Finite Group Databasebeta

← Group #13159701

Character table — Group #13159701

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156
size111122222222222222222222224444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444441212121224242424242424242424242424242424363636365454545472727272108108
order1222333334466666666666666633336666666666668812121212121212121212121212121212121212121212121212122424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242444441212121212121212121212121212121222224444666688
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ5111111111111111111111111111111111111111111-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1
χ6111111111111111111111111111111111111111111-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111
χ7111111111111111111111111111111111111111111-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-111
χ8111111111111111111111111111111111111111111-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1111111-1-111-1-1
χ911-1-1111111-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1i−ii−iiiii−i−i−i−iiiii−i−i−i−i1-11-1ii−i−i1-11-1i−i
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χ1211-1-1111111-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−ii−ii−i−i−i−iiiii−i−i−i−iiiii-11-11ii−i−i-11-11i−i
χ1311-1-1111111-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-11-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111111i−i−iiiiii−i−i−i−i−i−i−i−iiiii1-1-11ii−i−i1-1-11−ii
χ1411-1-1111111-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-11-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111111i−i−iiiiii−i−i−i−i−i−i−i−iiiii-111-1−i−iii-111-1i−i
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χ17222222222-2-2222222222222222222222222222222200-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000000000000000000000000000000000000000000000002-22-2000000
χ18222222222-2-2222222222222222222222222222222200-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000000000000000000000000000000000000000000000000-22-22000000
χ1922222222-122-1-12222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000022220000-1-1-1-100
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χ2322222-1-1-1222222-1-1-1222-1-1-1-1-1-12-1-1-122-1-1-1-1-1-12-1-1-1222-1-1-1222-1-1-1-1-1-12-1-1-1222-1-1-1-1-1-122-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-122222-1-1-12-1-1-12-1-1-12-1-1-100000000000000
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χ2622222-1-1-1222222-1-1-1222-1-1-1-1-1-12-1-1-122-1-1-1-1-1-12-1-1-1-2-22-1-1-1222-1-1-1-1-1-12-1-1-1222-1-1-1-1-1-1-2-2111111-2-2-2-2-2-2111111111111-2-2111111-2-2-2-2-2-2111111111111-2-222-2111-21112-1-1-12-1-1-100000000000000
χ272222-12-1-122222-12-1-12-1-122-1-1-1-1-12-1-1-1-122-1-1-1-1-12-1-122-12-1-12-1-122-1-1-1-1-12-1-12-1-122-1-1-1-1-1-122-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-12222-12-1-1-12-1-1-12-1-1-12-1-100000000000000
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χ302222-12-1-122222-12-1-12-1-122-1-1-1-1-12-1-1-1-122-1-1-1-1-12-1-1-2-2-12-1-12-1-122-1-1-1-1-12-1-12-1-122-1-1-1-111-2-21111-2-21111-2-2-2-21111111111-2-21111-2-21111-2-2-2-211111111-2-2221-2111-211-12-1-1-12-1-100000000000000
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χ1484-4-44-2-24-2-2002-222-4222-22-2-442-211-21-11-112-2-11-1-12-100000003i−3i−3i3i003i−3i00000−3i3i3i−3i00−3i3i−666−600−66i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23i6−i6i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ136−6−66006−6−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−i6i6−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ130000000000000000000000000000000000
χ1494-4-44-2-24-2-2002-222-4222-22-2-442-211-21-11-112-2-11-1-12-10000000−3i3i3i−3i00−3i3i000003i−3i−3i3i003i−3i6−6−66006−6i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13i6−i6i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23−666−600−66−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−i6i6−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ230000000000000000000000000000000000
χ1504-4-44-2-24-2-2002-222-4222-22-2-442-211-21-11-112-2-11-1-12-10000000−3i3i3i−3i00−3i3i000003i−3i−3i3i003i−3i−666−600−66−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−i6i6−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ236−6−66006−6i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13i6−i6i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ230000000000000000000000000000000000
χ1514-4-44-2-2-24400-44222-4-42-22-22-2-44-2-2-242-22-22-2-44222-400000000000000000000000000006−66−6−6600006−6−666−6−66−666−60000−66−666−60000−666−6−666−66−6−6600000000000000000000000000000000000000
χ1524-4-44-2-2-24400-44222-4-42-22-22-2-44-2-2-242-22-22-2-44222-40000000000000000000000000000−66−666−60000−666−6−666−66−6−6600006−66−6−6600006−6−666−6−66−666−600000000000000000000000000000000000000
χ1534-4-44-2-2-24-2002-2222-422-22-22-2-44111-2-11-11-112-2-1-1-1200000003i−3i3i−3i−3i3i0000000−3i3i−3i3i3i−3i006−66−6−6600−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−i6i6−i6i6−66−666−600i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23i6−i6i6−i60000000000000000000000000000000000
χ1544-4-44-2-2-24-2002-2222-422-22-22-2-44111-2-11-11-112-2-1-1-1200000003i−3i3i−3i−3i3i0000000−3i3i−3i3i3i−3i00−66−666−600i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23i6−i6i6−i66−66−6−6600−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−i6i6−i6i60000000000000000000000000000000000
χ1554-4-44-2-2-24-2002-2222-422-22-22-2-44111-2-11-11-112-2-1-1-120000000−3i3i−3i3i3i−3i00000003i−3i3i−3i−3i3i006−66−6−6600i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13i6−i6i6−i6−66−666−600−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−i6i6−i6i60000000000000000000000000000000000
χ1564-4-44-2-2-24-2002-2222-422-22-22-2-44111-2-11-11-112-2-1-1-120000000−3i3i−3i3i3i−3i00000003i−3i3i−3i−3i3i00−66−666−600−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−i6i6−i6i66−66−6−6600i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13i6−i6i6−i60000000000000000000000000000000000

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