Finite Group Databasebeta

← Group #13166518

Character table — Group #13166518

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size111122444444444444444499991818181818181818181822224488888888888888881818181836363636363636363636333366121212121212121212121212121212122727272754545454545454545454
order122244336666661212121212121212222244444444443666121233666666121212121212121266661212121212121212121222224466666666121212121212121222224444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111-1-1-1-1-1-1iiii−i−i−i−i1111111111111111111111-1-1-1-1-1-1iiii−i−i−i−i1111111111111111111111-1-1-1-1-1-1iiii−i−i−i−i
χ41111111111111111111111-1-1-1-1-1-1−i−i−i−iiiii1111111111111111111111-1-1-1-1-1-1−i−i−i−iiiii1111111111111111111111-1-1-1-1-1-1−i−i−i−iiiii
χ51111-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-11111-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-11111-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1
χ61111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1111111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1111111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111
χ71111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111ii−i−i−i−iii1111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111ii−i−i−i−iii1111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111ii−i−i−i−iii
χ81111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111−i−iiiii−i−i1111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111−i−iiiii−i−i1111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111−i−iiiii−i−i
χ911-1-1i−i1111-1-1-1-1iiii−i−i−i−i1-11-1i−i1-1i−i1-1i−i11-1-1i−i1111-1-1-1-1iiii−i−i−i−i1-11-1i−i1-1i−i1-1i−i11-1-1i−i1111-1-1-1-1iiii−i−i−i−i1-11-1i−i1-1i−i1-1i−i
χ1011-1-1i−i1111-1-1-1-1iiii−i−i−i−i1-11-1i−i-11−ii-11−ii11-1-1i−i1111-1-1-1-1iiii−i−i−i−i1-11-1i−i-11−ii-11−ii11-1-1i−i1111-1-1-1-1iiii−i−i−i−i1-11-1i−i-11−ii-11−ii
χ1111-1-1i−i1111-1-1-1-1iiii−i−i−i−i-11-11−iii−i-11−ii1-111-1-1i−i1111-1-1-1-1iiii−i−i−i−i-11-11−iii−i-11−ii1-111-1-1i−i1111-1-1-1-1iiii−i−i−i−i-11-11−iii−i-11−ii1-1
χ1211-1-1i−i1111-1-1-1-1iiii−i−i−i−i-11-11−ii−ii1-1i−i-1111-1-1i−i1111-1-1-1-1iiii−i−i−i−i-11-11−ii−ii1-1i−i-1111-1-1i−i1111-1-1-1-1iiii−i−i−i−i-11-11−ii−ii1-1i−i-11
χ1311-1-1−ii1111-1-1-1-1−i−i−i−iiiii1-11-1−ii1-1−ii1-1−ii11-1-1−ii1111-1-1-1-1−i−i−i−iiiii1-11-1−ii1-1−ii1-1−ii11-1-1−ii1111-1-1-1-1−i−i−i−iiiii1-11-1−ii1-1−ii1-1−ii
χ1411-1-1−ii1111-1-1-1-1−i−i−i−iiiii1-11-1−ii-11i−i-11i−i11-1-1−ii1111-1-1-1-1−i−i−i−iiiii1-11-1−ii-11i−i-11i−i11-1-1−ii1111-1-1-1-1−i−i−i−iiiii1-11-1−ii-11i−i-11i−i
χ1511-1-1−ii1111-1-1-1-1−i−i−i−iiiii-11-11i−ii−i1-1−ii-1111-1-1−ii1111-1-1-1-1−i−i−i−iiiii-11-11i−ii−i1-1−ii-1111-1-1−ii1111-1-1-1-1−i−i−i−iiiii-11-11i−ii−i1-1−ii-11
χ1611-1-1−ii1111-1-1-1-1−i−i−i−iiiii-11-11i−i−ii-11i−i1-111-1-1−ii1111-1-1-1-1−i−i−i−iiiii-11-11i−i−ii-11i−i1-111-1-1−ii1111-1-1-1-1−i−i−i−iiiii-11-11i−i−ii-11i−i1-1
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χ202-2-220022-2-2-2-22200000000-222-200000000002-2-220022-2-2-2-22200000000-222-200000000002-2-220022-2-2-2-22200000000-222-20000000000
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χ2744-4-4−4i4i1-21-2-12-12−i−i2i2iii−2i−2i0000000000000044-4-4−4i4i1-21-2-12-12−i−i2i2iii−2i−2i0000000000000044-4-4−4i4i1-21-2-12-12−i−i2i2iii−2i−2i00000000000000
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χ294-44-4001-2-121-2-123i−3i003i−3i00000000000000004-44-4001-2-121-2-123i−3i003i−3i00000000000000004-44-4001-2-121-2-123i−3i003i−3i0000000000000000
χ304-44-4001-2-121-2-12−3i3i00−3i3i00000000000000004-44-4001-2-121-2-12−3i3i00−3i3i00000000000000004-44-4001-2-121-2-12−3i3i00−3i3i0000000000000000
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χ354-4-4400-212-12-1-21003-300-33000000000000004-4-4400-212-12-1-21003-300-33000000000000004-4-4400-212-12-1-21003-300-3300000000000000
χ364-4-4400-212-12-1-2100-33003-3000000000000004-4-4400-212-12-1-2100-33003-3000000000000004-4-4400-212-12-1-2100-33003-300000000000000
χ37111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ381111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ391111111111111111111111-1-1-1-1-1-1iiii−i−i−i−i1111111111111111111111-1-1-1-1-1-1iiii−i−i−i−i-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111−i−i−i−iiiii
χ401111111111111111111111-1-1-1-1-1-1−i−i−i−iiiii1111111111111111111111-1-1-1-1-1-1−i−i−i−iiiii-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111iiii−i−i−i−i
χ411111-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-11111-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-111
χ421111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1111111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-111-1-1
χ431111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111ii−i−i−i−iii1111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111ii−i−i−i−iii-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1−i−iiiii−i−i
χ441111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111−i−iiiii−i−i1111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111−i−iiiii−i−i-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1ii−i−i−i−iii
χ4511-1-1i−i1111-1-1-1-1iiii−i−i−i−i1-11-1i−i1-1i−i1-1i−i11-1-1i−i1111-1-1-1-1iiii−i−i−i−i1-11-1i−i1-1i−i1-1i−i-1-111−ii-1-1-1-11111−i−i−i−iiiii-11-11−ii-11−ii-11−ii
χ4611-1-1i−i1111-1-1-1-1iiii−i−i−i−i1-11-1i−i-11−ii-11−ii11-1-1i−i1111-1-1-1-1iiii−i−i−i−i1-11-1i−i-11−ii-11−ii-1-111−ii-1-1-1-11111−i−i−i−iiiii-11-11−ii1-1i−i1-1i−i
χ4711-1-1i−i1111-1-1-1-1iiii−i−i−i−i-11-11−iii−i-11−ii1-111-1-1i−i1111-1-1-1-1iiii−i−i−i−i-11-11−iii−i-11−ii1-1-1-111−ii-1-1-1-11111−i−i−i−iiiii1-11-1i−i−ii1-1i−i-11
χ4811-1-1i−i1111-1-1-1-1iiii−i−i−i−i-11-11−ii−ii1-1i−i-1111-1-1i−i1111-1-1-1-1iiii−i−i−i−i-11-11−ii−ii1-1i−i-11-1-111−ii-1-1-1-11111−i−i−i−iiiii1-11-1i−ii−i-11−ii1-1
χ4911-1-1−ii1111-1-1-1-1−i−i−i−iiiii1-11-1−ii1-1−ii1-1−ii11-1-1−ii1111-1-1-1-1−i−i−i−iiiii1-11-1−ii1-1−ii1-1−ii-1-111i−i-1-1-1-11111iiii−i−i−i−i-11-11i−i-11i−i-11i−i
χ5011-1-1−ii1111-1-1-1-1−i−i−i−iiiii1-11-1−ii-11i−i-11i−i11-1-1−ii1111-1-1-1-1−i−i−i−iiiii1-11-1−ii-11i−i-11i−i-1-111i−i-1-1-1-11111iiii−i−i−i−i-11-11i−i1-1−ii1-1−ii
χ5111-1-1−ii1111-1-1-1-1−i−i−i−iiiii-11-11i−ii−i1-1−ii-1111-1-1−ii1111-1-1-1-1−i−i−i−iiiii-11-11i−ii−i1-1−ii-11-1-111i−i-1-1-1-11111iiii−i−i−i−i1-11-1−ii−ii-11i−i1-1
χ5211-1-1−ii1111-1-1-1-1−i−i−i−iiiii-11-11i−i−ii-11i−i1-111-1-1−ii1111-1-1-1-1−i−i−i−iiiii-11-11i−i−ii-11i−i1-1-1-111i−i-1-1-1-11111iiii−i−i−i−i1-11-1−iii−i1-1−ii-11
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χ574444441-21-21-21-211-2-211-2-2000000000000004444441-21-21-21-211-2-211-2-200000000000000-4-4-4-4-4-4-12-12-12-12-1-122-1-12200000000000000
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χ73222222222222222222222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000000000000000
χ742222222222222222222222222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111000000000000000000000000000000000000
χ752222222222222222222222-2-2-2-2-2-22i2i2i2i−2i−2i−2i−2i-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111−i−i−i−iiiii000000000000000000000000000000000000
χ762222222222222222222222-2-2-2-2-2-2−2i−2i−2i−2i2i2i2i2i-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111iiii−i−i−i−i000000000000000000000000000000000000
χ772222-2-222222222-2-2-2-2-2-2-2-22222-2-222-2-222-2-2-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-111000000000000000000000000000000000000
χ782222-2-222222222-2-2-2-2-2-2-2-22222-2-2-2-222-2-222-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-111-1-1000000000000000000000000000000000000
χ792222-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2222i2i−2i−2i−2i−2i2i2i-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1−i−iiiii−i−i000000000000000000000000000000000000
χ802222-2-222222222-2-2-2-2-2-2-2-2-2-2-2-222−2i−2i2i2i2i2i−2i−2i-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1ii−i−i−i−iii000000000000000000000000000000000000
χ8122-2-22i−2i2222-2-2-2-22i2i2i2i−2i−2i−2i−2i2-22-22i−2i2-22i−2i2-22i−2i-1-111−ii-1-1-1-11111−i−i−i−iiiii-11-11−ii-11−ii-11−ii000000000000000000000000000000000000
χ8222-2-22i−2i2222-2-2-2-22i2i2i2i−2i−2i−2i−2i2-22-22i−2i-22−2i2i-22−2i2i-1-111−ii-1-1-1-11111−i−i−i−iiiii-11-11−ii1-1i−i1-1i−i000000000000000000000000000000000000
χ8322-2-22i−2i2222-2-2-2-22i2i2i2i−2i−2i−2i−2i-22-22−2i2i2i−2i-22−2i2i2-2-1-111−ii-1-1-1-11111−i−i−i−iiiii1-11-1i−i−ii1-1i−i-11000000000000000000000000000000000000
χ8422-2-22i−2i2222-2-2-2-22i2i2i2i−2i−2i−2i−2i-22-22−2i2i−2i2i2-22i−2i-22-1-111−ii-1-1-1-11111−i−i−i−iiiii1-11-1i−ii−i-11−ii1-1000000000000000000000000000000000000
χ8522-2-2−2i2i2222-2-2-2-2−2i−2i−2i−2i2i2i2i2i2-22-2−2i2i2-2−2i2i2-2−2i2i-1-111i−i-1-1-1-11111iiii−i−i−i−i-11-11i−i-11i−i-11i−i000000000000000000000000000000000000
χ8622-2-2−2i2i2222-2-2-2-2−2i−2i−2i−2i2i2i2i2i2-22-2−2i2i-222i−2i-222i−2i-1-111i−i-1-1-1-11111iiii−i−i−i−i-11-11i−i1-1−ii1-1−ii000000000000000000000000000000000000
χ8722-2-2−2i2i2222-2-2-2-2−2i−2i−2i−2i2i2i2i2i-22-222i−2i2i−2i2-2−2i2i-22-1-111i−i-1-1-1-11111iiii−i−i−i−i1-11-1−ii−ii-11i−i1-1000000000000000000000000000000000000
χ8822-2-2−2i2i2222-2-2-2-2−2i−2i−2i−2i2i2i2i2i-22-222i−2i−2i2i-222i−2i2-2-1-111i−i-1-1-1-11111iiii−i−i−i−i1-11-1−iii−i1-1−ii-11000000000000000000000000000000000000
χ894-44-40044-4-444-4-40000000044-4-40000000000-22-2200-2-222-2-22200000000-2-2220000000000000000000000000000000000000000000000
χ904-44-40044-4-444-4-400000000-4-4440000000000-22-2200-2-222-2-2220000000022-2-20000000000000000000000000000000000000000000000
χ914-4-440044-4-4-4-444000000004-4-440000000000-222-200-2-22222-2-200000000-222-20000000000000000000000000000000000000000000000
χ924-4-440044-4-4-4-44400000000-444-40000000000-222-200-2-22222-2-2000000002-2-220000000000000000000000000000000000000000000000
χ938888882-42-42-42-422-4-422-4-400000000000000-4-4-4-4-4-4-12-12-12-12-1-122-1-12200000000000000000000000000000000000000000000000000
χ94888888-42-42-42-42-4-422-4-42200000000000000-4-4-4-4-4-42-12-12-12-122-1-122-1-100000000000000000000000000000000000000000000000000
χ958888-8-82-42-42-42-4-2-244-2-24400000000000000-4-4-4-444-12-12-12-1211-2-211-2-200000000000000000000000000000000000000000000000000
χ968888-8-8-42-42-42-4244-2-244-2-200000000000000-4-4-4-4442-12-12-12-1-2-211-2-21100000000000000000000000000000000000000000000000000
χ9788-8-88i−8i2-42-4-24-242i2i−4i−4i−2i−2i4i4i00000000000000-4-444−4i4i-12-121-21-2−i−i2i2iii−2i−2i00000000000000000000000000000000000000000000000000
χ9888-8-88i−8i-42-424-24-2−4i−4i2i2i4i4i−2i−2i00000000000000-4-444−4i4i2-12-1-21-212i2i−i−i−2i−2iii00000000000000000000000000000000000000000000000000
χ9988-8-8−8i8i2-42-4-24-24−2i−2i4i4i2i2i−4i−4i00000000000000-4-4444i−4i-12-121-21-2ii−2i−2i−i−i2i2i00000000000000000000000000000000000000000000000000
χ10088-8-8−8i8i-42-424-24-24i4i−2i−2i−4i−4i2i2i00000000000000-4-4444i−4i2-12-1-21-21−2i−2iii2i2i−i−i00000000000000000000000000000000000000000000000000
χ1018-88-8002-4-242-4-246i−6i006i−6i0000000000000000-44-4400-121-2-121-2−3i3i00−3i3i0000000000000000000000000000000000000000000000000000
χ1028-88-8002-4-242-4-24−6i6i00−6i6i0000000000000000-44-4400-121-2-121-23i−3i003i−3i0000000000000000000000000000000000000000000000000000
χ1038-88-800-424-2-424-2006i−6i006i−6i00000000000000-44-44002-1-212-1-2100−3i3i00−3i3i00000000000000000000000000000000000000000000000000
χ1048-88-800-424-2-424-200−6i6i00−6i6i00000000000000-44-44002-1-212-1-21003i−3i003i−3i00000000000000000000000000000000000000000000000000
χ1058-8-88002-4-24-242-46-600-660000000000000000-444-400-121-21-2-12-33003-30000000000000000000000000000000000000000000000000000
χ1068-8-88002-4-24-242-4-66006-60000000000000000-444-400-121-21-2-123-300-330000000000000000000000000000000000000000000000000000
χ1078-8-8800-424-24-2-42006-600-6600000000000000-444-4002-1-21-212-100-33003-300000000000000000000000000000000000000000000000000
χ1088-8-8800-424-24-2-4200-66006-600000000000000-444-4002-1-21-212-1003-300-3300000000000000000000000000000000000000000000000000

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