Finite Group Databasebeta

← Group #11757413

Character table — Group #11757413

Order 972.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111133333333399999999999999999999999999999999363636363636363636363636363636363636
order13333333326666666633666666999999181818181818181818181818181818181818333333333333999999
χ111111111111111111111111111111111111111111111111111111111111111111111
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χ311111111111111111111111111111111111111111111111111−1−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
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χ543−3−3i32−3+3i32−3−3i32−3+3i32−3+3i32−3−3i3233-11+i321−i321+i321−i321−i321+i32-1-1002−1−i3−1+i32−1−i3−1+i3ζ+2ζ4ζ−ζ4−2ζ−ζ4−ζ2−2ζ52ζ2+ζ5−ζ2+ζ5−ζ−ζ7−ζ4−ζ−ζ7−ζ4ζ−2ζ4−3ζ−ζ42ζ+3ζ4−ζ2−ζ5−ζ83ζ2+2ζ5−2ζ2+ζ5−ζ2−3ζ5−ζ2−ζ5−ζ8000000000000000000
χ553−3−3i32−3+3i32−3−3i32−3+3i32−3+3i32−3−3i3233-11+i321−i321+i321−i321−i321+i32-1-1002−1−i3−1+i32−1−i3−1+i3ζ−ζ4−2ζ−ζ4ζ+2ζ42ζ2+ζ5−ζ2+ζ5−ζ2−2ζ5−ζ7−ζ4−ζ−ζ7−ζ4−ζ−3ζ−ζ42ζ+3ζ4ζ−2ζ4−ζ5−ζ8−ζ2−2ζ2+ζ5−ζ2−3ζ53ζ2+2ζ5−ζ5−ζ8−ζ2000000000000000000
χ563−3−3i32−3+3i32−3−3i32−3+3i32−3+3i32−3−3i3233-11+i321−i321+i321−i321−i321+i32-1-1002−1−i3−1+i32−1−i3−1+i3−2ζ−ζ4ζ+2ζ4ζ−ζ4−ζ2+ζ5−ζ2−2ζ52ζ2+ζ5−ζ4−ζ−ζ7−ζ4−ζ−ζ72ζ+3ζ4ζ−2ζ4−3ζ−ζ4−ζ8−ζ2−ζ5−ζ2−3ζ53ζ2+2ζ5−2ζ2+ζ5−ζ8−ζ2−ζ5000000000000000000
χ573−3−3i32−3+3i32−3−3i32−3+3i32−3+3i32−3−3i3233-11+i321−i321+i321−i321−i321+i32-1-100−1+i32−1−i3−1−i3−1+i32ζ+2ζ4ζ−ζ4−2ζ−ζ4−ζ2−2ζ52ζ2+ζ5−ζ2+ζ5ζ−2ζ4−3ζ−ζ42ζ+3ζ4−ζ−ζ7−ζ4−ζ−ζ7−ζ43ζ2+2ζ5−2ζ2+ζ5−ζ2−3ζ5−ζ2−ζ5−ζ8−ζ2−ζ5−ζ8000000000000000000
χ583−3−3i32−3+3i32−3−3i32−3+3i32−3+3i32−3−3i3233-11+i321−i321+i321−i321−i321+i32-1-100−1+i32−1−i3−1−i3−1+i32ζ−ζ4−2ζ−ζ4ζ+2ζ42ζ2+ζ5−ζ2+ζ5−ζ2−2ζ5−3ζ−ζ42ζ+3ζ4ζ−2ζ4−ζ7−ζ4−ζ−ζ7−ζ4−ζ−2ζ2+ζ5−ζ2−3ζ53ζ2+2ζ5−ζ5−ζ8−ζ2−ζ5−ζ8−ζ2000000000000000000
χ593−3−3i32−3+3i32−3−3i32−3+3i32−3+3i32−3−3i3233-11+i321−i321+i321−i321−i321+i32-1-100−1+i32−1−i3−1−i3−1+i32−2ζ−ζ4ζ+2ζ4ζ−ζ4−ζ2+ζ5−ζ2−2ζ52ζ2+ζ52ζ+3ζ4ζ−2ζ4−3ζ−ζ4−ζ4−ζ−ζ7−ζ4−ζ−ζ7−ζ2−3ζ53ζ2+2ζ5−2ζ2+ζ5−ζ8−ζ2−ζ5−ζ8−ζ2−ζ5000000000000000000
χ603−3−3i32−3+3i32−3−3i32−3+3i32−3+3i32−3−3i3233-11+i321−i321+i321−i321−i321+i32-1-100−1−i3−1+i32−1+i32−1−i3ζ+2ζ4ζ−ζ4−2ζ−ζ4−ζ2−2ζ52ζ2+ζ5−ζ2+ζ5−ζ−ζ7−ζ4ζ−2ζ4−3ζ−ζ42ζ+3ζ4−ζ−ζ7−ζ4−ζ2−ζ5−ζ8−ζ2−ζ5−ζ83ζ2+2ζ5−2ζ2+ζ5−ζ2−3ζ5000000000000000000
χ613−3−3i32−3+3i32−3−3i32−3+3i32−3+3i32−3−3i3233-11+i321−i321+i321−i321−i321+i32-1-100−1−i3−1+i32−1+i32−1−i3ζ−ζ4−2ζ−ζ4ζ+2ζ42ζ2+ζ5−ζ2+ζ5−ζ2−2ζ5−ζ7−ζ4−ζ−3ζ−ζ42ζ+3ζ4ζ−2ζ4−ζ7−ζ4−ζ−ζ5−ζ8−ζ2−ζ5−ζ8−ζ2−2ζ2+ζ5−ζ2−3ζ53ζ2+2ζ5000000000000000000
χ623−3−3i32−3+3i32−3−3i32−3+3i32−3+3i32−3−3i3233-11+i321−i321+i321−i321−i321+i32-1-100−1−i3−1+i32−1+i32−1−i3−2ζ−ζ4ζ+2ζ4ζ−ζ4−ζ2+ζ5−ζ2−2ζ52ζ2+ζ5−ζ4−ζ−ζ72ζ+3ζ4ζ−2ζ4−3ζ−ζ4−ζ4−ζ−ζ7−ζ8−ζ2−ζ5−ζ8−ζ2−ζ5−ζ2−3ζ53ζ2+2ζ5−2ζ2+ζ5000000000000000000
χ63999−9+9i32−9−9i32−9+9i32−9−9i32−9+9i32−9−9i32-3-3-33−3i323+3i323−3i323+3i323−3i323+3i3200000000000000000000000000000000000000000000000000
χ64999−9−9i32−9+9i32−9−9i32−9+9i32−9−9i32−9+9i32-3-3-33+3i323−3i323+3i323−3i323+3i323−3i3200000000000000000000000000000000000000000000000000
χ659−9+9i32−9−9i3299−9+9i32−9−9i32−9−9i32−9+9i32-33−3i323+3i32-3-33−3i323+3i323+3i323−3i3200000000000000000000000000000000000000000000000000
χ669−9+9i32−9−9i32−9−9i32−9+9i3299−9+9i32−9−9i32-33−3i323+3i323+3i323−3i32-3-33−3i323+3i3200000000000000000000000000000000000000000000000000
χ679−9−9i32−9+9i3299−9−9i32−9+9i32−9+9i32−9−9i32-33+3i323−3i32-3-33+3i323−3i323−3i323+3i3200000000000000000000000000000000000000000000000000
χ689−9−9i32−9+9i32−9+9i32−9−9i3299−9−9i32−9+9i32-33+3i323−3i323−3i323+3i32-3-33+3i323−3i3200000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 9 (ζ9 = 1); i = ζ2.