38−ζ58ζ2−ζ22−ζ38+ζ58ζ14−ζ26+ζ34−ζ46−ζ14+ζ26−ζ34+ζ46ζ14+ζ26−ζ34−ζ46−ζ14−ζ26+ζ34+ζ46−ζ2−ζ22+ζ38+ζ58ζ2+ζ22−ζ38−ζ58ζ2−ζ22+ζ38−ζ58−ζ2+ζ22−ζ38+ζ58000000000000000000
χ514-4000-2−1−5−1+52−2i32i31+51−52ζ14−2ζ26+2ζ34−2ζ46−2ζ14+2ζ26−2ζ34+2ζ46−2ζ2−2ζ22+2ζ38+2ζ582ζ2+2ζ22−2ζ38−2ζ580000001+521−52−1−52−ζ14+ζ26+ζ34−ζ46ζ14−ζ26−ζ34+ζ46−1+52ζ2−ζ22−ζ38+ζ58−ζ2+ζ22+ζ38−ζ58−ζ14+ζ26−ζ34+ζ46ζ14−ζ26+ζ34−ζ46ζ14+ζ26−ζ34−ζ46−ζ14−ζ26+ζ34+ζ46ζ2+ζ22−ζ38−ζ58−ζ2−ζ22+ζ38+ζ58ζ2−ζ22+ζ38−ζ58−ζ2+ζ22−ζ38+ζ58000000000000000000
χ524-4000-2−1−5−1+522i3−2i31+51−5−2ζ14+2ζ26−2ζ34+2ζ462ζ14−2ζ26+2ζ34−2ζ462ζ2+2ζ22−2ζ38−2ζ58−2ζ2−2ζ22+2ζ38+2ζ580000001+521−52−1−52−ζ14+ζ26+ζ34−ζ46ζ14−ζ26−ζ34+ζ46−1+52ζ2−ζ22−ζ38+ζ58−ζ2+ζ22+ζ38−ζ58ζ14−ζ26+ζ34−ζ46−ζ14+ζ26−ζ34+ζ46−ζ14−ζ26+ζ34+ζ46ζ14+ζ26−ζ34−ζ46−ζ2−ζ22+ζ38+ζ58ζ2+ζ22−ζ38−ζ58−ζ2+ζ22−ζ38+ζ58ζ2−ζ22+ζ38−ζ58000000000000000000
χ534-4000-2−1−5−1+522i3−2i31+51−52ζ14−2ζ26+2ζ34−2ζ46−2ζ14+2ζ26−2ζ34+2ζ46−2ζ2−2ζ22+2ζ38+2ζ582ζ2+2ζ22−2ζ38−2ζ580000001+521−52−1−52ζ14−ζ26−ζ34+ζ46−ζ14+ζ26+ζ34−ζ46−1+52−ζ2+ζ22+ζ38−ζ58ζ2−ζ22−ζ38+ζ58−ζ14+ζ26−ζ34+ζ46ζ14−ζ26+ζ34−ζ46−ζ14−ζ26+ζ34+ζ46ζ14+ζ26−ζ34−ζ46ζ2+ζ22−ζ38−ζ58−ζ2−ζ22+ζ38+ζ58−ζ2+ζ22−ζ38+ζ58ζ2−ζ22+ζ38−ζ58000000000000000000
χ544-4000-2−1+5−1−52−2i32i31−51+52ζ2+2ζ22−2ζ38−2ζ58−2ζ2−2ζ22+2ζ38+2ζ582ζ14−2ζ26+2ζ34−2ζ46−2ζ14+2ζ26−2ζ34+2ζ460000001−521+52−1+52−ζ2+ζ22+ζ38−ζ58ζ2−ζ22−ζ38+ζ58−1−52−ζ14+ζ26+ζ34−ζ46ζ14−ζ26−ζ34+ζ46−ζ2−ζ22+ζ38+ζ58ζ2+ζ22−ζ38−ζ58ζ2−ζ22+ζ38−ζ58−ζ2+ζ22−ζ38+ζ58−ζ14+ζ26−ζ34+ζ46ζ14−ζ26+ζ34−ζ46ζ14+ζ26−ζ34−ζ46−ζ14−ζ26+ζ34+ζ46000000000000000000
χ554-4000-2−1+5−1−52−2i32i31−51+5−2ζ2−2ζ22+2ζ38+2ζ582ζ2+2ζ22−2ζ38−2ζ58−2ζ14+2ζ26−2ζ34+2ζ462ζ14−2ζ26+2ζ34−2ζ460000001−521+52−1+52ζ2−ζ22−ζ38+ζ58−ζ2+ζ22+ζ38−ζ58−1−52ζ14−ζ26−ζ34+ζ46−ζ14+ζ26+ζ34−ζ46ζ2+ζ22−ζ38−ζ58−ζ2−ζ22+ζ38+ζ58ζ2−ζ22+ζ38−ζ58−ζ2+ζ22−ζ38+ζ58ζ14−ζ26+ζ34−ζ46−ζ14+ζ26−ζ34+ζ46ζ14+ζ26−ζ34−ζ46−ζ14−ζ26+ζ34+ζ46000000000000000000
χ564-4000-2−1+5−1−522i3−2i31−51+52ζ2+2ζ22−2ζ38−2ζ58−2ζ2−2ζ22+2ζ38+2ζ582ζ14−2ζ26+2ζ34−2ζ46−2ζ14+2ζ26−2ζ34+2ζ460000001−521+52−1+52ζ2−ζ22−ζ38+ζ58−ζ2+ζ22+ζ38−ζ58−1−52ζ14−ζ26−ζ34+ζ46−ζ14+ζ26+ζ34−ζ46−ζ2−ζ22+ζ38+ζ58ζ2+ζ22−ζ38−ζ58−ζ2+ζ22−ζ38+ζ58ζ2−ζ22+ζ38−ζ58−ζ14+ζ26−ζ34+ζ46ζ14−ζ26+ζ34−ζ46−ζ14−ζ26+ζ34+ζ46ζ14+ζ26−ζ34−ζ46000000000000000000
χ574-4000-2−1+5−1−522i3−2i31−51+5−2ζ2−2ζ22+2ζ38+2ζ582ζ2+2ζ22−2ζ38−2ζ58−2ζ14+2ζ26−2ζ34+2ζ462ζ14−2ζ26+2ζ34−2ζ460000001−521+52−1+52−ζ2+ζ22+ζ38−ζ58ζ2−ζ22−ζ38+ζ58−1−52−ζ14+ζ26+ζ34−ζ46ζ14−ζ26−ζ34+ζ46ζ2+ζ22−ζ38−ζ58−ζ2−ζ22+ζ38+ζ58−ζ2+ζ22−ζ38+ζ58ζ2−ζ22+ζ38−ζ58ζ14−ζ26+ζ34−ζ46−ζ14+ζ26−ζ34+ζ46−ζ14−ζ26+ζ34+ζ46ζ14+ζ26−ζ34−ζ46000000000000000000

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