Finite Group Databasebeta

← Group #10624321

Character table — Group #10624321

Order 720.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36
size124445101515361212121530454548161616204060604816161620406060
order135151526442610303026443315151566121233151515661212
χ1111111111111111111111111111111111111
χ21111111-1-11111111-1-11111111-1-11111111-1-1
χ311111-1-1i−i11111-1-1i−i11111-1-1i−i11111-1-1i−i
χ411111-1-1−ii11111-1-1−ii11111-1-1−ii11111-1-1−ii
χ52-12-1-12-1002-12-1-12-1002-12-1-12-1002-12-1-12-100
χ62-12-1-1-21002-12-1-1-21002-12-1-1-21002-12-1-1-2100
χ744-1-1-1000044-1-1-1000044-1-1-1000044-1-1-10000
χ84-2-11−i1521+i15200004-2-11−i1521+i15200004-2-11−i1521+i15200004-2-11−i1521+i1520000
χ94-2-11+i1521−i15200004-2-11+i1521−i15200004-2-11+i1521−i15200004-2-11+i1521−i1520000
χ10111111111111111111−1+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
χ111111111-1-11111111-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32
χ1211111-1-1i−i11111-1-1i−i−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−ζ11−ζ23−ζ47−ζ59ζ11+ζ23+ζ47+ζ59−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−ζ7−ζ19−ζ31−ζ43ζ7+ζ19+ζ31+ζ43
χ1311111-1-1−ii11111-1-1−ii−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32ζ11+ζ23+ζ47+ζ59−ζ11−ζ23−ζ47−ζ59−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32ζ7+ζ19+ζ31+ζ43−ζ7−ζ19−ζ31−ζ43
χ142-12-1-12-1002-12-1-12-100−1+i31−i32−1+i31−i321−i32−1+i31−i3200−1−i31+i32−1−i31+i321+i32−1−i31+i3200
χ152-12-1-1-21002-12-1-1-2100−1+i31−i32−1+i31−i321−i321−i3−1+i3200−1−i31+i32−1−i31+i321+i321+i3−1−i3200
χ1644-1-1-1000044-1-1-10000−2+2i3−2+2i31−i321−i321−i320000−2−2i3−2−2i31+i321+i321+i320000
χ174-2-11−i1521+i15200004-2-11−i1521+i1520000−2+2i31−i31−i32ζ2+ζ22−ζ34+ζ38−ζ46+ζ58ζ14−ζ22+ζ26+ζ34+ζ46−ζ580000−2−2i31+i31+i32−ζ2+ζ14+ζ26+ζ34−ζ38+ζ46ζ2−ζ14+ζ22−ζ26+ζ38+ζ580000
χ184-2-11+i1521−i15200004-2-11+i1521−i1520000−2+2i31−i31−i32ζ14−ζ22+ζ26+ζ34+ζ46−ζ58ζ2+ζ22−ζ34+ζ38−ζ46+ζ580000−2−2i31+i31+i32ζ2−ζ14+ζ22−ζ26+ζ38+ζ58−ζ2+ζ14+ζ26+ζ34−ζ38+ζ460000
χ19111111111111111111−1−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
χ201111111-1-11111111-1-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32
χ2111111-1-1i−i11111-1-1i−i−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−ζ7−ζ19−ζ31−ζ43ζ7+ζ19+ζ31+ζ43−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−ζ11−ζ23−ζ47−ζ59ζ11+ζ23+ζ47+ζ59
χ2211111-1-1−ii11111-1-1−ii−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32ζ7+ζ19+ζ31+ζ43−ζ7−ζ19−ζ31−ζ43−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32ζ11+ζ23+ζ47+ζ59−ζ11−ζ23−ζ47−ζ59
χ232-12-1-12-1002-12-1-12-100−1−i31+i32−1−i31+i321+i32−1−i31+i3200−1+i31−i32−1+i31−i321−i32−1+i31−i3200
χ242-12-1-1-21002-12-1-1-2100−1−i31+i32−1−i31+i321+i321+i3−1−i3200−1+i31−i32−1+i31−i321−i321−i3−1+i3200
χ2544-1-1-1000044-1-1-10000−2−2i3−2−2i31+i321+i321+i320000−2+2i3−2+2i31−i321−i321−i320000
χ264-2-11−i1521+i15200004-2-11−i1521+i1520000−2−2i31+i31+i32−ζ2+ζ14+ζ26+ζ34−ζ38+ζ46ζ2−ζ14+ζ22−ζ26+ζ38+ζ580000−2+2i31−i31−i32ζ2+ζ22−ζ34+ζ38−ζ46+ζ58ζ14−ζ22+ζ26+ζ34+ζ46−ζ580000
χ274-2-11+i1521−i15200004-2-11+i1521−i1520000−2−2i31+i31+i32ζ2−ζ14+ζ22−ζ26+ζ38+ζ58−ζ2+ζ14+ζ26+ζ34−ζ38+ζ460000−2+2i31−i31−i32ζ14−ζ22+ζ26+ζ34+ζ46−ζ58ζ2+ζ22−ζ34+ζ38−ζ46+ζ580000
χ28333333333-1-1-1-1-1-1-1-1-1000000000000000000
χ293333333-3-3-1-1-1-1-1-1-111000000000000000000
χ3033333-3-33i−3i-1-1-1-1-111−ii000000000000000000
χ3133333-3-3−3i3i-1-1-1-1-111i−i000000000000000000
χ326-36-3-36-300-21-211-2100000000000000000000
χ336-36-3-3-6300-21-2112-100000000000000000000
χ341212-3-3-30000-4-41110000000000000000000000
χ3512-6-33−3i1523+3i1520000-421−1+i152−1−i1520000000000000000000000
χ3612-6-33+3i1523−3i1520000-421−1−i152−1+i1520000000000000000000000

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