Finite Group Databasebeta

← Group #13166492

Character table — Group #13166492

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size111122222233334444444444444444446688888888888888889999121212121212121212121212121212121818181818181818181818181818272727273636363636363636363654545454545454545454
order122234466644443366666612121212121212121212443366666612121212121212124444121212121212121212121212121212124488888888121212124444121224242424242424242288888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111-1-1-1-11111111111111111-1-1iiii−i−i−i−i-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i-1-1iiii−i−i−i−i
χ411111111111111111111111111111111111111111111111111-1-1-1-11111111111111111-1-1−i−i−i−iiiii-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii-1-1−i−i−i−iiiii
χ51111111111-1-1-1-1111111111111111111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1
χ61111111111-1-1-1-1111111111111111111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111
χ71111111111-1-1-1-1111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i-1-1-1-11111-1-1iiii−i−i−i−i11−i−i−i−iiiii
χ81111111111-1-1-1-1111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii-1-1-1-11111-1-1−i−i−i−iiiii11iiii−i−i−i−i
χ911111-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111111111-1-111-1-111-1-1-1-111-1-111-1-1
χ1011111-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-111-1-111-1-1-1-111-1-111
χ1111111-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111ii−i−i−i−iii-1-1-1-1-1-1-1-111ii−i−i−i−iii11ii−i−i−i−iii
χ1211111-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111−i−iiiii−i−i-1-1-1-1-1-1-1-111−i−iiiii−i−i11−i−iiiii−i−i
χ1311111-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-111-1-111-1-11111-1-1-1-1-1-111-1-111-1-111-1-111-1-111
χ1411111-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-111-1-1111111-1-111-1-1
χ1511111-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111ii−i−i−i−iii-1-1-1-1111111ii−i−i−i−iii-1-1−i−iiiii−i−i
χ1611111-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111−i−iiiii−i−i-1-1-1-1111111−i−iiiii−i−i-1-1ii−i−i−i−iii
χ1711-1-11i−i-11-1ii−i−i11-1-111-1-1i−iiiii−i−i−i−i1-11111-1-1-1-1iiii−i−i−i−i11-1-1iiii−i−i−i−i1111-1-1-1-1i−i1-1i−i1-1i−i11-1-1ii−i−ii−i1-1i−i1-1i−i1-1i−i1-1i−i1-1
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χ1911-1-11i−i-11-1ii−i−i11-1-111-1-1i−iiiii−i−i−i−i1-11111-1-1-1-1iiii−i−i−i−i-1-111iiii−i−i−i−i1111-1-1-1-1−iii−i-11−ii1-1-1-111−i−iii−iii−i-11−ii1-1-11-11i−i1-1−ii
χ2011-1-11i−i-11-1ii−i−i11-1-111-1-1i−iiiii−i−i−i−i1-11111-1-1-1-1iiii−i−i−i−i-1-111iiii−i−i−i−i1111-1-1-1-1−ii−ii1-1i−i-11-1-111−i−iii−ii−ii1-1i−i-11-111-1−ii-11i−i
χ2111-1-11i−i-11-1−i−iii11-1-111-1-1i−iiiii−i−i−i−i-111111-1-1-1-1iiii−i−i−i−i11-1-1−i−i−i−iiiii-1-1-1-11111i−i1-1i−i1-1i−i11-1-1−i−iiii−i1-1i−i1-1i−i-11−ii-11−ii-11
χ2211-1-11i−i-11-1−i−iii11-1-111-1-1i−iiiii−i−i−i−i-111111-1-1-1-1iiii−i−i−i−i11-1-1−i−i−i−iiiii-1-1-1-11111i−i-11−ii-11−ii11-1-1−i−iiii−i-11−ii-11−ii-11i−i1-1i−i1-1
χ2311-1-11i−i-11-1−i−iii11-1-111-1-1i−iiiii−i−i−i−i-111111-1-1-1-1iiii−i−i−i−i-1-111−i−i−i−iiiii-1-1-1-11111−iii−i-11−ii1-1-1-111ii−i−i−iii−i-11−ii1-11-11-1−ii-11i−i
χ2411-1-11i−i-11-1−i−iii11-1-111-1-1i−iiiii−i−i−i−i-111111-1-1-1-1iiii−i−i−i−i-1-111−i−i−i−iiiii-1-1-1-11111−ii−ii1-1i−i-11-1-111ii−i−i−ii−ii1-1i−i-111-1-11i−i1-1−ii
χ2511-1-11−ii-11-1ii−i−i11-1-111-1-1−ii−i−i−i−iiiii-111111-1-1-1-1−i−i−i−iiiii11-1-1iiii−i−i−i−i-1-1-1-11111−ii1-1−ii1-1−ii11-1-1ii−i−i−ii1-1−ii1-1−ii-11i−i-11i−i-11
χ2611-1-11−ii-11-1ii−i−i11-1-111-1-1−ii−i−i−i−iiiii-111111-1-1-1-1−i−i−i−iiiii11-1-1iiii−i−i−i−i-1-1-1-11111−ii-11i−i-11i−i11-1-1ii−i−i−ii-11i−i-11i−i-11−ii1-1−ii1-1
χ2711-1-11−ii-11-1ii−i−i11-1-111-1-1−ii−i−i−i−iiiii-111111-1-1-1-1−i−i−i−iiiii-1-111iiii−i−i−i−i-1-1-1-11111i−ii−i1-1−ii-11-1-111−i−iiii−ii−i1-1−ii-111-1-11−ii1-1i−i
χ2811-1-11−ii-11-1ii−i−i11-1-111-1-1−ii−i−i−i−iiiii-111111-1-1-1-1−i−i−i−iiiii-1-111iiii−i−i−i−i-1-1-1-11111i−i−ii-11i−i1-1-1-111−i−iiii−i−ii-11i−i1-11-11-1i−i-11−ii
χ2911-1-11−ii-11-1−i−iii11-1-111-1-1−ii−i−i−i−iiiii1-11111-1-1-1-1−i−i−i−iiiii11-1-1−i−i−i−iiiii1111-1-1-1-1−ii1-1−ii1-1−ii11-1-1−i−iii−ii1-1−ii1-1−ii1-1−ii1-1−ii1-1
χ3011-1-11−ii-11-1−i−iii11-1-111-1-1−ii−i−i−i−iiiii1-11111-1-1-1-1−i−i−i−iiiii11-1-1−i−i−i−iiiii1111-1-1-1-1−ii-11i−i-11i−i11-1-1−i−iii−ii-11i−i-11i−i1-1i−i-11i−i-11
χ3111-1-11−ii-11-1−i−iii11-1-111-1-1−ii−i−i−i−iiiii1-11111-1-1-1-1−i−i−i−iiiii-1-111−i−i−i−iiiii1111-1-1-1-1i−ii−i1-1−ii-11-1-111ii−i−ii−ii−i1-1−ii-11-111-1i−i-11−ii
χ3211-1-11−ii-11-1−i−iii11-1-111-1-1−ii−i−i−i−iiiii1-11111-1-1-1-1−i−i−i−iiiii-1-111−i−i−i−iiiii1111-1-1-1-1i−i−ii-11i−i1-1-1-111ii−i−ii−i−ii-11i−i1-1-11-11−ii1-1i−i
χ332222-122-1-1-1000022222222-1-12222222200-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222200000000000000002222222222-1-1-1-10000-1-1-1-1-1-1-1-1-1-10000000000
χ342222-122-1-1-1000022222222-1-12222222200-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222000000000000000022-2-2-2-2-2-2-2-2-1-1-1-10000-1-1111111110000000000
χ352222-122-1-1-1000022222222-1-12222222200-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-20000000000000000-2-22i2i2i2i−2i−2i−2i−2i1111000011−i−i−i−iiiii0000000000
χ362222-122-1-1-1000022222222-1-12222222200-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-20000000000000000-2-2−2i−2i−2i−2i2i2i2i2i1111000011iiii−i−i−i−i0000000000
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χ382222-1-2-2-1-1-100002222222211-2-2-2-2-2-2-2-200-1-1-1-1-1-1-1-11111111122220000000000000000-2-2-2-222-2-222-1-1-1-100001111-1-111-1-10000000000
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χ774-44-4400-4-44-44-441-2-12-121-2003i−3i003i−3i00001-2-121-2-123i−3i003i−3i000000-121-2-121-2−3i3i00−3i3i0000000000000000000000000000000000000000
χ784-44-4400-4-44-44-441-2-12-121-200−3i3i00−3i3i00001-2-121-2-12−3i3i00−3i3i000000-121-2-121-23i−3i003i−3i0000000000000000000000000000000000000000
χ794-44-4400-4-44-44-44-212-12-1-2100003i−3i003i−3i00-212-1-212-1003i−3i003i−3i00002-1-212-1-2100−3i3i00−3i3i00000000000000000000000000000000000000
χ804-44-4400-4-44-44-44-212-12-1-210000−3i3i00−3i3i00-212-1-212-100−3i3i00−3i3i00002-1-212-1-21003i−3i003i−3i00000000000000000000000000000000000000
χ814-44-4-20022-2000044-4-4-4-444000000000000-2-222-2-222000000004i−4i4i−4i00000000000000000000000000−2i2i−2i2i000000000000000000000000
χ824-44-4-20022-2000044-4-4-4-444000000000000-2-222-2-22200000000−4i4i−4i4i000000000000000000000000002i−2i2i−2i000000000000000000000000
χ834-4-444004-4-44i−4i−4i4i1-21-2-12-12003-300-3300001-2-12-121-23-300-33000000i−2i−i2i−i2ii−2i−3i3i003i−3i0000000000000000000000000000000000000000
χ844-4-444004-4-44i−4i−4i4i1-21-2-12-1200-33003-300001-2-12-121-2-33003-3000000i−2i−i2i−i2ii−2i3i−3i00−3i3i0000000000000000000000000000000000000000
χ854-4-444004-4-44i−4i−4i4i-21-212-12-100003-300-3300-212-12-1-21003-300-330000−2ii2i−i2i−i−2ii00−3i3i003i−3i00000000000000000000000000000000000000
χ864-4-444004-4-44i−4i−4i4i-21-212-12-10000-33003-300-212-12-1-2100-33003-30000−2ii2i−i2i−i−2ii003i−3i00−3i3i00000000000000000000000000000000000000
χ874-4-444004-4-4−4i4i4i−4i1-21-2-12-12003-300-3300001-2-12-121-23-300-33000000−i2ii−2ii−2i−i2i3i−3i00−3i3i0000000000000000000000000000000000000000
χ884-4-444004-4-4−4i4i4i−4i1-21-2-12-1200-33003-300001-2-12-121-2-33003-3000000−i2ii−2ii−2i−i2i−3i3i003i−3i0000000000000000000000000000000000000000
χ894-4-444004-4-4−4i4i4i−4i-21-212-12-100003-300-3300-212-12-1-21003-300-3300002i−i−2ii−2ii2i−i003i−3i00−3i3i00000000000000000000000000000000000000
χ904-4-444004-4-4−4i4i4i−4i-21-212-12-10000-33003-300-212-12-1-2100-33003-300002i−i−2ii−2ii2i−i00−3i3i003i−3i00000000000000000000000000000000000000
χ914-4-44-200-22200004444-4-4-4-4000000000000-2-22222-2-2000000004i−4i−4i4i00000000000000000000000000−2i2i2i−2i000000000000000000000000
χ924-4-44-200-22200004444-4-4-4-4000000000000-2-22222-2-200000000−4i4i4i−4i000000000000000000000000002i−2i−2i2i000000000000000000000000
χ938888-488-4-4-400002-42-42-42-4-4-422-4-422-4-400-12-12-12-12-1-122-1-1220000000000000000000000000000000000000000000000000000000000
χ948888-488-4-4-40000-42-42-42-42-4-4-4-422-4-422002-12-12-12-122-1-122-1-10000000000000000000000000000000000000000000000000000000000
χ958888-4-8-8-4-4-400002-42-42-42-444-2-244-2-24400-12-12-12-1211-2-211-2-20000000000000000000000000000000000000000000000000000000000
χ968888-4-8-8-4-4-40000-42-42-42-424444-2-244-2-2002-12-12-12-1-2-211-2-2110000000000000000000000000000000000000000000000000000000000
χ9788-8-8-48i−8i4-4400002-4-242-4-24−4i4i2i2i−4i−4i−2i−2i4i4i00-12-121-21-2−i−i2i2iii−2i−2i0000000000000000000000000000000000000000000000000000000000
χ9888-8-8-48i−8i4-440000-424-2-424-2−4i4i−4i−4i2i2i4i4i−2i−2i002-12-1-21-212i2i−i−i−2i−2iii0000000000000000000000000000000000000000000000000000000000
χ9988-8-8-4−8i8i4-4400002-4-242-4-244i−4i−2i−2i4i4i2i2i−4i−4i00-12-121-21-2ii−2i−2i−i−i2i2i0000000000000000000000000000000000000000000000000000000000
χ10088-8-8-4−8i8i4-440000-424-2-424-24i−4i4i4i−2i−2i−4i−4i2i2i002-12-1-21-21−2i−2iii2i2i−i−i0000000000000000000000000000000000000000000000000000000000
χ1018-88-8-40044-400002-4-24-242-4006i−6i006i−6i0000-121-2-121-2−3i3i00−3i3i000000000000000000000000000000000000000000000000000000000000
χ1028-88-8-40044-400002-4-24-242-400−6i6i00−6i6i0000-121-2-121-23i−3i003i−3i000000000000000000000000000000000000000000000000000000000000
χ1038-88-8-40044-40000-424-24-2-4200006i−6i006i−6i002-1-212-1-2100−3i3i00−3i3i0000000000000000000000000000000000000000000000000000000000
χ1048-88-8-40044-40000-424-24-2-420000−6i6i00−6i6i002-1-212-1-21003i−3i003i−3i0000000000000000000000000000000000000000000000000000000000
χ1058-8-88-400-44400002-42-4-24-24006-600-660000-121-21-2-12-33003-3000000000000000000000000000000000000000000000000000000000000
χ1068-8-88-400-44400002-42-4-24-2400-66006-60000-121-21-2-123-300-33000000000000000000000000000000000000000000000000000000000000
χ1078-8-88-400-4440000-42-424-24-200006-600-66002-1-21-212-100-33003-30000000000000000000000000000000000000000000000000000000000
χ1088-8-88-400-4440000-42-424-24-20000-66006-6002-1-21-212-1003-300-330000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).