Finite Group Databasebeta

← Group #14276910

Character table — Group #14276910

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size1111222222222222444444444444444444444444444448888888888888888888888888888888888888888881010101010102020202020202020204040404040406060606060606060120120120120
order122222344666666645101010101010101212121215153030303030303030303030303030441212121220202020202020202020202060606060606060606060606060606060606060606060606022444426666121212124412121212444444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iii−i−i
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−iii
χ5111111111111111111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-111111111-1-1-1-1
χ6111111111111111111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ7111111111111111111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111iiii−i−i−i−i−i−iii
χ8111111111111111111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111−i−i−i−iiiiiii−i−i
χ91111-1-111111-1-1-1-11-1111-1-11-1-111-1-1111111-1-1-1-111-1-1-1-1i−iii−i−i11-1-1iiii−i−i−i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-111-1-111-1-1i−iii−i−i11-1-111-1-1i−ii−i
χ101111-1-111111-1-1-1-11-1111-1-11-1-111-1-1111111-1-1-1-111-1-1-1-1i−iii−i−i11-1-1iiii−i−i−i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-111-1-111-1-1i−iii−i−i-1-111-1-111−ii−ii
χ111111-1-111111-1-1-1-11-1111-1-11-1-111-1-1111111-1-1-1-111-1-1-1-1i−iii−i−i11-1-1iiii−i−i−i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1111-1-111-1-111−ii−i−iiiii−i−i−i−iii-111-1
χ121111-1-111111-1-1-1-11-1111-1-11-1-111-1-1111111-1-1-1-111-1-1-1-1i−iii−i−i11-1-1iiii−i−i−i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1111-1-111-1-111−ii−i−iii−i−iiiii−i−i1-1-11
χ131111-1-111111-1-1-1-11-1111-1-11-1-111-1-1111111-1-1-1-111-1-1-1-1−ii−i−iii11-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-111-1-111-1-1−ii−i−iii11-1-111-1-1−ii−ii
χ141111-1-111111-1-1-1-11-1111-1-11-1-111-1-1111111-1-1-1-111-1-1-1-1−ii−i−iii11-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-111-1-111-1-1−ii−i−iii-1-111-1-111i−ii−i
χ151111-1-111111-1-1-1-11-1111-1-11-1-111-1-1111111-1-1-1-111-1-1-1-1−ii−i−iii11-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1111-1-111-1-111i−iii−i−iii−i−i−i−iii1-1-11
χ161111-1-111111-1-1-1-11-1111-1-11-1-111-1-1111111-1-1-1-111-1-1-1-1−ii−i−iii11-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1111-1-111-1-111i−iii−i−i−i−iiiii−i−i-111-1
χ172222222-2-22222222-222222222-2-2-2-22222222222222222000000-2-2-2-200000000-2-2-2-2-2-2-2-2000000000000000022-2-2-2-222222-2-2-2-2000000000000000000
χ182222222-2-22222222-222222222-2-2-2-22222222222222222000000-2-2-2-200000000-2-2-2-2-2-2-2-20000000000000000-2-22222-2-2-2-2-22222000000000000000000
χ19222222-122-1-1-1-1-1-1-1222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-122-1-1-1-1000000000000
χ20222222-122-1-1-1-1-1-1-1222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-211111111-2-21111000000000000
χ21222222-122-1-1-1-1-1-1-1222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-211112222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111112222222-1-1-1-1-1-1-1-1-2-21111000000000000
χ22222222-122-1-1-1-1-1-1-1222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-211112222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2-2-2-2-2-21111111122-1-1-1-1000000000000
χ23222222-1-2-2-1-1-1-1-1-1-1-2222222221111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100−i3i3−i3i3-2-2-2-20000000011111111−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i322-2-2-2-22-1-1-1-1111100−i3i3−i3i3000000000000
χ24222222-1-2-2-1-1-1-1-1-1-1-2222222221111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100−i3i3−i3i3-2-2-2-20000000011111111−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3-2-22222-21111-1-1-1-100i3−i3i3−i3000000000000
χ25222222-1-2-2-1-1-1-1-1-1-1-2222222221111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100i3−i3i3−i3-2-2-2-20000000011111111i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i322-2-2-2-22-1-1-1-1111100i3−i3i3−i3000000000000
χ26222222-1-2-2-1-1-1-1-1-1-1-2222222221111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100i3−i3i3−i3-2-2-2-20000000011111111i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3-2-22222-21111-1-1-1-100−i3i3−i3i3000000000000
χ272222-2-22-2-222-2-2-2-222222-2-22-2-2-2-222222222-2-2-2-222-2-2-2-2000000-2-22200000000-2-2-2-22222000000000000000022-2-222-222-2-2-2-222000000000000000000
χ282222-2-22-2-222-2-2-2-222222-2-22-2-2-2-222222222-2-2-2-222-2-2-2-2000000-2-22200000000-2-2-2-222220000000000000000-2-222-2-22-2-22222-2-2000000000000000000
χ292222-2-2-122-1-11111-1-2222-2-22-2-2-1-111-1-1-1-1-1-11111-1-111112i−2i−i−iii22-2-22i2i2i2i−2i−2i−2i−2i-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii2222-2-2-2-1-111-1-1112i−2i−i−iii000000000000
χ302222-2-2-122-1-11111-1-2222-2-22-2-2-1-111-1-1-1-1-1-11111-1-111112i−2i−i−iii22-2-22i2i2i2i−2i−2i−2i−2i-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii-2-2-2-222211-1-111-1-1−2i2iii−i−i000000000000
χ312222-2-2-122-1-11111-1-2222-2-22-2-2-1-111-1-1-1-1-1-11111-1-11111−2i2iii−i−i22-2-2−2i−2i−2i−2i2i2i2i2i-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i2222-2-2-2-1-111-1-111−2i2iii−i−i000000000000
χ322222-2-2-122-1-11111-1-2222-2-22-2-2-1-111-1-1-1-1-1-11111-1-11111−2i2iii−i−i22-2-2−2i−2i−2i−2i2i2i2i2i-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i-2-2-2-222211-1-111-1-12i−2i−i−iii000000000000
χ332222-2-2-1-2-2-1-11111-12222-2-22-2-211-1-1-1-1-1-1-1-11111-1-11111003−3−33-2-222000000001111-1-1-1-13333−3−3−3−3−3−3−3−3333322-2-222-2-1-11111-1-1003−3−33000000000000
χ342222-2-2-1-2-2-1-11111-12222-2-22-2-211-1-1-1-1-1-1-1-11111-1-11111003−3−33-2-222000000001111-1-1-1-13333−3−3−3−3−3−3−3−33333-2-222-2-2211-1-1-1-11100−333−3000000000000
χ352222-2-2-1-2-2-1-11111-12222-2-22-2-211-1-1-1-1-1-1-1-11111-1-1111100−333−3-2-222000000001111-1-1-1-1−3−3−3−333333333−3−3−3−322-2-222-2-1-11111-1-100−333−3000000000000
χ362222-2-2-1-2-2-1-11111-12222-2-22-2-211-1-1-1-1-1-1-1-11111-1-1111100−333−3-2-222000000001111-1-1-1-1−3−3−3−333333333−3−3−3−3-2-222-2-2211-1-1-1-111003−3−33000000000000
χ3722-2-22-22002-222-2-2-2022-2-2-2-22200002222-2-2-2-2-2-2-2-22222000000000000000000000000000000000000000000002i−2i2i−2i000002i−2i2i−2i0000001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000
χ3822-2-22-22002-222-2-2-2022-2-2-2-22200002222-2-2-2-2-2-2-2-22222000000000000000000000000000000000000000000002i−2i2i−2i000002i−2i2i−2i000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000
χ3922-2-22-22002-222-2-2-2022-2-2-2-22200002222-2-2-2-2-2-2-2-2222200000000000000000000000000000000000000000000−2i2i−2i2i00000−2i2i−2i2i0000001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000
χ4022-2-22-22002-222-2-2-2022-2-2-2-22200002222-2-2-2-2-2-2-2-2222200000000000000000000000000000000000000000000−2i2i−2i2i00000−2i2i−2i2i000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000
χ4122-2-2-222002-2-2-222-2022-222-2-2-200002222-2-22222-2-2-2-2-2-2000000000000000000000000000000000000000000002i−2i−2i2i000002i−2i−2i2i0000001+i−1−i−1−i1+i1−i−1+i−1+i1−i0000
χ4222-2-2-222002-2-2-222-2022-222-2-2-200002222-2-22222-2-2-2-2-2-2000000000000000000000000000000000000000000002i−2i−2i2i000002i−2i−2i2i000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i0000
χ4322-2-2-222002-2-2-222-2022-222-2-2-200002222-2-22222-2-2-2-2-2-200000000000000000000000000000000000000000000−2i2i2i−2i00000−2i2i2i−2i0000001−i−1+i−1+i1−i1+i−1−i−1−i1+i0000
χ4422-2-2-222002-2-2-222-2022-222-2-2-200002222-2-22222-2-2-2-2-2-200000000000000000000000000000000000000000000−2i2i2i−2i00000−2i2i2i−2i000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i0000
χ4544444444444444444-1-1-1-1-1-1-1-14444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1444444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000000000000
χ4644444444444444444-1-1-1-1-1-1-1-14444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-4-4-4-4-4-4-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111000000000000000000000000000000000
χ474444444-4-44444444-4-1-1-1-1-1-1-1-1-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000001111−5−555−5−55511111111−5−555−5−555−5−555−5−555000000000000000000000000000000000
χ484444444-4-44444444-4-1-1-1-1-1-1-1-1-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000111155−5−555−5−51111111155−5−555−5−555−5−555−5−5000000000000000000000000000000000
χ49444444-244-2-2-2-2-2-2-24-1-1-1-1-1-1-1-1-2-2-2-21−i1521+i1521−i1521+i1521−i1521+i1521−i1521−i1521+i1521+i1521−i1521+i1521−i1521−i1521+i1521+i15244-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11−i1521−i1521+i1521+i1521−i1521−i1521+i1521+i1521−i1521−i1521+i1521+i1521+i1521+i1521−i1521−i1521−i1521−i1521+i1521+i1521+i1521+i1521−i1521−i152000000000000000000000000000000000
χ50444444-244-2-2-2-2-2-2-24-1-1-1-1-1-1-1-1-2-2-2-21−i1521+i1521−i1521+i1521−i1521+i1521−i1521−i1521+i1521+i1521−i1521+i1521−i1521−i1521+i1521+i152-4-42222-1-1-1-1111111111−i1521−i1521+i1521+i1521−i1521−i1521+i1521+i152−1+i152−1+i152−1−i152−1−i152−1−i152−1−i152−1+i152−1+i152−1+i152−1+i152−1−i152−1−i152−1−i152−1−i152−1+i152−1+i152000000000000000000000000000000000
χ51444444-244-2-2-2-2-2-2-24-1-1-1-1-1-1-1-1-2-2-2-21+i1521−i1521+i1521−i1521+i1521−i1521+i1521+i1521−i1521−i1521+i1521−i1521+i1521+i1521−i1521−i15244-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11+i1521+i1521−i1521−i1521+i1521+i1521−i1521−i1521+i1521+i1521−i1521−i1521−i1521−i1521+i1521+i1521+i1521+i1521−i1521−i1521−i1521−i1521+i1521+i152000000000000000000000000000000000
χ52444444-244-2-2-2-2-2-2-24-1-1-1-1-1-1-1-1-2-2-2-21+i1521−i1521+i1521−i1521+i1521−i1521+i1521+i1521−i1521−i1521+i1521−i1521+i1521+i1521−i1521−i152-4-42222-1-1-1-1111111111+i1521+i1521−i1521−i1521+i1521+i1521−i1521−i152−1−i152−1−i152−1+i152−1+i152−1+i152−1+i152−1−i152−1−i152−1−i152−1−i152−1+i152−1+i152−1+i152−1+i152−1−i152−1−i152000000000000000000000000000000000
χ53444444-2-4-4-2-2-2-2-2-2-2-4-1-1-1-1-1-1-1-122221−i1521+i1521−i1521+i1521−i1521+i1521−i1521−i1521+i1521+i1521−i1521+i1521−i1521−i1521+i1521+i15200−2i32i3−2i32i3111155−5−555−5−5−1+i152−1+i152−1−i152−1−i152−1+i152−1+i152−1−i152−1−i152ζ14−ζ22+ζ26−ζ58ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46ζ2−ζ34+ζ38−ζ46−ζ2+ζ34−ζ38+ζ46−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58−ζ14+ζ22−ζ26+ζ58ζ14−ζ22+ζ26−ζ58ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46ζ2−ζ34+ζ38−ζ46−ζ2+ζ34−ζ38+ζ46−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58−ζ14+ζ22−ζ26+ζ58000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 60 (ζ60 = 1); i = ζ15.