Finite Group Databasebeta

← Group #13154797

Character table — Group #13154797

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222444444444444444444888888888888888812121212121212121212121212121212121218181818181818183636363636363636363636363636108108108108108108
order1244234612123366666661212121212121212123366666612121212121212124412121212121212121212121212121212224466121268888122424242424242424444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1ii−i−i-1iiii−i−i−i−i-1-1ii−i−i
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1−i−iii-1−i−i−i−iiiii-1-1−i−iii
χ511111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1
χ611111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i-1iiii−i−i−i−i11−i−iii
χ811111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii-1−i−i−i−iiiii11ii−i−i
χ91111-11-111111-111-1-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1i−iiiiiiiii−i−i−i−i−i−i−i−i1-1-111111-11-11-1-111-1-111-1-1i−ii−ii−i
χ101111-11-111111-111-1-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1i−iiiiiiiii−i−i−i−i−i−i−i−i1-1-111111-1-11-11-1-1-111-1-111i−i−ii−ii
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χ131111-11-111111-111-1-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1−ii−i−i−i−i−i−i−i−iiiiiiiii1-1-111111-11-11-1-111-1-111-1-1−ii−ii−ii
χ141111-11-111111-111-1-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1−ii−i−i−i−i−i−i−i−iiiiiiiii1-1-111111-1-11-11-1-1-111-1-111−iii−ii−i
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χ858-88i−8i0-404−4i4i-4204-2006-60−4i4i−2i2i006i−6i2-100-33-212i−2ii−i00−3i3i0000000000000000000000000000000000000000000000
χ868-88i−8i0-404−4i4i-4204-200-660−4i4i−2i2i00−6i6i2-1003-3-212i−2ii−i003i−3i0000000000000000000000000000000000000000000000
χ878-8−8i8i0-4044i−4i2-40-246-6000−2i2i−4i4i−6i6i00-12-33001-2i−i2i−2i3i−3i000000000000000000000000000000000000000000000000
χ888-8−8i8i0-4044i−4i2-40-24-66000−2i2i−4i4i6i−6i00-123-3001-2i−i2i−2i−3i3i000000000000000000000000000000000000000000000000
χ898-8−8i8i0-4044i−4i-4204-2006-604i−4i2i−2i00−6i6i2-100-33-21−2i2i−ii003i−3i0000000000000000000000000000000000000000000000
χ908-8−8i8i0-4044i−4i-4204-200-6604i−4i2i−2i006i−6i2-1003-3-21−2i2i−ii00−3i3i0000000000000000000000000000000000000000000000

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