Finite Group Databasebeta

← Group #13180964

Character table — Group #13180964

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size112223344444444468888888899121212121212121218181818181818272736363636365454545454112223344444444468888888899121212121212121218181818181818272736363636365454545454
order12346443366121212121223366121212124466661212121228888121222624242424488882264644666612121212122666612121212446666121212122888812122262424242448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-111111-1-1-1-11-1-1-1-1111111111111111111111111111111111111-1-1-1-111111-1-1-1-11-1-1-1-1
χ31111111111111111111111111-1-111111111-1ii−i−i-1-1-1-1-1ii−i−i-1ii−i−i1111111111111111111111111-1-111111111-1ii−i−i-1-1-1-1-1ii−i−i-1ii−i−i
χ41111111111111111111111111-1-111111111-1−i−iii-1-1-1-1-1−i−iii-1−i−iii1111111111111111111111111-1-111111111-1−i−iii-1-1-1-1-1−i−iii-1−i−iii
χ511111-1-1111111111-11111111111-1-1-1-1-1-1-1-11111111-1-111111-1-1-1-1-111111-1-1111111111-11111111111-1-1-1-1-1-1-1-11111111-1-111111-1-1-1-1-1
χ611111-1-1111111111-11111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-11-1-1-1-1-1111111111-1-1111111111-11111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-11-1-1-1-1-11111
χ711111-1-1111111111-111111111-1-1-1-1-1-1-1-1-1-1-1ii−i−i-1-111-1ii−i−i1−i−iii11111-1-1111111111-111111111-1-1-1-1-1-1-1-1-1-1-1ii−i−i-1-111-1ii−i−i1−i−iii
χ811111-1-1111111111-111111111-1-1-1-1-1-1-1-1-1-1-1−i−iii-1-111-1−i−iii1ii−i−i11111-1-1111111111-111111111-1-1-1-1-1-1-1-1-1-1-1−i−iii-1-111-1−i−iii1ii−i−i
χ9111-11111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-11-11-11111-11-11-1-11-11-1111-11111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-11-11-11111-11-11-1-11-11-1
χ10111-11111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-11-111111-1-11-11-1-11-11111-11111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-11-111111-1-11-11-1-11-11
χ11111-11111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111i−i−ii-1-1-1-11i−i−ii1i−i−ii111-11111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111i−i−ii-1-1-1-11i−i−ii1i−i−ii
χ12111-11111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111−iii−i-1-1-1-11−iii−i1−iii−i111-11111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111−iii−i-1-1-1-11−iii−i1−iii−i
χ13111-11-1-11111-1-1-1-1-111111-1-1-1-1111111-1-1-1-1-11-11-111-1-1-11-11-11-11-11111-11-1-11111-1-1-1-1-111111-1-1-1-1111111-1-1-1-1-11-11-111-1-1-11-11-11-11-11
χ14111-11-1-11111-1-1-1-1-111111-1-1-1-1111111-1-1-1-1-1-11-1111-1-1-1-11-1111-11-1111-11-1-11111-1-1-1-1-111111-1-1-1-1111111-1-1-1-1-1-11-1111-1-1-1-11-1111-11-1
χ15111-11-1-11111-1-1-1-1-111111-1-1-1-1-1-11111-1-1-1-11i−i−ii-1-1111i−i−ii-1−iii−i111-11-1-11111-1-1-1-1-111111-1-1-1-1-1-11111-1-1-1-11i−i−ii-1-1111i−i−ii-1−iii−i
χ16111-11-1-11111-1-1-1-1-111111-1-1-1-1-1-11111-1-1-1-11−iii−i-1-1111−iii−i-1i−i−ii111-11-1-11111-1-1-1-1-111111-1-1-1-1-1-11111-1-1-1-11−iii−i-1-1111−iii−i-1i−i−ii
χ1722-12-1002222-122220-1-1-1-1-1-1-1-1220000000022222-1-100-1-1-1-1-10000022-12-1002222-122220-1-1-1-1-1-1-1-1220000000022222-1-100-1-1-1-1-100000
χ1822-12-1002222-122220-1-1-1-1-1-1-1-122000000002-2-2-2-2-1-100-111110000022-12-1002222-122220-1-1-1-1-1-1-1-122000000002-2-2-2-2-1-100-1111100000
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χ2222-1-2-10022221-2-2-2-20-1-1-1-111112200000000-2-22-22-1-10011-11-10000022-1-2-10022221-2-2-2-20-1-1-1-111112200000000-2-22-22-1-10011-11-100000
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χ262-220-22i−2i22-2-200000022-2-20000−2i2i00002i2i−2i−2i00000−2i2i-2200000000002-220-22i−2i22-2-200000022-2-20000−2i2i00002i2i−2i−2i00000−2i2i-220000000000
χ272-220-2−2i2i22-2-200000022-2-200002i−2i0000−2i−2i2i2i000002i−2i-2200000000002-220-2−2i2i22-2-200000022-2-200002i−2i0000−2i−2i2i2i000002i−2i-220000000000
χ282-220-2−2i2i22-2-200000022-2-20000−2i2i0000−2i−2i2i2i00000−2i2i2-200000000002-220-2−2i2i22-2-200000022-2-20000−2i2i0000−2i−2i2i2i00000−2i2i2-20000000000
χ2944444441-21-2411-2-241-21-211-2-20011-2-21-21-2000000000000000000044444441-21-2411-2-241-21-211-2-20011-2-21-21-20000000000000000000
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χ3244444-4-4-21-214-2-211-4-21-21-2-2110022-1-12-12-1000000000000000000044444-4-4-21-214-2-211-4-21-21-2-2110022-1-12-12-10000000000000000000
χ33444-44441-21-2-4-1-122-41-21-2-1-12200-1-1221-21-20000000000000000000444-44441-21-2-4-1-122-41-21-2-1-12200-1-1221-21-20000000000000000000
χ34444-4444-21-21-422-1-1-4-21-2122-1-10022-1-1-21-210000000000000000000444-4444-21-21-422-1-1-4-21-2122-1-10022-1-1-21-210000000000000000000
χ35444-44-4-41-21-2-4-1-12241-21-2-1-1220011-2-2-12-120000000000000000000444-44-4-41-21-2-4-1-12241-21-2-1-1220011-2-2-12-120000000000000000000
χ36444-44-4-4-21-21-422-1-14-21-2122-1-100-2-2112-12-10000000000000000000444-44-4-4-21-21-422-1-14-21-2122-1-100-2-2112-12-10000000000000000000
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χ384-440-44i−4i1-2-120−3i3i0001-2-12−3i3i0000-3300i−2i−i2i00000000000000000004-440-44i−4i1-2-120−3i3i0001-2-12−3i3i0000-3300i−2i−i2i0000000000000000000
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χ404-440-44i−4i-212-1000−3i3i0-212-100−3i3i0000-33−2ii2i−i00000000000000000004-440-44i−4i-212-1000−3i3i0-212-100−3i3i0000-33−2ii2i−i0000000000000000000
χ414-440-4−4i4i1-2-1203i−3i0001-2-123i−3i0000-3300−i2ii−2i00000000000000000004-440-4−4i4i1-2-1203i−3i0001-2-123i−3i0000-3300−i2ii−2i0000000000000000000
χ424-440-4−4i4i1-2-120−3i3i0001-2-12−3i3i00003-300−i2ii−2i00000000000000000004-440-4−4i4i1-2-120−3i3i0001-2-12−3i3i00003-300−i2ii−2i0000000000000000000
χ434-440-4−4i4i-212-10003i−3i0-212-1003i−3i0000-332i−i−2ii00000000000000000004-440-4−4i4i-212-10003i−3i0-212-1003i−3i0000-332i−i−2ii0000000000000000000
χ444-440-4−4i4i-212-1000−3i3i0-212-100−3i3i00003-32i−i−2ii00000000000000000004-440-4−4i4i-212-1000−3i3i0-212-100−3i3i00003-32i−i−2ii0000000000000000000
χ454-4-2020044-4-4000000-2-22200004i−4i0000000000000−2i2i0000000000004-4-2020044-4-4000000-2-22200004i−4i0000000000000−2i2i000000000000
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χ4788-48-4002-42-4-422-4-40-12-12-1-1220000000000000000000000000000088-48-4002-42-4-422-4-40-12-12-1-12200000000000000000000000000000
χ4888-48-400-42-42-4-4-42202-12-122-1-10000000000000000000000000000088-48-400-42-42-4-4-42202-12-122-1-100000000000000000000000000000
χ4988-4-8-4002-42-44-2-2440-12-1211-2-20000000000000000000000000000088-4-8-4002-42-44-2-2440-12-1211-2-200000000000000000000000000000
χ5088-4-8-400-42-42444-2-202-12-1-2-2110000000000000000000000000000088-4-8-400-42-42444-2-202-12-1-2-21100000000000000000000000000000
χ518-8-404002-4-2406i−6i000-121-2−3i3i00000000000000000000000000000008-8-404002-4-2406i−6i000-121-2−3i3i0000000000000000000000000000000
χ528-8-404002-4-240−6i6i000-121-23i−3i00000000000000000000000000000008-8-404002-4-240−6i6i000-121-23i−3i0000000000000000000000000000000
χ538-8-40400-424-20006i−6i02-1-2100−3i3i000000000000000000000000000008-8-40400-424-20006i−6i02-1-2100−3i3i00000000000000000000000000000
χ548-8-40400-424-2000−6i6i02-1-21003i−3i000000000000000000000000000008-8-40400-424-2000−6i6i02-1-21003i−3i00000000000000000000000000000
χ55111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ56111111111111111111111111111111111111-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111-11111
χ571111111111111111111111111-1-111111111-1ii−i−i-1-1-1-1-1ii−i−i-1ii−i−i-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11−i−iii11111−i−iii1−i−iii
χ581111111111111111111111111-1-111111111-1−i−iii-1-1-1-1-1−i−iii-1−i−iii-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11ii−i−i11111ii−i−i1ii−i−i
χ5911111-1-1111111111-11111111111-1-1-1-1-1-1-1-11111111-1-111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-111-1-1-1-1-111111
χ6011111-1-1111111111-11111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-11-1-1-1-1-11111-1-1-1-1-111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-111111111-11111-1-111-111111-1-1-1-1
χ6111111-1-1111111111-111111111-1-1-1-1-1-1-1-1-1-1-1ii−i−i-1-111-1ii−i−i1−i−iii-1-1-1-1-111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111111−i−iii11-1-11−i−iii-1ii−i−i
χ6211111-1-1111111111-111111111-1-1-1-1-1-1-1-1-1-1-1−i−iii-1-111-1−i−iii1ii−i−i-1-1-1-1-111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111111ii−i−i11-1-11ii−i−i-1−i−iii
χ63111-11111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-11-11-11111-11-11-1-11-11-1-1-1-11-1-1-1-1-1-1-1111111-1-1-1-11111-1-11111-1-1-1-11-11-11-1-1-1-11-11-111-11-11
χ64111-11111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-11-111111-1-11-11-1-11-11-1-1-11-1-1-1-1-1-1-1111111-1-1-1-11111-1-11111-1-1-1-111-11-1-1-1-1-111-11-111-11-1
χ65111-11111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111i−i−ii-1-1-1-11i−i−ii1i−i−ii-1-1-11-1-1-1-1-1-1-1111111-1-1-1-11111111111-1-1-1-1-1−iii−i1111-1−iii−i-1−iii−i
χ66111-11111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111−iii−i-1-1-1-11−iii−i1−iii−i-1-1-11-1-1-1-1-1-1-1111111-1-1-1-11111111111-1-1-1-1-1i−i−ii1111-1i−i−ii-1i−i−ii
χ67111-11-1-11111-1-1-1-1-111111-1-1-1-1111111-1-1-1-1-11-11-111-1-1-11-11-11-11-11-1-1-11-111-1-1-1-111111-1-1-1-1-11111-1-1-1-1-1-111111-11-11-1-1111-11-11-11-11-1
χ68111-11-1-11111-1-1-1-1-111111-1-1-1-1111111-1-1-1-1-1-11-1111-1-1-1-11-1111-11-1-1-1-11-111-1-1-1-111111-1-1-1-1-11111-1-1-1-1-1-1111111-11-1-1-11111-11-1-1-11-11
χ69111-11-1-11111-1-1-1-1-111111-1-1-1-1-1-11111-1-1-1-11i−i−ii-1-1111i−i−ii-1−iii−i-1-1-11-111-1-1-1-111111-1-1-1-1-1111111-1-1-1-11111-1−iii−i11-1-1-1−iii−i1i−i−ii
χ70111-11-1-11111-1-1-1-1-111111-1-1-1-1-1-11111-1-1-1-11−iii−i-1-1111−iii−i-1i−i−ii-1-1-11-111-1-1-1-111111-1-1-1-1-1111111-1-1-1-11111-1i−i−ii11-1-1-1i−i−ii1−iii−i
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χ7322-12-1002222-122220-1-1-1-1-1-1-1-1-2-200000000-22i2i−2i−2i11001−i−iii00000-2-21-2100-2-2-2-21-2-2-2-201111111122000000002−2i−2i2i2i-1-100-1ii−i−i00000
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χ7522-1-2-10022221-2-2-2-20-1-1-1-111112200000000-22-22-2-1-1001-11-1100000-2-212100-2-2-2-2-1222201111-1-1-1-1-2-2000000002-22-221100-11-11-100000
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χ7822-1-2-10022221-2-2-2-20-1-1-1-11111-2-2000000002−2i2i2i−2i1100-1i−i−ii00000-2-212100-2-2-2-2-1222201111-1-1-1-12200000000-22i−2i−2i2i-1-1001−iii−i00000
χ792-220-22i−2i22-2-200000022-2-200002i−2i00002i2i−2i−2i000002i−2i2-20000000000-22-202−2i2i-2-222000000-2-2220000−2i2i0000−2i−2i2i2i00000−2i2i-220000000000
χ802-220-22i−2i22-2-200000022-2-20000−2i2i00002i2i−2i−2i00000−2i2i-220000000000-22-202−2i2i-2-222000000-2-22200002i−2i0000−2i−2i2i2i000002i−2i2-20000000000
χ812-220-2−2i2i22-2-200000022-2-200002i−2i0000−2i−2i2i2i000002i−2i-220000000000-22-2022i−2i-2-222000000-2-2220000−2i2i00002i2i−2i−2i00000−2i2i2-20000000000
χ822-220-2−2i2i22-2-200000022-2-20000−2i2i0000−2i−2i2i2i00000−2i2i2-20000000000-22-2022i−2i-2-222000000-2-22200002i−2i00002i2i−2i−2i000002i−2i-220000000000
χ8344444441-21-2411-2-241-21-211-2-20011-2-21-21-20000000000000000000-4-4-4-4-4-4-4-12-12-4-1-122-4-12-12-1-12200-1-122-12-120000000000000000000
χ844444444-21-214-2-2114-21-21-2-21100-2-211-21-210000000000000000000-4-4-4-4-4-4-42-12-1-422-1-1-42-12-122-1-10022-1-12-12-10000000000000000000
χ8544444-4-41-21-2411-2-2-41-21-211-2-200-1-122-12-120000000000000000000-4-4-4-4-444-12-12-4-1-1224-12-12-1-1220011-2-21-21-20000000000000000000
χ8644444-4-4-21-214-2-211-4-21-21-2-2110022-1-12-12-10000000000000000000-4-4-4-4-4442-12-1-422-1-142-12-122-1-100-2-211-21-210000000000000000000
χ87444-44441-21-2-4-1-122-41-21-2-1-12200-1-1221-21-20000000000000000000-4-4-44-4-4-4-12-12411-2-24-12-1211-2-20011-2-2-12-120000000000000000000
χ88444-4444-21-21-422-1-1-4-21-2122-1-10022-1-1-21-210000000000000000000-4-4-44-4-4-42-12-14-2-21142-12-1-2-21100-2-2112-12-10000000000000000000
χ89444-44-4-41-21-2-4-1-12241-21-2-1-1220011-2-2-12-120000000000000000000-4-4-44-444-12-12411-2-2-4-12-1211-2-200-1-1221-21-20000000000000000000
χ90444-44-4-4-21-21-422-1-14-21-2122-1-100-2-2112-12-10000000000000000000-4-4-44-4442-12-14-2-211-42-12-1-2-2110022-1-1-21-210000000000000000000
χ914-440-44i−4i1-2-1203i−3i0001-2-123i−3i00003-300i−2i−i2i0000000000000000000-44-404−4i4i-121-20−3i3i000-121-2−3i3i0000-3300−i2ii−2i0000000000000000000
χ924-440-44i−4i1-2-120−3i3i0001-2-12−3i3i0000-3300i−2i−i2i0000000000000000000-44-404−4i4i-121-203i−3i000-121-23i−3i00003-300−i2ii−2i0000000000000000000
χ934-440-44i−4i-212-10003i−3i0-212-1003i−3i00003-3−2ii2i−i0000000000000000000-44-404−4i4i2-1-21000−3i3i02-1-2100−3i3i0000-332i−i−2ii0000000000000000000
χ944-440-44i−4i-212-1000−3i3i0-212-100−3i3i0000-33−2ii2i−i0000000000000000000-44-404−4i4i2-1-210003i−3i02-1-21003i−3i00003-32i−i−2ii0000000000000000000
χ954-440-4−4i4i1-2-1203i−3i0001-2-123i−3i0000-3300−i2ii−2i0000000000000000000-44-4044i−4i-121-20−3i3i000-121-2−3i3i00003-300i−2i−i2i0000000000000000000
χ964-440-4−4i4i1-2-120−3i3i0001-2-12−3i3i00003-300−i2ii−2i0000000000000000000-44-4044i−4i-121-203i−3i000-121-23i−3i0000-3300i−2i−i2i0000000000000000000
χ974-440-4−4i4i-212-10003i−3i0-212-1003i−3i0000-332i−i−2ii0000000000000000000-44-4044i−4i2-1-21000−3i3i02-1-2100−3i3i00003-3−2ii2i−i0000000000000000000
χ984-440-4−4i4i-212-1000−3i3i0-212-100−3i3i00003-32i−i−2ii0000000000000000000-44-4044i−4i2-1-210003i−3i02-1-21003i−3i0000-33−2ii2i−i0000000000000000000
χ994-4-2020044-4-4000000-2-22200004i−4i0000000000000−2i2i000000000000-4420-200-4-44400000022-2-20000−4i4i00000000000002i−2i000000000000
χ1004-4-2020044-4-4000000-2-2220000−4i4i00000000000002i−2i000000000000-4420-200-4-44400000022-2-200004i−4i0000000000000−2i2i000000000000
χ10188-48-4002-42-4-422-4-40-12-12-1-12200000000000000000000000000000-8-84-8400-24-244-2-24401-21-211-2-200000000000000000000000000000
χ10288-48-400-42-42-4-4-42202-12-122-1-100000000000000000000000000000-8-84-84004-24-2444-2-20-21-21-2-21100000000000000000000000000000
χ10388-4-8-4002-42-44-2-2440-12-1211-2-200000000000000000000000000000-8-848400-24-24-422-4-401-21-2-1-12200000000000000000000000000000
χ10488-4-8-400-42-42444-2-202-12-1-2-21100000000000000000000000000000-8-8484004-24-2-4-4-4220-21-2122-1-100000000000000000000000000000
χ1058-8-404002-4-2406i−6i000-121-2−3i3i0000000000000000000000000000000-8840-400-242-40−6i6i0001-2-123i−3i0000000000000000000000000000000
χ1068-8-404002-4-240−6i6i000-121-23i−3i0000000000000000000000000000000-8840-400-242-406i−6i0001-2-12−3i3i0000000000000000000000000000000
χ1078-8-40400-424-20006i−6i02-1-2100−3i3i00000000000000000000000000000-8840-4004-2-42000−6i6i0-212-1003i−3i00000000000000000000000000000
χ1088-8-40400-424-2000−6i6i02-1-21003i−3i00000000000000000000000000000-8840-4004-2-420006i−6i0-212-100−3i3i00000000000000000000000000000

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