Finite Group Databasebeta

← Group #63189

Character table — Group #63189

Order 270.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44
size1113333333322266666666222666666665551515151515151515
order1333399999951515151545454545454551515151545454545454526666181818181818
χ111111111111111111111111111111111111111111111
χ211111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32
χ311111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32
χ4111−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32111−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32111−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32111−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32
χ5111−1+i32−1−i32−1+i32−1−i321−1−i321−1+i32111−1+i32−1−i32−1+i32−1−i321−1−i321−1+i32111−1+i32−1−i32−1+i32−1−i321−1−i321−1+i32111−1+i32−1−i32−1+i32−1−i321−1−i321−1+i32
χ6111−1+i32−1−i32−1−i321−1+i32−1+i32−1−i321111−1+i32−1−i32−1−i321−1+i32−1+i32−1−i321111−1+i32−1−i32−1−i321−1+i32−1+i32−1−i321111−1+i32−1−i32−1−i321−1+i32−1+i32−1−i321
χ7111−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32111−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32111−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32111−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32
χ8111−1−i32−1+i32−1+i321−1−i32−1−i32−1+i321111−1−i32−1+i32−1+i321−1−i32−1−i32−1+i321111−1−i32−1+i32−1+i321−1−i32−1−i32−1+i321111−1−i32−1+i32−1+i321−1−i32−1−i32−1+i321
χ9111−1−i32−1+i32−1−i32−1+i321−1+i321−1−i32111−1−i32−1+i32−1−i32−1+i321−1+i321−1−i32111−1−i32−1+i32−1−i32−1+i321−1+i321−1−i32111−1−i32−1+i32−1−i32−1+i321−1+i321−1−i32
χ103−3+3i32−3−3i32000000003−3+3i32−3−3i32000000003−3+3i32−3−3i32000000003−3+3i32−3−3i3200000000
χ113−3−3i32−3+3i32000000003−3−3i32−3+3i32000000003−3−3i32−3+3i32000000003−3−3i32−3+3i3200000000
χ12111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1
χ1311111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-1-1-1-11−i321−i321−i321+i321+i321+i32
χ1411111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-1-1-1-11+i321+i321+i321−i321−i321−i32
χ15111−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32111−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32111−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32-1-1-11−i321+i32-11−i321+i32-11−i321+i32
χ16111−1+i32−1−i32−1+i32−1−i321−1−i321−1+i32111−1+i32−1−i32−1+i32−1−i321−1−i321−1+i32111−1+i32−1−i32−1+i32−1−i321−1−i321−1+i32-1-1-11−i321+i321−i321+i32-11+i32-11−i32
χ17111−1+i32−1−i32−1−i321−1+i32−1+i32−1−i321111−1+i32−1−i32−1−i321−1+i32−1+i32−1−i321111−1+i32−1−i32−1−i321−1+i32−1+i32−1−i321-1-1-11−i321+i321+i32-11−i321−i321+i32-1
χ18111−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32111−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32111−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32-1-1-11+i321−i32-11+i321−i32-11+i321−i32
χ19111−1−i32−1+i32−1+i321−1−i32−1−i32−1+i321111−1−i32−1+i32−1+i321−1−i32−1−i32−1+i321111−1−i32−1+i32−1+i321−1−i32−1−i32−1+i321-1-1-11+i321−i321−i32-11+i321+i321−i32-1
χ20111−1−i32−1+i32−1−i32−1+i321−1+i321−1−i32111−1−i32−1+i32−1−i32−1+i321−1+i321−1−i32111−1−i32−1+i32−1−i32−1+i321−1+i321−1−i32-1-1-11+i321−i321+i321−i32-11−i32-11+i32
χ213−3+3i32−3−3i32000000003−3+3i32−3−3i32000000003−3+3i32−3−3i3200000000-33−3i323+3i3200000000
χ223−3−3i32−3+3i32000000003−3−3i32−3+3i32000000003−3−3i32−3+3i3200000000-33+3i323−3i3200000000
χ2322222222222−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−5200000000000
χ2422222−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3−1+52−1+52−1+52−1+52−1+52ζ2+ζ8ζ2+ζ8ζ2+ζ8ζ7+ζ13ζ7+ζ13ζ7+ζ13−1−52−1−52−1−52−1−52−1−52ζ11+ζ14ζ11+ζ14ζ11+ζ14ζ+ζ4ζ+ζ4ζ+ζ400000000000
χ2522222−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3−1+52−1+52−1+52−1+52−1+52ζ7+ζ13ζ7+ζ13ζ7+ζ13ζ2+ζ8ζ2+ζ8ζ2+ζ8−1−52−1−52−1−52−1−52−1−52ζ+ζ4ζ+ζ4ζ+ζ4ζ11+ζ14ζ11+ζ14ζ11+ζ1400000000000
χ26222−1+i3−1−i32−1+i3−1−i32−1+i3−1−i3−1+52−1+52−1+52ζ2+ζ8ζ7+ζ13−1+52ζ2+ζ8ζ7+ζ13−1+52ζ2+ζ8ζ7+ζ13−1−52−1−52−1−52ζ11+ζ14ζ+ζ4−1−52ζ11+ζ14ζ+ζ4−1−52ζ11+ζ14ζ+ζ400000000000
χ27222−1+i3−1−i3−1+i3−1−i32−1−i32−1+i3−1+52−1+52−1+52ζ2+ζ8ζ7+ζ13ζ2+ζ8ζ7+ζ13−1+52ζ7+ζ13−1+52ζ2+ζ8−1−52−1−52−1−52ζ11+ζ14ζ+ζ4ζ11+ζ14ζ+ζ4−1−52ζ+ζ4−1−52ζ11+ζ1400000000000
χ28222−1+i3−1−i3−1−i32−1+i3−1+i3−1−i32−1+52−1+52−1+52ζ2+ζ8ζ7+ζ13ζ7+ζ13−1+52ζ2+ζ8ζ2+ζ8ζ7+ζ13−1+52−1−52−1−52−1−52ζ11+ζ14ζ+ζ4ζ+ζ4−1−52ζ11+ζ14ζ11+ζ14ζ+ζ4−1−5200000000000
χ29222−1−i3−1+i32−1−i3−1+i32−1−i3−1+i3−1+52−1+52−1+52ζ7+ζ13ζ2+ζ8−1+52ζ7+ζ13ζ2+ζ8−1+52ζ7+ζ13ζ2+ζ8−1−52−1−52−1−52ζ+ζ4ζ11+ζ14−1−52ζ+ζ4ζ11+ζ14−1−52ζ+ζ4ζ11+ζ1400000000000
χ30222−1−i3−1+i3−1+i32−1−i3−1−i3−1+i32−1+52−1+52−1+52ζ7+ζ13ζ2+ζ8ζ2+ζ8−1+52ζ7+ζ13ζ7+ζ13ζ2+ζ8−1+52−1−52−1−52−1−52ζ+ζ4ζ11+ζ14ζ11+ζ14−1−52ζ+ζ4ζ+ζ4ζ11+ζ14−1−5200000000000
χ31222−1−i3−1+i3−1−i3−1+i32−1+i32−1−i3−1+52−1+52−1+52ζ7+ζ13ζ2+ζ8ζ7+ζ13ζ2+ζ8−1+52ζ2+ζ8−1+52ζ7+ζ13−1−52−1−52−1−52ζ+ζ4ζ11+ζ14ζ+ζ4ζ11+ζ14−1−52ζ11+ζ14−1−52ζ+ζ400000000000
χ326−3+3i3−3−3i300000000−3+3523ζ2+3ζ83ζ7+3ζ1300000000−3−3523ζ11+3ζ143ζ+3ζ40000000000000000000
χ336−3−3i3−3+3i300000000−3+3523ζ7+3ζ133ζ2+3ζ800000000−3−3523ζ+3ζ43ζ11+3ζ140000000000000000000
χ3422222222222−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+5200000000000
χ3522222−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3−1−52−1−52−1−52−1−52−1−52ζ11+ζ14ζ11+ζ14ζ11+ζ14ζ+ζ4ζ+ζ4ζ+ζ4−1+52−1+52−1+52−1+52−1+52ζ2+ζ8ζ2+ζ8ζ2+ζ8ζ7+ζ13ζ7+ζ13ζ7+ζ1300000000000
χ3622222−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3−1−52−1−52−1−52−1−52−1−52ζ+ζ4ζ+ζ4ζ+ζ4ζ11+ζ14ζ11+ζ14ζ11+ζ14−1+52−1+52−1+52−1+52−1+52ζ7+ζ13ζ7+ζ13ζ7+ζ13ζ2+ζ8ζ2+ζ8ζ2+ζ800000000000
χ37222−1+i3−1−i32−1+i3−1−i32−1+i3−1−i3−1−52−1−52−1−52ζ11+ζ14ζ+ζ4−1−52ζ11+ζ14ζ+ζ4−1−52ζ11+ζ14ζ+ζ4−1+52−1+52−1+52ζ2+ζ8ζ7+ζ13−1+52ζ2+ζ8ζ7+ζ13−1+52ζ2+ζ8ζ7+ζ1300000000000
χ38222−1+i3−1−i3−1+i3−1−i32−1−i32−1+i3−1−52−1−52−1−52ζ11+ζ14ζ+ζ4ζ11+ζ14ζ+ζ4−1−52ζ+ζ4−1−52ζ11+ζ14−1+52−1+52−1+52ζ2+ζ8ζ7+ζ13ζ2+ζ8ζ7+ζ13−1+52ζ7+ζ13−1+52ζ2+ζ800000000000
χ39222−1+i3−1−i3−1−i32−1+i3−1+i3−1−i32−1−52−1−52−1−52ζ11+ζ14ζ+ζ4ζ+ζ4−1−52ζ11+ζ14ζ11+ζ14ζ+ζ4−1−52−1+52−1+52−1+52ζ2+ζ8ζ7+ζ13ζ7+ζ13−1+52ζ2+ζ8ζ2+ζ8ζ7+ζ13−1+5200000000000
χ40222−1−i3−1+i32−1−i3−1+i32−1−i3−1+i3−1−52−1−52−1−52ζ+ζ4ζ11+ζ14−1−52ζ+ζ4ζ11+ζ14−1−52ζ+ζ4ζ11+ζ14−1+52−1+52−1+52ζ7+ζ13ζ2+ζ8−1+52ζ7+ζ13ζ2+ζ8−1+52ζ7+ζ13ζ2+ζ800000000000
χ41222−1−i3−1+i3−1+i32−1−i3−1−i3−1+i32−1−52−1−52−1−52ζ+ζ4ζ11+ζ14ζ11+ζ14−1−52ζ+ζ4ζ+ζ4ζ11+ζ14−1−52−1+52−1+52−1+52ζ7+ζ13ζ2+ζ8ζ2+ζ8−1+52ζ7+ζ13ζ7+ζ13ζ2+ζ8−1+5200000000000
χ42222−1−i3−1+i3−1−i3−1+i32−1+i32−1−i3−1−52−1−52−1−52ζ+ζ4ζ11+ζ14ζ+ζ4ζ11+ζ14−1−52ζ11+ζ14−1−52ζ+ζ4−1+52−1+52−1+52ζ7+ζ13ζ2+ζ8ζ7+ζ13ζ2+ζ8−1+52ζ2+ζ8−1+52ζ7+ζ1300000000000
χ436−3+3i3−3−3i300000000−3−3523ζ11+3ζ143ζ+3ζ400000000−3+3523ζ2+3ζ83ζ7+3ζ130000000000000000000
χ446−3−3i3−3+3i300000000−3−3523ζ+3ζ43ζ11+3ζ1400000000−3+3523ζ7+3ζ133ζ2+3ζ80000000000000000000

Here ζ is a primitive root of unity of order 15 (ζ15 = 1); i = ζ3.