Finite Group Databasebeta

← Group #10624054

Character table — Group #10624054

Order 720.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63
size11222222223344444444446666666666688881010101212121212121212121818181818202020303030306090
order1233556610104436151515153030303041212202020202020202015153030412121260606060606060602101010101212122466122
χ1111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-1-1-111111111111111-1-1-1-1-1-1-1-1-1
χ31111111111111111111111-1111111-1-1-1-11111111-11111-1-1-1-1-1-1-1-1-11111-111-1-1
χ41111111111111111111111-1111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111
χ51111111111-1-111111111111-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1111-11-1-11-1
χ61111111111-1-111111111111-1-1-1-1-1-111111111-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-11-111-11
χ71111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-111111111-1-1-1-1-11
χ81111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-111111-1
χ92222−1−52−1+5222−1−52−1+522222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+520002−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+522−1−52−1−52−1+52−1+52000000000
χ102222−1−52−1+5222−1−52−1+522222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-222−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1+52−1−52−1+52000-2−1−52−1−52−1+52−1+521+521+521−521−52-21+521+521−521−52000000000
χ112222−1−52−1+5222−1−52−1+52-2-222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+522-2-21+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+5200021+521+521−521−52−1−52−1−52−1+52−1+52-21+521+521−521−52000000000
χ122222−1−52−1+5222−1−52−1+52-2-222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-2-2-21+521+521−521−521+521+521−521−52−1−52−1+52−1−52−1+52000-21+521+521−521−521+521+521−521−522−1−52−1−52−1+52−1+52000000000
χ132222−1+52−1−5222−1+52−1−522222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−520002−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−522−1+52−1+52−1−52−1−52000000000
χ142222−1+52−1−5222−1+52−1−522222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-222−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1−52−1+52−1−52000-2−1+52−1+52−1−52−1−521−521−521+521+52-21−521−521+521+52000000000
χ152222−1+52−1−5222−1+52−1−52-2-222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−522-2-21−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−5200021−521−521+521+52−1+52−1+52−1−52−1−52-21−521−521+521+52000000000
χ162222−1+52−1−5222−1+52−1−52-2-222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-2-2-21−521−521+521+521−521−521+521+52−1+52−1−52−1+52−1−52000-21−521−521+521+521−521−521+521+522−1+52−1+52−1−52−1−52000000000
χ17222-122-122222-1-12-12-12-12-10-1-122220000-1-1-1-12-1-10-1-1-1-10000000002-1-120-1-100
χ18222-122-122222-1-12-12-12-12-10-1-122220000-1-1-1-1-2110-1-1-1-1000000000-211-201100
χ19222-122-1222-2-2-1-12-12-12-12-1011-2-2-2-20000-1-1-1-12-1-1011110000000002-1-1-201100
χ20222-122-1222-2-2-1-12-12-12-12-1011-2-2-2-20000-1-1-1-1-21101111000000000-21120-1-100
χ2122-12222-12200-1-1-12-12-12-1220000002222-1-1-1-1222-10000-1-1-1-100000-1-1-10200-10
χ2222-12222-12200-1-1-12-12-12-1220000002222-1-1-1-1-2-2-2-10000-1-1-1-1000001110-20010
χ2322-12222-12200-1-1-12-12-12-12-2000000-2-2-2-2-1-1-1-122210000111100000-1-1-10-20010
χ2422-12222-12200-1-1-12-12-12-12-2000000-2-2-2-2-1-1-1-1-2-2-2100001111000001110200-10
χ252-22222-2-2-2-22i−2i2-22222-2-2-2-202i−2i2i−2i2i−2i000022-2-200002i−2i2i−2i000000000000000000
χ262-22222-2-2-2-2−2i2i2-22222-2-2-2-20−2i2i−2i2i−2i2i000022-2-20000−2i2i−2i2i000000000000000000
χ272-222−1−52−1+52-2-21+521−522i−2i2-2−1−52−1−52−1+52−1+521+521+521−521−5202i−2i−ζ11−ζ19−ζ31−ζ59ζ11+ζ19+ζ31+ζ59−ζ7−ζ23−ζ43−ζ47ζ7+ζ23+ζ43+ζ47−ζ11+ζ19−ζ31+ζ59ζ11−ζ19+ζ31−ζ59ζ7−ζ23−ζ43+ζ47−ζ7+ζ23+ζ43−ζ47−1−52−1+521+521−520000−ζ11−ζ19−ζ31−ζ59ζ11+ζ19+ζ31+ζ59−ζ7−ζ23−ζ43−ζ47ζ7+ζ23+ζ43+ζ47−ζ11+ζ19−ζ31+ζ59ζ11−ζ19+ζ31−ζ59ζ7−ζ23−ζ43+ζ47−ζ7+ζ23+ζ43−ζ470−ζ14+ζ26−ζ34+ζ46ζ14−ζ26+ζ34−ζ46ζ2+ζ22−ζ38−ζ58−ζ2−ζ22+ζ38+ζ58000000000
χ282-222−1−52−1+52-2-21+521−522i−2i2-2−1−52−1−52−1+52−1+521+521+521−521−5202i−2i−ζ11−ζ19−ζ31−ζ59ζ11+ζ19+ζ31+ζ59−ζ7−ζ23−ζ43−ζ47ζ7+ζ23+ζ43+ζ47ζ11−ζ19+ζ31−ζ59−ζ11+ζ19−ζ31+ζ59−ζ7+ζ23+ζ43−ζ47ζ7−ζ23−ζ43+ζ47−1−52−1+521+521−520000−ζ11−ζ19−ζ31−ζ59ζ11+ζ19+ζ31+ζ59−ζ7−ζ23−ζ43−ζ47ζ7+ζ23+ζ43+ζ47ζ11−ζ19+ζ31−ζ59−ζ11+ζ19−ζ31+ζ59−ζ7+ζ23+ζ43−ζ47ζ7−ζ23−ζ43+ζ470ζ14−ζ26+ζ34−ζ46−ζ14+ζ26−ζ34+ζ46−ζ2−ζ22+ζ38+ζ58ζ2+ζ22−ζ38−ζ58000000000
χ292-222−1−52−1+52-2-21+521−52−2i2i2-2−1−52−1−52−1+52−1+521+521+521−521−520−2i2iζ11+ζ19+ζ31+ζ59−ζ11−ζ19−ζ31−ζ59ζ7+ζ23+ζ43+ζ47−ζ7−ζ23−ζ43−ζ47−ζ11+ζ19−ζ31+ζ59ζ11−ζ19+ζ31−ζ59ζ7−ζ23−ζ43+ζ47−ζ7+ζ23+ζ43−ζ47−1−52−1+521+521−520000ζ11+ζ19+ζ31+ζ59−ζ11−ζ19−ζ31−ζ59ζ7+ζ23+ζ43+ζ47−ζ7−ζ23−ζ43−ζ47−ζ11+ζ19−ζ31+ζ59ζ11−ζ19+ζ31−ζ59ζ7−ζ23−ζ43+ζ47−ζ7+ζ23+ζ43−ζ470ζ14−ζ26+ζ34−ζ46−ζ14+ζ26−ζ34+ζ46−ζ2−ζ22+ζ38+ζ58ζ2+ζ22−ζ38−ζ58000000000
χ302-222−1−52−1+52-2-21+521−52−2i2i2-2−1−52−1−52−1+52−1+521+521+521−521−520−2i2iζ11+ζ19+ζ31+ζ59−ζ11−ζ19−ζ31−ζ59ζ7+ζ23+ζ43+ζ47−ζ7−ζ23−ζ43−ζ47ζ11−ζ19+ζ31−ζ59−ζ11+ζ19−ζ31+ζ59−ζ7+ζ23+ζ43−ζ47ζ7−ζ23−ζ43+ζ47−1−52−1+521+521−520000ζ11+ζ19+ζ31+ζ59−ζ11−ζ19−ζ31−ζ59ζ7+ζ23+ζ43+ζ47−ζ7−ζ23−ζ43−ζ47ζ11−ζ19+ζ31−ζ59−ζ11+ζ19−ζ31+ζ59−ζ7+ζ23+ζ43−ζ47ζ7−ζ23−ζ43+ζ470−ζ14+ζ26−ζ34+ζ46ζ14−ζ26+ζ34−ζ46ζ2+ζ22−ζ38−ζ58−ζ2−ζ22+ζ38+ζ58000000000
χ312-222−1+52−1−52-2-21−521+522i−2i2-2−1+52−1+52−1−52−1−521−521−521+521+5202i−2i−ζ7−ζ23−ζ43−ζ47ζ7+ζ23+ζ43+ζ47−ζ11−ζ19−ζ31−ζ59ζ11+ζ19+ζ31+ζ59ζ7−ζ23−ζ43+ζ47−ζ7+ζ23+ζ43−ζ47ζ11−ζ19+ζ31−ζ59−ζ11+ζ19−ζ31+ζ59−1+52−1−521−521+520000−ζ7−ζ23−ζ43−ζ47ζ7+ζ23+ζ43+ζ47−ζ11−ζ19−ζ31−ζ59ζ11+ζ19+ζ31+ζ59ζ7−ζ23−ζ43+ζ47−ζ7+ζ23+ζ43−ζ47ζ11−ζ19+ζ31−ζ59−ζ11+ζ19−ζ31+ζ590−ζ2−ζ22+ζ38+ζ58ζ2+ζ22−ζ38−ζ58−ζ14+ζ26−ζ34+ζ46ζ14−ζ26+ζ34−ζ46000000000
χ322-222−1+52−1−52-2-21−521+522i−2i2-2−1+52−1+52−1−52−1−521−521−521+521+5202i−2i−ζ7−ζ23−ζ43−ζ47ζ7+ζ23+ζ43+ζ47−ζ11−ζ19−ζ31−ζ59ζ11+ζ19+ζ31+ζ59−ζ7+ζ23+ζ43−ζ47ζ7−ζ23−ζ43+ζ47−ζ11+ζ19−ζ31+ζ59ζ11−ζ19+ζ31−ζ59−1+52−1−521−521+520000−ζ7−ζ23−ζ43−ζ47ζ7+ζ23+ζ43+ζ47−ζ11−ζ19−ζ31−ζ59ζ11+ζ19+ζ31+ζ59−ζ7+ζ23+ζ43−ζ47ζ7−ζ23−ζ43+ζ47−ζ11+ζ19−ζ31+ζ59ζ11−ζ19+ζ31−ζ590ζ2+ζ22−ζ38−ζ58−ζ2−ζ22+ζ38+ζ58ζ14−ζ26+ζ34−ζ46−ζ14+ζ26−ζ34+ζ46000000000
χ332-222−1+52−1−52-2-21−521+52−2i2i2-2−1+52−1+52−1−52−1−521−521−521+521+520−2i2iζ7+ζ23+ζ43+ζ47−ζ7−ζ23−ζ43−ζ47ζ11+ζ19+ζ31+ζ59−ζ11−ζ19−ζ31−ζ59ζ7−ζ23−ζ43+ζ47−ζ7+ζ23+ζ43−ζ47ζ11−ζ19+ζ31−ζ59−ζ11+ζ19−ζ31+ζ59−1+52−1−521−521+520000ζ7+ζ23+ζ43+ζ47−ζ7−ζ23−ζ43−ζ47ζ11+ζ19+ζ31+ζ59−ζ11−ζ19−ζ31−ζ59ζ7−ζ23−ζ43+ζ47−ζ7+ζ23+ζ43−ζ47ζ11−ζ19+ζ31−ζ59−ζ11+ζ19−ζ31+ζ590ζ2+ζ22−ζ38−ζ58−ζ2−ζ22+ζ38+ζ58ζ14−ζ26+ζ34−ζ46−ζ14+ζ26−ζ34+ζ46000000000
χ342-222−1+52−1−52-2-21−521+52−2i2i2-2−1+52−1+52−1−52−1−521−521−521+521+520−2i2iζ7+ζ23+ζ43+ζ47−ζ7−ζ23−ζ43−ζ47ζ11+ζ19+ζ31+ζ59−ζ11−ζ19−ζ31−ζ59−ζ7+ζ23+ζ43−ζ47ζ7−ζ23−ζ43+ζ47−ζ11+ζ19−ζ31+ζ59ζ11−ζ19+ζ31−ζ59−1+52−1−521−521+520000ζ7+ζ23+ζ43+ζ47−ζ7−ζ23−ζ43−ζ47ζ11+ζ19+ζ31+ζ59−ζ11−ζ19−ζ31−ζ59−ζ7+ζ23+ζ43−ζ47ζ7−ζ23−ζ43+ζ47−ζ11+ζ19−ζ31+ζ59ζ11−ζ19+ζ31−ζ590−ζ2−ζ22+ζ38+ζ58ζ2+ζ22−ζ38−ζ58−ζ14+ζ26−ζ34+ζ46ζ14−ζ26+ζ34−ζ46000000000
χ352-22-1221-2-2-22i−2i-112-12-1-21-210−ii2i−2i2i−2i0000-1-11103−30−ii−ii00000000003−300−i3i300
χ362-22-1221-2-2-22i−2i-112-12-1-21-210−ii2i−2i2i−2i0000-1-1110−330−ii−ii0000000000−3300i3−i300
χ372-22-1221-2-2-2−2i2i-112-12-1-21-210i−i−2i2i−2i2i0000-1-11103−30i−ii−i00000000003−300i3−i300
χ382-22-1221-2-2-2−2i2i-112-12-1-21-210i−i−2i2i−2i2i0000-1-1110−330i−ii−i0000000000−3300−i3i300
χ39444-2−1−5−1+5-24−1−5−1+544-2-2−1−51+52−1+51−52−1−51+52−1+51−520-2-2−1−5−1−5−1+5−1+500001+521−521+521−5200001+521+521−521−52000000000000000000
χ40444-2−1−5−1+5-24−1−5−1+5-4-4-2-2−1−51+52−1+51−52−1−51+52−1+51−520221+51+51−51−500001+521−521+521−520000−1−52−1−52−1+52−1+52000000000000000000
χ41444-2−1+5−1−5-24−1+5−1−544-2-2−1+51−52−1−51+52−1+51−52−1−51+520-2-2−1+5−1+5−1−5−1−500001−521+521−521+5200001−521−521+521+52000000000000000000
χ42444-2−1+5−1−5-24−1+5−1−5-4-4-2-2−1+51−52−1−51+52−1+51−52−1−51+520221−51−51+51+500001−521+521−521+520000−1+52−1+52−1−52−1−52000000000000000000
χ4344-24−1−5−1+54-2−1−5−1+500-2-21+52−1−51−52−1+51+52−1−51−52−1+54000000−1−5−1−5−1+5−1+51+521−521+521−52000-200001+521+521−521−5200000000000000
χ4444-24−1−5−1+54-2−1−5−1+500-2-21+52−1−51−52−1+51+52−1−51−52−1+5-40000001+51+51−51−51+521−521+521−5200020000−1−52−1−52−1+52−1+5200000000000000
χ4544-24−1+5−1−54-2−1+5−1−500-2-21−52−1+51+52−1−51−52−1+51+52−1−54000000−1+5−1+5−1−5−1−51−521+521−521+52000-200001−521−521+521+5200000000000000
χ4644-24−1+5−1−54-2−1+5−1−500-2-21−52−1+51+52−1−51−52−1+51+52−1−5-40000001−51−51+51+51−521+521−521+5200020000−1+52−1+52−1−52−1−5200000000000000
χ4744-2-244-2-2440011-2-2-2-2-2-2-2-20000000000011114-2-200000000000000-211000000
χ4844-2-244-2-2440011-2-2-2-2-2-2-2-2000000000001111-422000000000000002-1-1000000
χ494-44-2−1−5−1+52-41+51−54i−4i-22−1−51+52−1+51−521+5−1−521−5−1+520−2i2i−2ζ11−2ζ19−2ζ31−2ζ592ζ11+2ζ19+2ζ31+2ζ59−2ζ7−2ζ23−2ζ43−2ζ472ζ7+2ζ23+2ζ43+2ζ4700001+521−52−1−52−1+520000ζ11+ζ19+ζ31+ζ59−ζ11−ζ19−ζ31−ζ59ζ7+ζ23+ζ43+ζ47−ζ7−ζ23−ζ43−ζ47000000000000000000
χ504-44-2−1−5−1+52-41+51−5−4i4i-22−1−51+52−1+51−521+5−1−521−5−1+5202i−2i2ζ11+2ζ19+2ζ31+2ζ59−2ζ11−2ζ19−2ζ31−2ζ592ζ7+2ζ23+2ζ43+2ζ47−2ζ7−2ζ23−2ζ43−2ζ4700001+521−52−1−52−1+520000−ζ11−ζ19−ζ31−ζ59ζ11+ζ19+ζ31+ζ59−ζ7−ζ23−ζ43−ζ47ζ7+ζ23+ζ43+ζ47000000000000000000
χ514-44-2−1+5−1−52-41−51+54i−4i-22−1+51−52−1−51+521−5−1+521+5−1−520−2i2i−2ζ7−2ζ23−2ζ43−2ζ472ζ7+2ζ23+2ζ43+2ζ47−2ζ11−2ζ19−2ζ31−2ζ592ζ11+2ζ19+2ζ31+2ζ5900001−521+52−1+52−1−520000ζ7+ζ23+ζ43+ζ47−ζ7−ζ23−ζ43−ζ47ζ11+ζ19+ζ31+ζ59−ζ11−ζ19−ζ31−ζ59000000000000000000
χ524-44-2−1+5−1−52-41−51+5−4i4i-22−1+51−52−1−51+521−5−1+521+5−1−5202i−2i2ζ7+2ζ23+2ζ43+2ζ47−2ζ7−2ζ23−2ζ43−2ζ472ζ11+2ζ19+2ζ31+2ζ59−2ζ11−2ζ19−2ζ31−2ζ5900001−521+52−1+52−1−520000−ζ7−ζ23−ζ43−ζ47ζ7+ζ23+ζ43+ζ47−ζ11−ζ19−ζ31−ζ59ζ11+ζ19+ζ31+ζ59000000000000000000
χ534-4-2444-42-4-400-22-24-242-42-400000000000-2-22200000000000000000000000000
χ544-4-24−1−5−1+5-421+51−500-221+52−1−51−52−1+5−1−521+5−1+521−50000000−2ζ11+2ζ19−2ζ31+2ζ592ζ11−2ζ19+2ζ31−2ζ592ζ7−2ζ23−2ζ43+2ζ47−2ζ7+2ζ23+2ζ43−2ζ471+521−52−1−52−1+5200000000ζ11−ζ19+ζ31−ζ59−ζ11+ζ19−ζ31+ζ59−ζ7+ζ23+ζ43−ζ47ζ7−ζ23−ζ43+ζ4700000000000000
χ554-4-24−1−5−1+5-421+51−500-221+52−1−51−52−1+5−1−521+5−1+521−500000002ζ11−2ζ19+2ζ31−2ζ59−2ζ11+2ζ19−2ζ31+2ζ59−2ζ7+2ζ23+2ζ43−2ζ472ζ7−2ζ23−2ζ43+2ζ471+521−52−1−52−1+5200000000−ζ11+ζ19−ζ31+ζ59ζ11−ζ19+ζ31−ζ59ζ7−ζ23−ζ43+ζ47−ζ7+ζ23+ζ43−ζ4700000000000000
χ564-4-24−1+5−1−5-421−51+500-221−52−1+51+52−1−5−1+521−5−1−521+500000002ζ7−2ζ23−2ζ43+2ζ47−2ζ7+2ζ23+2ζ43−2ζ472ζ11−2ζ19+2ζ31−2ζ59−2ζ11+2ζ19−2ζ31+2ζ591−521+52−1+52−1−5200000000−ζ7+ζ23+ζ43−ζ47ζ7−ζ23−ζ43+ζ47−ζ11+ζ19−ζ31+ζ59ζ11−ζ19+ζ31−ζ5900000000000000
χ574-4-24−1+5−1−5-421−51+500-221−52−1+51+52−1−5−1+521−5−1−521+50000000−2ζ7+2ζ23+2ζ43−2ζ472ζ7−2ζ23−2ζ43+2ζ47−2ζ11+2ζ19−2ζ31+2ζ592ζ11−2ζ19+2ζ31−2ζ591−521+52−1+52−1−5200000000ζ7−ζ23−ζ43+ζ47−ζ7+ζ23+ζ43−ζ47ζ11−ζ19+ζ31−ζ59−ζ11+ζ19−ζ31+ζ5900000000000000
χ584-4-2-24422-4-4001-1-2-2-2-222220000000000011-1-1023−23000000000000000−33000000
χ594-4-2-24422-4-4001-1-2-2-2-222220000000000011-1-10−23230000000000000003−3000000
χ6088-4-4−2−25−2+25-4-4−2−25−2+2500221+51+51−51−51+51+51−51−500000000000−1−52−1+52−1−52−1+5200000000000000000000000000
χ6188-4-4−2+25−2−25-4-4−2+25−2−2500221−51−51+51+51−51−51+51+500000000000−1+52−1−52−1+52−1−5200000000000000000000000000
χ628-8-4-4−2−25−2+25442+252−25002-21+51+51−51−5−1−5−1−5−1+5−1+500000000000−1−52−1+521+521−5200000000000000000000000000
χ638-8-4-4−2+25−2−25442−252+25002-21−51−51+51+5−1+5−1+5−1−5−1−500000000000−1+52−1−521−521+5200000000000000000000000000

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