Finite Group Databasebeta

← Group #13088971

Character table — Group #13088971

Order 1440.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size112222222334444466666661212181822444444466888881212121212121224243636224444444668888812121212121212242436365510101010101010151520202020203030303030303060609090
order12233666644366662441212121261224510101515303030302020153030303010202060606060306010205101015153030303020201530303030102020606060603060102022266666644666662441212121261224
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111-11-11111-1-1-1-11111111111111111-11-11111-1-1-1-11111111111111111-11-11111-1-1-1-11111111111111111-11-11111-1-1-1-1
χ3111111111-1-1111111-11-1-1-1-111-1-1111111111-1-1111111-11-1-1-1-111-1-1111111111-1-1111111-11-1-1-1-111-1-1111111111-1-1111111-11-1-1-1-111-1-1
χ4111111111-1-111111-1-1-1-1-1-1-1-1-111111111111-1-111111-1-1-1-1-1-1-1-1-111111111111-1-111111-1-1-1-1-1-1-1-1-111111111111-1-111111-1-1-1-1-1-1-1-1-111
χ511-111-1-111111-11-1-11-1-111-1-11-1-1111-111-1-111111-11-1-11-1-111-1-11-1-1111-111-1-111111-11-1-11-1-111-1-11-1-1111-111-1-111111-11-1-11-1-111-1-11-1-11
χ611-111-1-111111-11-1-1-1-1111-1-1-111-111-111-1-111111-11-1-1-1-1111-1-1-111-111-111-1-111111-11-1-1-1-1111-1-1-111-111-111-1-111111-11-1-1-1-1111-1-1-111-1
χ711-111-1-111-1-11-11-1-111-1-1-1111-11-111-111-1-111-1-11-11-1-111-1-1-1111-11-111-111-1-111-1-11-11-1-111-1-1-1111-11-111-111-1-111-1-11-11-1-111-1-1-1111-11-1
χ811-111-1-111-1-11-11-1-1-111-1-111-11-1111-111-1-111-1-11-11-1-1-111-1-111-11-1111-111-1-111-1-11-11-1-1-111-1-111-11-1111-111-1-111-1-11-11-1-1-111-1-111-11-11
χ92222-122-1200-1-1-1-1-12020000-1-1002222-122-1200-1-1-1-1-12020000-1-1002222-122-1200-1-1-1-1-12020000-1-1002222-122-1200-1-1-1-1-12020000-1-100
χ102222-122-1200-1-1-1-1-1-20-2000011002222-122-1200-1-1-1-1-1-20-2000011002222-122-1200-1-1-1-1-1-20-2000011002222-122-1200-1-1-1-1-1-20-200001100
χ11222-12-1-12-122-12-1-1-1020-1-1-1-10000222-12-1-12-122-12-1-1-1020-1-1-1-10000222-12-1-12-122-12-1-1-1020-1-1-1-10000222-12-1-12-122-12-1-1-1020-1-1-1-10000
χ12222-12-1-12-1-2-2-12-1-1-10-2011110000222-12-1-12-1-2-2-12-1-1-10-2011110000222-12-1-12-1-2-2-12-1-1-10-2011110000222-12-1-12-1-2-2-12-1-1-10-2011110000
χ1322-22-1-2-2-1200-11-11120-20000-110022-22-1-2-2-1200-11-11120-20000-110022-22-1-2-2-1200-11-11120-20000-110022-22-1-2-2-1200-11-11120-20000-1100
χ1422-22-1-2-2-1200-11-111-20200001-10022-22-1-2-2-1200-11-111-20200001-10022-22-1-2-2-1200-11-111-20200001-10022-22-1-2-2-1200-11-111-20200001-100
χ1522-2-12112-122-1-2-1110-20-1-111000022-2-12112-122-1-2-1110-20-1-111000022-2-12112-122-1-2-1110-20-1-111000022-2-12112-122-1-2-1110-20-1-1110000
χ1622-2-12112-1-2-2-1-2-11102011-1-1000022-2-12112-1-2-2-1-2-11102011-1-1000022-2-12112-1-2-2-1-2-11102011-1-1000022-2-12112-1-2-2-1-2-11102011-1-10000
χ172-202200-2-22i−2i20-2000002i−2i0000002-202200-2-22i−2i20-2000002i−2i0000002-202200-2-22i−2i20-2000002i−2i0000002-202200-2-22i−2i20-2000002i−2i000000
χ182-202200-2-2−2i2i20-200000−2i2i0000002-202200-2-2−2i2i20-200000−2i2i0000002-202200-2-2−2i2i20-200000−2i2i0000002-202200-2-2−2i2i20-200000−2i2i000000
χ192-20-12−i3i3-212i−2i-101−i3i3000−ii3−300002-20-12−i3i3-212i−2i-101−i3i3000−ii3−300002-20-12−i3i3-212i−2i-101−i3i3000−ii3−300002-20-12−i3i3-212i−2i-101−i3i3000−ii3−30000
χ202-20-12−i3i3-21−2i2i-101−i3i3000i−i−3300002-20-12−i3i3-21−2i2i-101−i3i3000i−i−3300002-20-12−i3i3-21−2i2i-101−i3i3000i−i−3300002-20-12−i3i3-21−2i2i-101−i3i3000i−i−330000
χ212-20-12i3−i3-212i−2i-101i3−i3000−ii−3300002-20-12i3−i3-212i−2i-101i3−i3000−ii−3300002-20-12i3−i3-212i−2i-101i3−i3000−ii−3300002-20-12i3−i3-212i−2i-101i3−i3000−ii−330000
χ222-20-12i3−i3-21−2i2i-101i3−i3000i−i3−300002-20-12i3−i3-21−2i2i-101i3−i3000i−i3−300002-20-12i3−i3-21−2i2i-101i3−i3000i−i3−300002-20-12i3−i3-21−2i2i-101i3−i3000i−i3−30000
χ23444-2-2-2-2-2-2001-211100000000000444-2-2-2-2-2-2001-211100000000000444-2-2-2-2-2-2001-211100000000000444-2-2-2-2-2-2001-211100000000000
χ2444-4-2-222-2-200121-1-10000000000044-4-2-222-2-200121-1-10000000000044-4-2-222-2-200121-1-10000000000044-4-2-222-2-200121-1-100000000000
χ254-404-2002-400-20200000000000004-404-2002-400-20200000000000004-404-2002-400-20200000000000004-404-2002-400-2020000000000000
χ264-40-2-2−2i32i3220010-1i3−i3000000000004-40-2-2−2i32i3220010-1i3−i3000000000004-40-2-2−2i32i3220010-1i3−i3000000000004-40-2-2−2i32i3220010-1i3−i300000000000
χ274-40-2-22i3−2i3220010-1−i3i3000000000004-40-2-22i3−2i3220010-1−i3i3000000000004-40-2-22i3−2i3220010-1−i3i3000000000004-40-2-22i3−2i3220010-1−i3i300000000000
χ28111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ291111111111111111-11-11111-1-1-1-11111111111111111-11-11111-1-1-1-11111111111111111-11-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-11111
χ30111111111-1-1111111-11-1-1-1-111-1-1111111111-1-1111111-11-1-1-1-111-1-1111111111-1-1111111-11-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11-11111-1-111
χ31111111111-1-111111-1-1-1-1-1-1-1-1-111111111111-1-111111-1-1-1-1-1-1-1-1-111111111111-1-111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-111-1-1-1-1-1111111111-1-1
χ3211-111-1-111111-11-1-11-1-111-1-11-1-1111-111-1-111111-11-1-11-1-111-1-11-1-1111-111-1-111111-11-1-11-1-111-1-11-1-11-1-11-1-111-1-1-1-1-11-111-111-1-111-111-1
χ3311-111-1-111111-11-1-1-1-1111-1-1-111-111-111-1-111111-11-1-1-1-1111-1-1-111-111-111-1-111111-11-1-1-1-1111-1-1-111-1-1-11-1-111-1-1-1-1-11-11111-1-1-1111-1-11
χ3411-111-1-111-1-11-11-1-111-1-1-1111-11-111-111-1-111-1-11-11-1-111-1-1-1111-11-111-111-1-111-1-11-11-1-111-1-1-1111-11-1-1-11-1-111-1-111-11-111-1-1111-1-1-11-11
χ3511-111-1-111-1-11-11-1-1-111-1-111-11-1111-111-1-111-1-11-11-1-1-111-1-111-11-1111-111-1-111-1-11-11-1-1-111-1-111-11-11-1-11-1-111-1-111-11-1111-1-111-1-11-11-1
χ362222-122-1200-1-1-1-1-12020000-1-1002222-122-1200-1-1-1-1-12020000-1-1002222-122-1200-1-1-1-1-12020000-1-100-2-2-2-21-2-21-20011111-20-200001100
χ372222-122-1200-1-1-1-1-1-20-2000011002222-122-1200-1-1-1-1-1-20-2000011002222-122-1200-1-1-1-1-1-20-200001100-2-2-2-21-2-21-200111112020000-1-100
χ38222-12-1-12-122-12-1-1-1020-1-1-1-10000222-12-1-12-122-12-1-1-1020-1-1-1-10000222-12-1-12-122-12-1-1-1020-1-1-1-10000-2-2-21-211-21-2-21-21110-2011110000
χ39222-12-1-12-1-2-2-12-1-1-10-2011110000222-12-1-12-1-2-2-12-1-1-10-2011110000222-12-1-12-1-2-2-12-1-1-10-2011110000-2-2-21-211-21221-2111020-1-1-1-10000
χ4022-22-1-2-2-1200-11-11120-20000-110022-22-1-2-2-1200-11-11120-20000-110022-22-1-2-2-1200-11-11120-20000-1100-2-22-21221-2001-11-1-1-20200001-100
χ4122-22-1-2-2-1200-11-111-20200001-10022-22-1-2-2-1200-11-111-20200001-10022-22-1-2-2-1200-11-111-20200001-100-2-22-21221-2001-11-1-120-20000-1100
χ4222-2-12112-122-1-2-1110-20-1-111000022-2-12112-122-1-2-1110-20-1-111000022-2-12112-122-1-2-1110-20-1-1110000-2-221-2-1-1-21-2-2121-1-102011-1-10000
χ4322-2-12112-1-2-2-1-2-11102011-1-1000022-2-12112-1-2-2-1-2-11102011-1-1000022-2-12112-1-2-2-1-2-11102011-1-10000-2-221-2-1-1-2122121-1-10-20-1-1110000
χ442-202200-2-22i−2i20-2000002i−2i0000002-202200-2-22i−2i20-2000002i−2i0000002-202200-2-22i−2i20-2000002i−2i000000-220-2-20022−2i2i-20200000−2i2i000000
χ452-202200-2-2−2i2i20-200000−2i2i0000002-202200-2-2−2i2i20-200000−2i2i0000002-202200-2-2−2i2i20-200000−2i2i000000-220-2-200222i−2i-202000002i−2i000000
χ462-20-12−i3i3-212i−2i-101−i3i3000−ii3−300002-20-12−i3i3-212i−2i-101−i3i3000−ii3−300002-20-12−i3i3-212i−2i-101−i3i3000−ii3−30000-2201-2i3−i32-1−2i2i10-1i3−i3000i−i−330000
χ472-20-12−i3i3-21−2i2i-101−i3i3000i−i−3300002-20-12−i3i3-21−2i2i-101−i3i3000i−i−3300002-20-12−i3i3-21−2i2i-101−i3i3000i−i−330000-2201-2i3−i32-12i−2i10-1i3−i3000−ii3−30000
χ482-20-12i3−i3-212i−2i-101i3−i3000−ii−3300002-20-12i3−i3-212i−2i-101i3−i3000−ii−3300002-20-12i3−i3-212i−2i-101i3−i3000−ii−330000-2201-2−i3i32-1−2i2i10-1−i3i3000i−i3−30000
χ492-20-12i3−i3-21−2i2i-101i3−i3000i−i3−300002-20-12i3−i3-21−2i2i-101i3−i3000i−i3−300002-20-12i3−i3-21−2i2i-101i3−i3000i−i3−30000-2201-2−i3i32-12i−2i10-1−i3i3000−ii−330000
χ50444-2-2-2-2-2-2001-211100000000000444-2-2-2-2-2-2001-211100000000000444-2-2-2-2-2-2001-211100000000000-4-4-422222200-12-1-1-100000000000
χ5144-4-2-222-2-200121-1-10000000000044-4-2-222-2-200121-1-10000000000044-4-2-222-2-200121-1-100000000000-4-4422-2-22200-1-2-11100000000000
χ524-404-2002-400-20200000000000004-404-2002-400-20200000000000004-404-2002-400-2020000000000000-440-4200-240020-20000000000000
χ534-40-2-2−2i32i3220010-1i3−i3000000000004-40-2-2−2i32i3220010-1i3−i3000000000004-40-2-2−2i32i3220010-1i3−i300000000000-440222i3−2i3-2-200-101−i3i300000000000
χ544-40-2-22i3−2i3220010-1−i3i3000000000004-40-2-22i3−2i3220010-1−i3i3000000000004-40-2-22i3−2i3220010-1−i3i300000000000-44022−2i32i3-2-200-101i3−i300000000000
χ55222222222222222222222222222−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52000000000000000000000000000
χ562222222222222222-22-22222-2-2-2-2−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+521−52−1+521−52−1+52−1+52−1+52−1+521−521−521−521−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−521+52−1−521+52−1−52−1−52−1−52−1−521+521+521+521+52000000000000000000000000000
χ57222222222-2-2222222-22-2-2-2-222-2-2−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+521−521−52−1+52−1+52−1+52−1+52−1+52−1+521−52−1+521−521−521−521−52−1+52−1+521−521−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−521+521+52−1−52−1−52−1−52−1−52−1−52−1−521+52−1−521+521+521+521+52−1−52−1−521+521+52000000000000000000000000000
χ58222222222-2-222222-2-2-2-2-2-2-2-2-222−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+521−521−52−1+52−1+52−1+52−1+52−1+521−521−521−521−521−521−521−521−521−52−1+52−1+52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−521+521+52−1−52−1−52−1−52−1−52−1−521+521+521+521+521+521+521+521+521+52−1−52−1−52000000000000000000000000000
χ5922-222-2-222222-22-2-22-2-222-2-22-2-22−1+52−1+521−52−1+52−1+521−521−52−1+52−1+52−1+52−1+52−1+521−52−1+521−521−52−1+521−521−52−1+52−1+521−521−52−1+521−521−52−1+52−1−52−1−521+52−1−52−1−521+521+52−1−52−1−52−1−52−1−52−1−521+52−1−521+521+52−1−521+521+52−1−52−1−521+521+52−1−521+521+52−1−52000000000000000000000000000
χ6022-222-2-222222-22-2-2-2-2222-2-2-222-2−1+52−1+521−52−1+52−1+521−521−52−1+52−1+52−1+52−1+52−1+521−52−1+521−521−521−521−52−1+52−1+52−1+521−521−521−52−1+52−1+521−52−1−52−1−521+52−1−52−1−521+521+52−1−52−1−52−1−52−1−52−1−521+52−1−521+521+521+521+52−1−52−1−52−1−521+521+521+52−1−52−1−521+52000000000000000000000000000
χ6122-222-2-222-2-22-22-2-222-2-2-2222-22-2−1+52−1+521−52−1+52−1+521−521−52−1+52−1+521−521−52−1+521−52−1+521−521−52−1+52−1+521−521−521−52−1+52−1+52−1+521−52−1+521−52−1−52−1−521+52−1−52−1−521+521+52−1−52−1−521+521+52−1−521+52−1−521+521+52−1−52−1−521+521+521+52−1−52−1−52−1−521+52−1−521+52000000000000000000000000000
χ6222-222-2-222-2-22-22-2-2-222-2-222-22-22−1+52−1+521−52−1+52−1+521−521−52−1+52−1+521−521−52−1+521−52−1+521−521−521−52−1+52−1+521−521−52−1+52−1+521−52−1+521−52−1+52−1−52−1−521+52−1−52−1−521+521+52−1−52−1−521+521+52−1−521+52−1−521+521+521+52−1−52−1−521+521+52−1−52−1−521+52−1−521+52−1−52000000000000000000000000000
χ634444-244-2400-2-2-2-2-24040000-2-200−1+5−1+5−1+5−1+51−52−1+5−1+51−52−1+5001−521−521−521−521−52−1+50−1+500001−521−5200−1−5−1−5−1−5−1−51+52−1−5−1−51+52−1−5001+521+521+521+521+52−1−50−1−500001+521+5200000000000000000000000000000
χ644444-244-2400-2-2-2-2-2-40-400002200−1+5−1+5−1+5−1+51−52−1+5−1+51−52−1+5001−521−521−521−521−521−501−50000−1+52−1+5200−1−5−1−5−1−5−1−51+52−1−5−1−51+52−1−5001+521+521+521+521+521+501+50000−1−52−1−5200000000000000000000000000000
χ65444-24-2-24-244-24-2-2-2040-2-2-2-20000−1+5−1+5−1+51−52−1+51−521−52−1+51−52−1+5−1+51−52−1+51−521−521−520−1+501−521−521−521−520000−1−5−1−5−1−51+52−1−51+521+52−1−51+52−1−5−1−51+52−1−51+521+521+520−1−501+521+521+521+520000000000000000000000000000000
χ66444-24-2-24-2-4-4-24-2-2-20-4022220000−1+5−1+5−1+51−52−1+51−521−52−1+51−521−51−51−52−1+51−521−521−5201−50−1+52−1+52−1+52−1+520000−1−5−1−5−1−51+52−1−51+521+52−1−51+521+51+51+52−1−51+521+521+5201+50−1−52−1−52−1−52−1−520000000000000000000000000000000
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χ1068-808-4004-800-4040000000000000−2−252+250−2−251+500−1−52+25001+50−1−50000000000000−2+252−250−2+251−500−1+52−25001−50−1+50000000000000000000000000000000000000000
χ1078-80-4-4−4i34i3440020-22i3−2i300000000000−2−252+2501+51+52ζ14+2ζ26−2ζ34−2ζ46−2ζ14−2ζ26+2ζ34+2ζ46−1−5−1−500−1−5201+52−ζ14−ζ26+ζ34+ζ46ζ14+ζ26−ζ34−ζ4600000000000−2+252−2501−51−52ζ2−2ζ22+2ζ38−2ζ58−2ζ2+2ζ22−2ζ38+2ζ58−1+5−1+500−1+5201−52−ζ2+ζ22−ζ38+ζ58ζ2−ζ22+ζ38−ζ5800000000000000000000000000000000000000
χ1088-80-4-44i3−4i3440020-2−2i32i300000000000−2−252+2501+51+5−2ζ14−2ζ26+2ζ34+2ζ462ζ14+2ζ26−2ζ34−2ζ46−1−5−1−500−1−5201+52ζ14+ζ26−ζ34−ζ46−ζ14−ζ26+ζ34+ζ4600000000000−2+252−2501−51−5−2ζ2+2ζ22−2ζ38+2ζ582ζ2−2ζ22+2ζ38−2ζ58−1+5−1+500−1+5201−52ζ2−ζ22+ζ38−ζ58−ζ2+ζ22−ζ38+ζ5800000000000000000000000000000000000000

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