Finite Group Databasebeta

← Group #11775906

Character table — Group #11775906

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222444444444444444444444888888888888888888888818181818181824242424242424242424242424242424363636363648484848
order1222334444666666346668888121212121212121212121212121212121212242424242424242424242424242424242244444444888824242424242424244888812121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-111-1-1
χ411111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-111
χ5111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111
χ6111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1
χ7111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1111111-1-1
χ8111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-11111-1-111
χ9111111-1-1-1-111111111111ii−i−i-1-1-1-1-1-1-1-1-1-1-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-11-11-1i−ii−iii−i−iii−i−i-1ii−i−i1-11-1
χ10111111-1-1-1-111111111111ii−i−i-1-1-1-1-1-1-1-1-1-1-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-11-11−ii−ii−i−iii−i−iii-1ii−i−i-11-11
χ11111111-1-1-1-111111111111ii−i−i-1-1-1-1-1-1-1-1-1-1-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1111-1-11i−i−iiii−i−i−i−iii1−i−iii1-1-11
χ12111111-1-1-1-111111111111ii−i−i-1-1-1-1-1-1-1-1-1-1-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-111-111-1−iii−i−i−iiiii−i−i1−i−iii-111-1
χ13111111-1-1-1-111111111111−i−iii-1-1-1-1-1-1-1-1-1-1-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii1111-1-11-11-1−ii−ii−i−iii−i−iii-1−i−iii1-11-1
χ14111111-1-1-1-111111111111−i−iii-1-1-1-1-1-1-1-1-1-1-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-11-11i−ii−iii−i−iii−i−i-1−i−iii-11-11
χ15111111-1-1-1-111111111111−i−iii-1-1-1-1-1-1-1-1-1-1-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1111-1-11−iii−i−i−iiiii−i−i1ii−i−i1-1-11
χ16111111-1-1-1-111111111111−i−iii-1-1-1-1-1-1-1-1-1-1-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-111-111-1i−i−iiii−i−i−i−iii1ii−i−i-111-1
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χ1822222222-2-22222222-22220000-2-2-2-2-2-2-2-22222-2-2-2-2220000000000000000-2-222220000000000000000-200000000
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χ20222222-2-2222222222-2222000022222222-2-2-2-2-2-2-2-2-2-20000000000000000-2-222-2-20000000000000000200000000
χ2122222-122222-122-1-1-12-1-1-1222222-1-1-1-1-1-122-1-12-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1000000002200220000-1-1-1-10000000-1-1
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χ2322222-122222-122-1-1-12-1-1-1-2-2-2-222-1-1-1-1-1-122-1-12-1-1-1-1-1-2-2111111-2-2111111000000002200-2-2000011110000000-1-1
χ2422222-122222-122-1-1-12-1-1-1-2-2-2-222-1-1-1-1-1-122-1-12-1-1-1-1-1-2-2111111-2-211111100000000-2-200220000-1-1-1-1000000011
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χ2622222-1-2-2-2-22-122-1-1-12-1-1-12i2i−2i−2i-2-2111111-2-2112-1-1-1112i2i−i−i−i−i−i−i−2i−2iiiiiii00000000-2200−2i2i0000ii−i−i00000001-1
χ2722222-1-2-2-2-22-122-1-1-12-1-1-1−2i−2i2i2i-2-2111111-2-2112-1-1-111−2i−2iiiiiii2i2i−i−i−i−i−i−i000000002-200−2i2i0000ii−i−i0000000-11
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χ292222-122222-12-1-122-12-1-1-12222-1-122-1-1-1-1-1-122-12-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-100000022002200-1-1-1-1000000000-1-100
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χ322222-122222-12-1-122-12-1-1-1-2-2-2-2-1-122-1-1-1-1-1-122-12-1-1-1-111-2-2111111-2-21111000000-2-2002200-1-1-1-10000000001100
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χ824-4-44-24004i−4i2-42-2-44-2022-20000−2i2i4i−4i−2i2i−2i2i0000000000000000000000000000000000000000ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ110000000000000
χ834-4-44-2400−4i4i2-42-2-44-2022-200002i−2i−4i4i2i−2i2i−2i0000000000000000000000000000000000000000−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ110000000000000
χ844-4-44-2400−4i4i2-42-2-44-2022-200002i−2i−4i4i2i−2i2i−2i0000000000000000000000000000000000000000ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ110000000000000
χ8588-8-88-400008-4-8-844-404-44000000000000000000000000000000000000000000000000000000000000000000000
χ8688-8-8-480000-4844-8-8-404-44000000000000000000000000000000000000000000000000000000000000000000000
χ8788-8-8-4-40000-4-4444420-22-2000000006i−6i−6i6i000000000000000000000000000000000000000000000000000000000
χ8888-8-8-4-40000-4-4444420-22-200000000−6i6i6i−6i000000000000000000000000000000000000000000000000000000000
χ898-8-88-4-4008i−8i444-44-420-2-220000−4i4i−4i4i2i−2i2i−2i000000000000000000000000000000000000000000000000000000000
χ908-8-88-4-400−8i8i444-44-420-2-2200004i−4i4i−4i−2i2i−2i2i000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.