Finite Group Databasebeta

← Group #72277362

Character table — Group #72277362

Order 3840.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106
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order12445102224362020204212121215153030410101020246060606060606624444121212448888224410102224662020204212121230303030410101020246060606060606624444121212448888
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χ4111111-1-11111111-111111111-11111-1-1111111-1-1-1−i−iii-1-1-1−ii−ii−ii111111-1-11111111-111111111-11111-1-1111111-1-1-1−i−iii-1-1-1−ii−ii−ii
χ5111-1111111111-1-11-11-1-11111-11-1-111111-1-1-1-111-111111-1-1-1-111-1-1111-1111111111-1-11-11-1-11111-11-1-111111-1-1-1-111-111111-1-1-1-111-1-1
χ6111-1111111111-1-11-11-1-11111-11-1-111111-1-1-1-111-1-1-1-1-11-1-111-1-111111-1111111111-1-11-11-1-11111-11-1-111111-1-1-1-111-1-1-1-1-11-1-111-1-111
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χ8111-111-1-111111-1-1-1-11-1-1111111-1-11-1-111-1-1-1-1-1-11−i−iii-111i−i−iii−i111-111-1-111111-1-1-1-11-1-1111111-1-11-1-111-1-1-1-1-1-11−i−iii-111i−i−iii−i
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χ83444-4-1-1004444-1110-44-4-4-1-1-1-10-111-100-1-111110000000000000000-4-4-441100-4-4-4-41-1-104-444111101-1-110011-1-1-1-10000000000000000
χ84444-4-1-10044-2-2-1110-4-2221−i1521+i1521−i1521+i1520-111-1001−i1521+i152−1+i152−1−i152−1+i152−1−i1520000000000000000-4-4-441100-4-4221-1-1042-2-2−1+i152−1−i152−1+i152−1−i15201-1-1100−1+i152−1−i1521−i1521+i1521−i1521+i1520000000000000000
χ85444-4-1-10044-2-2-1110-4-2221+i1521−i1521+i1521−i1520-111-1001+i1521−i152−1−i152−1+i152−1−i152−1+i1520000000000000000-4-4-441100-4-4221-1-1042-2-2−1−i152−1+i152−1−i152−1+i15201-1-1100−1−i152−1+i1521+i1521−i1521+i1521−i1520000000000000000
χ8644-40-1-100-44441−5500-400-1-1-1-101−55-10011−555−50000000000000000-4-44011004-4-4-4-15−50040011110-15−5100-1-15−5−550000000000000000
χ8744-40-1-100-444415−500-400-1-1-1-1015−5-100115−5−550000000000000000-4-44011004-4-4-4-1−550040011110-1−55100-1-1−555−50000000000000000
χ8844-40-1-100-44-2-21−55002−2i32i31+i1521−i1521+i1521−i15201−55-100−1−i152−1+i152ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ580000000000000000-4-44011004-422-15−500-22i3−2i3−1−i152−1+i152−1−i152−1+i1520-15−51001+i1521−i152−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ580000000000000000
χ8944-40-1-100-44-2-21−550022i3−2i31−i1521+i1521−i1521+i15201−55-100−1+i152−1−i152−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ460000000000000000-4-44011004-422-15−500-2−2i32i3−1+i152−1−i152−1+i152−1−i1520-15−51001−i1521+i152ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ460000000000000000
χ9044-40-1-100-44-2-215−5002−2i32i31−i1521+i1521−i1521+i152015−5-100−1+i152−1−i152ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ460000000000000000-4-44011004-422-1−5500-22i3−2i3−1+i152−1−i152−1+i152−1−i1520-1−551001−i1521+i152−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ460000000000000000
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χ924-4004-44-400-2200000000-2-22200000000000002-202i−2i2i−2i000000000-4400-44-44002-20000000022-2-20000000000000-220−2i2i−2i2i000000000
χ934-4004-44-400-2200000000-2-22200000000000002-20−2i2i−2i2i000000000-4400-44-44002-20000000022-2-20000000000000-2202i−2i2i−2i000000000
χ944-4004-4-4400-2200000000-2-2220000000000000-2202-2-22000000000-4400-444-4002-20000000022-2-200000000000002-20-222-2000000000
χ954-4004-4-4400-2200000000-2-2220000000000000-220-222-2000000000-4400-444-4002-20000000022-2-200000000000002-202-2-22000000000
χ9666-6066662-200-600-6000000000200-22-20000000000000000000000-6-660-6-6-6-6-22006006000000000-2002-220000000000000000000000
χ9766-6066-6-62-200-6006000000000200-2-220000000000000000000000-6-660-6-666-2200600-6000000000-20022-20000000000000000000000
χ988-8008-88-8002-20000000022-2-20000000000000-2200000000000000-8800-88-8800-2200000000-2-22200000000000002-200000000000000
χ998-8008-8-88002-20000000022-2-200000000000002-200000000000000-8800-888-800-2200000000-2-2220000000000000-2200000000000000
χ10012121212-3-300-4-400-3-3-30-4000000001111000000000000000000000000-12-12-12-12330044003330400000000-1-1-1-1000000000000000000000000
χ101121212-12-3-300-4-400-33304000000001-1-11000000000000000000000000-12-12-1212330044003-3-30-400000000-111-1000000000000000000000000
χ1021212-120-3-3004-4003−35350000000000-15−51000000000000000000000000-12-121203300-4400-335−3500000000001−55-1000000000000000000000000
χ1031212-120-3-3004-400335−350000000000-1−551000000000000000000000000-12-121203300-4400-3−3535000000000015−5-1000000000000000000000000
χ10416-1600-4400004-400000000−1−i15−1+i151+i151−i1500000000000000000000000000000-1616004-40000-44000000001+i151−i15−1−i15−1+i1500000000000000000000000000000
χ10516-1600-4400004-400000000−1+i15−1−i151−i151+i1500000000000000000000000000000-1616004-40000-44000000001−i151+i15−1+i15−1−i1500000000000000000000000000000
χ10616-1600-440000-880000000022-2-200000000000000000000000000000-1616004-400008-800000000-2-22200000000000000000000000000000

Here ζ is a primitive root of unity of order 60 (ζ60 = 1); i = ζ15.