Finite Group Databasebeta

← Group #13088716

Character table — Group #13088716

Order 1440.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1122222223344444444444444444556666688888888888810101010101010121212121212121212121212151520202020203030303030303030306060606090909090
order122336666443566661010101515303030303030444121212121515153030303030303030304121212121212202020206060606060606060221212121212266668888242424248888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-111111111111111111-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−iii−i−i
χ41111111111111111111111111111-1-111111111111111111-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii−i−iii
χ5111111111-1-11111111111111111111-1-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-111111111-1-1-1-1
χ6111111111-1-11111111111111111111-1-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ7111111111-1-111111111111111111-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111111ii−i−iii−i−i−i−iii
χ8111111111-1-111111111111111111-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111111−i−iii−i−iiiii−i−i
χ911-111-1-1111111-1-1-11-1-1111-1-1-1-11111-111-1-1111111-1-1-1-1-1-1-111-1-11111-1-11111-1-1-1-111-111-1-1-111-1-11-11-11-11-11-11-1
χ1011-111-1-1111111-1-1-11-1-1111-1-1-1-11111-111-1-1111111-1-1-1-1-1-1-111-1-11111-1-11111-1-1-1-111-111-1-1-111-1-1-11-11-11-11-11-11
χ1111-111-1-1111111-1-1-11-1-1111-1-1-1-111-1-1-111-1-1111111-1-1-1-1-1-11-1-111-1-111-1-11111-1-1-1-1-1-11-1-1111-1-111i−i−iii−i−iii−i−ii
χ1211-111-1-1111111-1-1-11-1-1111-1-1-1-111-1-1-111-1-1111111-1-1-1-1-1-11-1-111-1-111-1-11111-1-1-1-1-1-11-1-1111-1-111−iii−i−iii−i−iii−i
χ1311-111-1-111-1-111-1-1-11-1-1111-1-1-1-111111-1-111111111-1-1-1-1-1-1-111-1-111-1-111-1-1-1-11111-1-1-111-1-11-1-1111-11-11-11-1-11-11
χ1411-111-1-111-1-111-1-1-11-1-1111-1-1-1-111111-1-111111111-1-1-1-1-1-1-111-1-111-1-111-1-1-1-11111-1-1-111-1-11-1-111-11-11-11-111-11-1
χ1511-111-1-111-1-111-1-1-11-1-1111-1-1-1-111-1-11-1-111111111-1-1-1-1-1-11-1-111-1-1-1-111-1-1-1-11111111-1-111-111-1-1i−i−iii−i−ii−iii−i
χ1611-111-1-111-1-111-1-1-11-1-1111-1-1-1-111-1-11-1-111111111-1-1-1-1-1-11-1-111-1-1-1-111-1-1-1-11111111-1-111-111-1-1−iii−i−iii−ii−i−ii
χ172222-1-1-12-122-122-1-1-1222-1-1-1-1-1-1-1-1222-1-1-1-12-1-12-1-122-1-1-1-12-1-1-1-1222222-1-1-1-1-1-1-1-1222-1-1-1-12-1-1-1-1000000000000
χ182222-1-1-12-122-122-1-1-1222-1-1-1-1-1-1-1-1-2-22-1-1-1-12-1-12-1-122-1-1-1-1-21111-2-22222-1-1-1-1-1-1-1-1-2-2-21111-21111000000000000
χ192222-1-1-12-1-2-2-122-1-1-1222-1-1-1-1-1-1-1-122-211112-1-12-1-122-1-1-1-12-1-1-1-122-2-2-2-211111111-2-22-1-1-1-1-21111000000000000
χ202222-1-1-12-1-2-2-122-1-1-1222-1-1-1-1-1-1-1-1-2-2-211112-1-12-1-122-1-1-1-1-21111-2-2-2-2-2-21111111122-211112-1-1-1-1000000000000
χ21222-1222-1200-12-1-1-1-1222222222222200000-1-1-1-1-1-1-1-1-1-1-1-122222-1-100000000000000-1-1-1-1-1000002222-1-1-1-10000
χ22222-1222-1200-12-1-1-1-1222222222222200000-1-1-1-1-1-1-1-1-1-1-1-122222-1-100000000000000-1-1-1-1-100000-2-2-2-211110000
χ23222-1222-1200-12-1-1-1-122222222222-2-200000-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2110000000000000011111000002i2i−2i−2i−i−iii0000
χ24222-1222-1200-12-1-1-1-122222222222-2-200000-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-211000000000000001111100000−2i−2i2i2iii−i−i0000
χ2522-22-1112-122-12-211-1-2-22-1-11111-1-122-2-1-1112-1-12-1-1-2-21111-2-1-1112222-2-2-1-1-1-1111122-2-1-111-2-1-111000000000000
χ2622-22-1112-122-12-211-1-2-22-1-11111-1-1-2-2-2-1-1112-1-12-1-1-2-21111211-1-1-2-222-2-2-1-1-1-11111-2-2211-1-1211-1-1000000000000
χ2722-22-1112-1-2-2-12-211-1-2-22-1-11111-1-122211-1-12-1-12-1-1-2-21111-2-1-11122-2-2221111-1-1-1-1-2-2-2-1-111211-1-1000000000000
χ2822-22-1112-1-2-2-12-211-1-2-22-1-11111-1-1-2-2211-1-12-1-12-1-1-2-21111211-1-1-2-2-2-2221111-1-1-1-122211-1-1-2-1-111000000000000
χ2922-2-12-2-2-1200-12111-1-2-2222-2-2-2-2222200000-1-1-1-1-1-1111111-222-2-2-1-1000000000000001-1-111000002-22-2-11-110000
χ3022-2-12-2-2-1200-12111-1-2-2222-2-2-2-2222200000-1-1-1-1-1-1111111-222-2-2-1-1000000000000001-1-11100000-22-221-11-10000
χ3122-2-12-2-2-1200-12111-1-2-2222-2-2-2-222-2-200000-1-1-1-1-1-11111112-2-2221100000000000000-111-1-1000002i−2i−2i2i−iii−i0000
χ3222-2-12-2-2-1200-12111-1-2-2222-2-2-2-222-2-200000-1-1-1-1-1-11111112-2-2221100000000000000-111-1-100000−2i2i2i−2ii−i−ii0000
χ332-202200-2-22i−2i22000-200-2220000-2-22i−2i02i−2i00222-2-2-200000002i−2i002i−2i2i−2i002i2i−2i−2i00002-202i−2i0002-200000000000000
χ342-202200-2-22i−2i22000-200-2220000-2-2−2i2i02i−2i00222-2-2-20000000−2i2i00−2i2i2i−2i002i2i−2i−2i0000-220−2i2i000-2200000000000000
χ352-202200-2-2−2i2i22000-200-2220000-2-22i−2i0−2i2i00222-2-2-200000002i−2i002i−2i−2i2i00−2i−2i2i2i0000-2202i−2i000-2200000000000000
χ362-202200-2-2−2i2i22000-200-2220000-2-2−2i2i0−2i2i00222-2-2-20000000−2i2i00−2i2i−2i2i00−2i−2i2i2i00002-20−2i2i0002-200000000000000
χ372-202-1−i3i3-212i−2i-120−i3i3100-2-1-1−i3−i3i3i3112i−2i0−ii3−32-1-1-21100−i3−i3i3i30−ii3−32i−2i2i−2i00−i−iii33−3−32-20−ii3−30-11−i3i3000000000000
χ382-202-1−i3i3-212i−2i-120−i3i3100-2-1-1−i3−i3i3i311−2i2i0−ii3−32-1-1-21100−i3−i3i3i30i−i−33−2i2i2i−2i00−i−iii33−3−3-220i−i−3301-1i3−i3000000000000
χ392-202-1−i3i3-21−2i2i-120−i3i3100-2-1-1−i3−i3i3i3112i−2i0i−i−332-1-1-21100−i3−i3i3i30−ii3−32i−2i−2i2i00ii−i−i−3−333-220−ii3−301-1i3−i3000000000000
χ402-202-1−i3i3-21−2i2i-120−i3i3100-2-1-1−i3−i3i3i311−2i2i0i−i−332-1-1-21100−i3−i3i3i30i−i−33−2i2i−2i2i00ii−i−i−3−3332-20i−i−330-11−i3i3000000000000
χ412-202-1i3−i3-212i−2i-120i3−i3100-2-1-1i3i3−i3−i3112i−2i0−ii−332-1-1-21100i3i3−i3−i30−ii−332i−2i2i−2i00−i−iii−3−3332-20−ii−330-11i3−i3000000000000
χ422-202-1i3−i3-212i−2i-120i3−i3100-2-1-1i3i3−i3−i311−2i2i0−ii−332-1-1-21100i3i3−i3−i30i−i3−3−2i2i2i−2i00−i−iii−3−333-220i−i3−301-1−i3i3000000000000
χ432-202-1i3−i3-21−2i2i-120i3−i3100-2-1-1i3i3−i3−i3112i−2i0i−i3−32-1-1-21100i3i3−i3−i30−ii−332i−2i−2i2i00ii−i−i33−3−3-220−ii−3301-1−i3i3000000000000
χ442-202-1i3−i3-21−2i2i-120i3−i3100-2-1-1i3i3−i3−i311−2i2i0i−i3−32-1-1-21100i3i3−i3−i30i−i3−3−2i2i−2i2i00ii−i−i33−3−32-20i−i3−30-11i3−i3000000000000
χ45444444444444-14444-1-1-1-1-1-1-1-1-1-1-10044444-1-1-1-1-1-1-1-1-1-1-1-10000000-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000
χ46444444444-4-44-14444-1-1-1-1-1-1-1-1-1-1-100-4-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-10000000111111111111000000000000000000000000
χ474444-2-2-24-244-2-14-2-2-2-1-1-11−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i152004-2-2-2-2-11−i1521+i152-11−i1521+i152-1-11−i1521+i1521−i1521+i1520000000-1-1-1-11−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i152000000000000000000000000
χ484444-2-2-24-244-2-14-2-2-2-1-1-11+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i152004-2-2-2-2-11+i1521−i152-11+i1521−i152-1-11+i1521−i1521+i1521−i1520000000-1-1-1-11+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i152000000000000000000000000
χ494444-2-2-24-2-4-4-2-14-2-2-2-1-1-11−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i15200-42222-11−i1521+i152-11−i1521+i152-1-11−i1521+i1521−i1521+i15200000001111−1+i152−1−i152−1+i152−1−i152−1+i152−1−i152−1+i152−1−i152000000000000000000000000
χ504444-2-2-24-2-4-4-2-14-2-2-2-1-1-11+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i15200-42222-11+i1521−i152-11+i1521−i152-1-11+i1521−i1521+i1521−i15200000001111−1−i152−1+i152−1−i152−1+i152−1−i152−1+i152−1−i152−1+i152000000000000000000000000
χ51444-2-2-2-2-2-20014-2111444-2-2-2-2-2-2-2-24400000-211-211-2-211114-2-2-2-2-2-200000000000000-2111100000000000000000
χ52444-2-2-2-2-2-20014-2111444-2-2-2-2-2-2-2-2-4-400000-211-211-2-21111-4222222000000000000002-1-1-1-100000000000000000
χ5344-444-4-444444-1-4-4-4411-1-1-11111-1-100-444-4-4-1-1-1-1-1-11111110000000-1-111-1-1-1-11111000000000000000000000000
χ5444-444-4-444-4-44-1-4-4-4411-1-1-11111-1-1004-4-444-1-1-1-1-1-1111111000000011-1-11111-1-1-1-1000000000000000000000000
χ5544-44-2224-244-2-1-422-211-11−i1521+i152−1+i152−1−i152−1+i152−1−i1521−i1521+i15200-4-2-222-11−i1521+i152-11−i1521+i15211−1+i152−1−i152−1+i152−1−i1520000000-1-1111−i1521+i1521−i1521+i152−1+i152−1−i152−1+i152−1−i152000000000000000000000000
χ5644-44-2224-244-2-1-422-211-11+i1521−i152−1−i152−1+i152−1−i152−1+i1521+i1521−i15200-4-2-222-11+i1521−i152-11+i1521−i15211−1−i152−1+i152−1−i152−1+i1520000000-1-1111+i1521−i1521+i1521−i152−1−i152−1+i152−1−i152−1+i152000000000000000000000000
χ5744-44-2224-2-4-4-2-1-422-211-11−i1521+i152−1+i152−1−i152−1+i152−1−i1521−i1521+i15200422-2-2-11−i1521+i152-11−i1521+i15211−1+i152−1−i152−1+i152−1−i152000000011-1-1−1+i152−1−i152−1+i152−1−i1521−i1521+i1521−i1521+i152000000000000000000000000
χ5844-44-2224-2-4-4-2-1-422-211-11+i1521−i152−1−i152−1+i152−1−i152−1+i1521+i1521−i15200422-2-2-11+i1521−i152-11+i1521−i15211−1−i152−1+i152−1−i152−1+i152000000011-1-1−1−i152−1+i152−1−i152−1+i1521+i1521−i1521+i1521−i152000000000000000000000000
χ5944-4-2-222-2-200142-1-11-4-44-2-22222-2-24400000-211-21122-1-1-1-1-4-2-222-2-200000000000000211-1-100000000000000000
χ6044-4-2-222-2-200142-1-11-4-44-2-22222-2-2-4-400000-211-21122-1-1-1-1422-2-22200000000000000-2-1-11100000000000000000
χ614-404400-4-44i−4i4-1000-4−551-1-1−555−5110004i−4i00-1-1-1111−55−555−50000000−ii−i5i5−i−iii−i5i5i5−i5000000000000000000000000
χ624-404400-4-44i−4i4-1000-45−51-1-15−5−55110004i−4i00-1-1-11115−55−5−550000000−iii5−i5−i−iiii5−i5−i5i5000000000000000000000000
χ634-404400-4-4−4i4i4-1000-4−551-1-1−555−511000−4i4i00-1-1-1111−55−555−50000000i−ii5−i5ii−i−ii5−i5−i5i5000000000000000000000000
χ644-404400-4-4−4i4i4-1000-45−51-1-15−5−5511000−4i4i00-1-1-11115−55−5−550000000i−i−i5i5ii−i−i−i5i5i5−i5000000000000000000000000
χ654-404-2−2i32i3-424i−4i-2-10−2i32i32−5511+i1521−i152ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58−1−i152−1+i152000−2i2i23−23-11+i1521−i1521−1−i152−1+i152−55ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ580000000−ii−i5i5ζ19+ζ23+ζ31+ζ47ζ7+ζ11+ζ43+ζ59−ζ19−ζ23−ζ31−ζ47−ζ7−ζ11−ζ43−ζ59ζ19−ζ23+ζ31−ζ47ζ7−ζ11+ζ43−ζ59−ζ19+ζ23−ζ31+ζ47−ζ7+ζ11−ζ43+ζ59000000000000000000000000
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χ684-404-2−2i32i3-42−4i4i-2-10−2i32i325−511−i1521+i152ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46−1+i152−1−i1520002i−2i−2323-11−i1521+i1521−1+i152−1−i1525−5ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ460000000i−i−i5i5−ζ7−ζ11−ζ43−ζ59−ζ19−ζ23−ζ31−ζ47ζ7+ζ11+ζ43+ζ59ζ19+ζ23+ζ31+ζ47−ζ7+ζ11−ζ43+ζ59−ζ19+ζ23−ζ31+ζ47ζ7−ζ11+ζ43−ζ59ζ19−ζ23+ζ31−ζ47000000000000000000000000
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χ734-40-24002-400-24000200-4440000-4-44i−4i00000-2-2-222200000004i−4i00−2i2i000000000000000−2i2i0000000000000000000
χ744-40-24002-400-24000200-4440000-4-4−4i4i00000-2-2-22220000000−4i4i002i−2i0000000000000002i−2i0000000000000000000
χ754-40-2-2−2i32i32200140i3−i3-100-4-2-2−2i3−2i32i32i3224i−4i00000-2112-1-100i3i3−i3−i30−2i2i23−23−2i2i000000000000000i−i−3300000000000000000
χ764-40-2-2−2i32i32200140i3−i3-100-4-2-2−2i3−2i32i32i322−4i4i00000-2112-1-100i3i3−i3−i302i−2i−23232i−2i000000000000000−ii3−300000000000000000
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χ784-40-2-22i3−2i32200140−i3i3-100-4-2-22i32i3−2i3−2i322−4i4i00000-2112-1-100−i3−i3i3i302i−2i23−232i−2i000000000000000−ii−3300000000000000000
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χ80888-4-4-4-4-4-4002-2-4222-2-2-21−i151+i151−i151+i151−i151+i151−i151+i1500000001−1+i152−1−i1521−1+i152−1−i15211−1+i152−1−i152−1+i152−1−i1520000000000000000000000000000000000000000000
χ81888-4-4-4-4-4-4002-2-4222-2-2-21+i151−i151+i151−i151+i151−i151+i151−i1500000001−1−i152−1+i1521−1−i152−1+i15211−1−i152−1+i152−1−i152−1+i1520000000000000000000000000000000000000000000
χ8288-8-48-8-8-4800-4-2444-422-2-2-22222-2-20000000111111-1-1-1-1-1-10000000000000000000000000000000000000000000
χ8388-8-4-444-4-4002-24-2-2222-21−i151+i15−1+i15−1−i15−1+i15−1−i151−i151+i1500000001−1+i152−1−i1521−1+i152−1−i152-1-11−i1521+i1521−i1521+i1520000000000000000000000000000000000000000000
χ8488-8-4-444-4-4002-24-2-2222-21+i151−i15−1−i15−1+i15−1−i15−1+i151+i151−i1500000001−1−i152−1+i1521−1−i152−1+i152-1-11+i1521−i1521+i1521−i1520000000000000000000000000000000000000000000
χ858-80-48004-800-4-20004−25252-2-2−252525−25220000000111-1-1-15−55−5−550000000000000000000000000000000000000000000
χ868-80-48004-800-4-2000425−252-2-225−25−2525220000000111-1-1-1−55−555−50000000000000000000000000000000000000000000
χ878-80-4-4−4i34i344002-202i3−2i3-2−252521+i151−i152ζ2−2ζ34+2ζ38−2ζ462ζ14−2ζ22+2ζ26−2ζ58−2ζ2+2ζ34−2ζ38+2ζ46−2ζ14+2ζ22−2ζ26+2ζ58−1−i15−1+i1500000001−1−i152−1+i152-11+i1521−i1525−5−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ580000000000000000000000000000000000000000000
χ888-80-4-4−4i34i344002-202i3−2i3-225−2521−i151+i152ζ14−2ζ22+2ζ26−2ζ582ζ2−2ζ34+2ζ38−2ζ46−2ζ14+2ζ22−2ζ26+2ζ58−2ζ2+2ζ34−2ζ38+2ζ46−1+i15−1−i1500000001−1+i152−1−i152-11−i1521+i152−55−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ460000000000000000000000000000000000000000000
χ898-80-4-44i3−4i344002-20−2i32i3-2−252521−i151+i15−2ζ14+2ζ22−2ζ26+2ζ58−2ζ2+2ζ34−2ζ38+2ζ462ζ14−2ζ22+2ζ26−2ζ582ζ2−2ζ34+2ζ38−2ζ46−1+i15−1−i1500000001−1+i152−1−i152-11−i1521+i1525−5ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ460000000000000000000000000000000000000000000
χ908-80-4-44i3−4i344002-20−2i32i3-225−2521+i151−i15−2ζ2+2ζ34−2ζ38+2ζ46−2ζ14+2ζ22−2ζ26+2ζ582ζ2−2ζ34+2ζ38−2ζ462ζ14−2ζ22+2ζ26−2ζ58−1−i15−1+i1500000001−1−i152−1+i152-11+i1521−i152−55ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ580000000000000000000000000000000000000000000

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