Finite Group Databasebeta

← Group #13146477

Character table — Group #13146477

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111222222222299991212121212121212181818181818181818181818181818181818181818181818181818181818181818182424242436363636363636367272727272727272
order12443688121224242424888833661212121224444466888812121212121212121212242424242424242424242424242424242244888866121224242424
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
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χ3111111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111-11-111-1-11-11-111-1-1
χ4111111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-11-11-1-111-11-11-1-111
χ5111111-1-111-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1111-11-1-1-111
χ6111111-1-111-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-1-11-1111-1-1
χ7111111-1-111-1-1-1-1-1-1-1-1111111111-1-1-1-11111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ8111111-1-111-1-1-1-1-1-1-1-1111111111-1-1-1-11111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111
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χ736-6−6i6i-33003i−3i−3ζ5+3ζ133ζ5−3ζ133ζ7−3ζ23−3ζ7+3ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000001+i−1−i1−i−1+i0−i3i3−22−i2i2−ζ4+ζ14−ζ20+ζ22ζ4−ζ14ζ20−ζ22−ζ20−ζ22−ζ4−ζ14ζ20+ζ22ζ4+ζ14−33−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ700000000000000000000
χ746-6−6i6i-33003i−3i−3ζ5+3ζ133ζ5−3ζ133ζ7−3ζ23−3ζ7+3ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000−1−i1+i−1+i1−i0−i3i32−2i2−i2ζ4−ζ14ζ20−ζ22−ζ4+ζ14−ζ20+ζ22ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14−33−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ700000000000000000000
χ756-6−6i6i-33003i−3i−3ζ5+3ζ133ζ5−3ζ133ζ7−3ζ23−3ζ7+3ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000001+i−1−i1−i−1+i0i3−i32−2i2−i2−ζ20+ζ22−ζ4+ζ14ζ20−ζ22ζ4−ζ14−ζ4−ζ14−ζ20−ζ22ζ4+ζ14ζ20+ζ223−3ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ2300000000000000000000
χ766-6−6i6i-33003i−3i−3ζ5+3ζ133ζ5−3ζ133ζ7−3ζ23−3ζ7+3ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000−1−i1+i−1+i1−i0i3−i3−22−i2i2ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14ζ4+ζ14ζ20+ζ22−ζ4−ζ14−ζ20−ζ223−3ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ2300000000000000000000
χ778-88i−8i8-8008i−8i000000002-4-242i−4i−2i4i000000000000000000000000000000000000000000000000000000
χ788-88i−8i8-8008i−8i00000000-424-2−4i2i4i−2i000000000000000000000000000000000000000000000000000000
χ798-8−8i8i8-800−8i8i000000002-4-24−2i4i2i−4i000000000000000000000000000000000000000000000000000000
χ808-8−8i8i8-800−8i8i00000000-424-24i−2i−4i2i000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.