Finite Group Databasebeta

← Group #63201

Character table — Group #63201

Order 270.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32
size11122222266666666666666666666454545
order1335515151515333315151515151515151515151515151515266
χ111111111111111111111111111111111
χ211111111111111111111111111111-1-1-1
χ32222222222-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000
χ4222222222-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000
χ5222222222-1-12-1-1-1-1-1-1-1-1-12222-1-1-1-1000
χ6222222222-1-1-12-1-1-1-1-1-1-1-1-1-1-1-12222000
χ7222−1+52−1−52−1+52−1+52−1−52−1−522222−1+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+52−1−52−1−52000
χ8222−1+52−1−52−1+52−1+52−1−52−1−522-1-1-1−1+52−1+52−1−52−1−52ζ2+ζ13ζ7+ζ8ζ4+ζ11ζ+ζ14ζ2+ζ13ζ7+ζ8ζ4+ζ11ζ+ζ14ζ2+ζ13ζ7+ζ8ζ4+ζ11ζ+ζ14000
χ9222−1+52−1−52−1+52−1+52−1−52−1−522-1-1-1−1+52−1+52−1−52−1−52ζ7+ζ8ζ2+ζ13ζ+ζ14ζ4+ζ11ζ7+ζ8ζ2+ζ13ζ+ζ14ζ4+ζ11ζ7+ζ8ζ2+ζ13ζ+ζ14ζ4+ζ11000
χ10222−1+52−1−52−1+52−1+52−1−52−1−52-12-1-1ζ2+ζ13ζ7+ζ8ζ4+ζ11ζ+ζ14−1+52−1+52−1−52−1−52ζ2+ζ13ζ7+ζ8ζ4+ζ11ζ+ζ14ζ7+ζ8ζ2+ζ13ζ+ζ14ζ4+ζ11000
χ11222−1+52−1−52−1+52−1+52−1−52−1−52-12-1-1ζ7+ζ8ζ2+ζ13ζ+ζ14ζ4+ζ11−1+52−1+52−1−52−1−52ζ7+ζ8ζ2+ζ13ζ+ζ14ζ4+ζ11ζ2+ζ13ζ7+ζ8ζ4+ζ11ζ+ζ14000
χ12222−1+52−1−52−1+52−1+52−1−52−1−52-1-12-1ζ2+ζ13ζ7+ζ8ζ4+ζ11ζ+ζ14ζ7+ζ8ζ2+ζ13ζ+ζ14ζ4+ζ11−1+52−1+52−1−52−1−52ζ2+ζ13ζ7+ζ8ζ4+ζ11ζ+ζ14000
χ13222−1+52−1−52−1+52−1+52−1−52−1−52-1-12-1ζ7+ζ8ζ2+ζ13ζ+ζ14ζ4+ζ11ζ2+ζ13ζ7+ζ8ζ4+ζ11ζ+ζ14−1+52−1+52−1−52−1−52ζ7+ζ8ζ2+ζ13ζ+ζ14ζ4+ζ11000
χ14222−1+52−1−52−1+52−1+52−1−52−1−52-1-1-12ζ2+ζ13ζ7+ζ8ζ4+ζ11ζ+ζ14ζ2+ζ13ζ7+ζ8ζ4+ζ11ζ+ζ14ζ7+ζ8ζ2+ζ13ζ+ζ14ζ4+ζ11−1+52−1+52−1−52−1−52000
χ15222−1+52−1−52−1+52−1+52−1−52−1−52-1-1-12ζ7+ζ8ζ2+ζ13ζ+ζ14ζ4+ζ11ζ7+ζ8ζ2+ζ13ζ+ζ14ζ4+ζ11ζ2+ζ13ζ7+ζ8ζ4+ζ11ζ+ζ14−1+52−1+52−1−52−1−52000
χ16222−1−52−1+52−1−52−1−52−1+52−1+522222−1−52−1−52−1+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+52000
χ17222−1−52−1+52−1−52−1−52−1+52−1+522-1-1-1−1−52−1−52−1+52−1+52ζ4+ζ11ζ+ζ14ζ7+ζ8ζ2+ζ13ζ4+ζ11ζ+ζ14ζ7+ζ8ζ2+ζ13ζ4+ζ11ζ+ζ14ζ7+ζ8ζ2+ζ13000
χ18222−1−52−1+52−1−52−1−52−1+52−1+522-1-1-1−1−52−1−52−1+52−1+52ζ+ζ14ζ4+ζ11ζ2+ζ13ζ7+ζ8ζ+ζ14ζ4+ζ11ζ2+ζ13ζ7+ζ8ζ+ζ14ζ4+ζ11ζ2+ζ13ζ7+ζ8000
χ19222−1−52−1+52−1−52−1−52−1+52−1+52-12-1-1ζ4+ζ11ζ+ζ14ζ7+ζ8ζ2+ζ13−1−52−1−52−1+52−1+52ζ4+ζ11ζ+ζ14ζ7+ζ8ζ2+ζ13ζ+ζ14ζ4+ζ11ζ2+ζ13ζ7+ζ8000
χ20222−1−52−1+52−1−52−1−52−1+52−1+52-12-1-1ζ+ζ14ζ4+ζ11ζ2+ζ13ζ7+ζ8−1−52−1−52−1+52−1+52ζ+ζ14ζ4+ζ11ζ2+ζ13ζ7+ζ8ζ4+ζ11ζ+ζ14ζ7+ζ8ζ2+ζ13000
χ21222−1−52−1+52−1−52−1−52−1+52−1+52-1-12-1ζ4+ζ11ζ+ζ14ζ7+ζ8ζ2+ζ13ζ+ζ14ζ4+ζ11ζ2+ζ13ζ7+ζ8−1−52−1−52−1+52−1+52ζ4+ζ11ζ+ζ14ζ7+ζ8ζ2+ζ13000
χ22222−1−52−1+52−1−52−1−52−1+52−1+52-1-12-1ζ+ζ14ζ4+ζ11ζ2+ζ13ζ7+ζ8ζ4+ζ11ζ+ζ14ζ7+ζ8ζ2+ζ13−1−52−1−52−1+52−1+52ζ+ζ14ζ4+ζ11ζ2+ζ13ζ7+ζ8000
χ23222−1−52−1+52−1−52−1−52−1+52−1+52-1-1-12ζ4+ζ11ζ+ζ14ζ7+ζ8ζ2+ζ13ζ4+ζ11ζ+ζ14ζ7+ζ8ζ2+ζ13ζ+ζ14ζ4+ζ11ζ2+ζ13ζ7+ζ8−1−52−1−52−1+52−1+52000
χ24222−1−52−1+52−1−52−1−52−1+52−1+52-1-1-12ζ+ζ14ζ4+ζ11ζ2+ζ13ζ7+ζ8ζ+ζ14ζ4+ζ11ζ2+ζ13ζ7+ζ8ζ4+ζ11ζ+ζ14ζ7+ζ8ζ2+ζ13−1−52−1−52−1+52−1+52000
χ253−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i32000000000000000000001−1+i32−1−i32
χ263−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i3200000000000000000000-11−i321+i32
χ273−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32000000000000000000001−1−i32−1+i32
χ283−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i3200000000000000000000-11+i321−i32
χ296−3+3i3−3−3i3−3+352−3−3523ζ2+3ζ83ζ7+3ζ133ζ11+3ζ143ζ+3ζ400000000000000000000000
χ306−3+3i3−3−3i3−3−352−3+3523ζ11+3ζ143ζ+3ζ43ζ2+3ζ83ζ7+3ζ1300000000000000000000000
χ316−3−3i3−3+3i3−3+352−3−3523ζ7+3ζ133ζ2+3ζ83ζ+3ζ43ζ11+3ζ1400000000000000000000000
χ326−3−3i3−3+3i3−3−352−3+3523ζ+3ζ43ζ11+3ζ143ζ7+3ζ133ζ2+3ζ800000000000000000000000

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