Finite Group Databasebeta

← Group #14283167

Character table — Group #14283167

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
χ91111-1-11-1-11-1-1-1-1111111-1-1-1-1111-1-1111111-1-1-1-1-1-1-1-1111-111-1-111-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-111-1-111-1-11-111-1-111-1-111-1-11-11-1
χ101111-1-11-1-11-1-1-1-1111111-1-1-1-1111-1-1111111-1-1-1-1-1-1-1-1111-111-1-111-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-111-1-111-1-11-111-1-1-1-111-1-111-11-11
χ111111-1-11-1-11-1-1-1-1111111-1-1-1-1111-1-1111111-1-1-1-1-1-1-1-1111-111-1-111-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-11-1-111-1-111-11-1-111ii−i−i−i−iiii−i−ii
χ121111-1-11-1-11-1-1-1-1111111-1-1-1-1111-1-1111111-1-1-1-1-1-1-1-1111-111-1-111-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-11-1-111-1-111-11-1-111−i−iiiii−i−i−iii−i
χ131111-1-11-1-11-1-1-1-1111111-1-1-1-1111-1-1111111-1-1-1-1-1-1-1-111-11-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-111-1-111-1-1-11-1-11111-1-111-1-1-11-11
χ141111-1-11-1-11-1-1-1-1111111-1-1-1-1111-1-1111111-1-1-1-1-1-1-1-111-11-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-111-1-111-1-1-11-1-111-1-111-1-1111-11-1
χ151111-1-11-1-11-1-1-1-1111111-1-1-1-1111-1-1111111-1-1-1-1-1-1-1-111-11-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-11-1-111-1-1111-111-1-1ii−i−i−i−iii−iii−i
χ161111-1-11-1-11-1-1-1-1111111-1-1-1-1111-1-1111111-1-1-1-1-1-1-1-111-11-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-11-1-111-1-1111-111-1-1−i−iiiii−i−ii−i−ii
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
χ272222-2-22222-2-2-2-222-2222-2-2-2-22-2-222222222-2-2-2-2-2-2-2-222000000-2-22200000000-2-2-2-2222200000000000000002222-2-2-222-2-2-2-222000000000000000000
χ282222-2-22222-2-2-2-222-2222-2-2-2-22-2-222222222-2-2-2-2-2-2-2-222000000-2-22200000000-2-2-2-222220000000000000000-2-2-2-2222-2-22222-2-2000000000000000000
χ292222-2-2-122-11111-1-1-2222-2-2-2-2211-1-1-1-1-1-1-1-111111111-1-100−i3i3i3−i3-2-222000000001111-1-1-1-1−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i32222-2-2-2-1-11111-1-100−i3i3i3−i3000000000000
χ302222-2-2-122-11111-1-1-2222-2-2-2-2211-1-1-1-1-1-1-1-111111111-1-100−i3i3i3−i3-2-222000000001111-1-1-1-1−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i3-2-2-2-222211-1-1-1-11100i3−i3−i3i3000000000000
χ312222-2-2-122-11111-1-1-2222-2-2-2-2211-1-1-1-1-1-1-1-111111111-1-100i3−i3−i3i3-2-222000000001111-1-1-1-1i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i32222-2-2-2-1-11111-1-100i3−i3−i3i3000000000000
χ322222-2-2-122-11111-1-1-2222-2-2-2-2211-1-1-1-1-1-1-1-111111111-1-100i3−i3−i3i3-2-222000000001111-1-1-1-1i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3-2-2-2-222211-1-1-1-11100−i3i3i3−i3000000000000
χ332222-2-2-1-2-2-11111-1-12222-2-2-2-22-1-111-1-1-1-1-1-111111111-1-12-2-1-11122-2-22222-2-2-2-2-1-1-1-11111-1-1-1-1-1-1-1-11111111122-2-222-2-1-111-1-1112-2-1-111000000000000
χ342222-2-2-1-2-2-11111-1-12222-2-2-2-22-1-111-1-1-1-1-1-111111111-1-12-2-1-11122-2-22222-2-2-2-2-1-1-1-11111-1-1-1-1-1-1-1-111111111-2-222-2-2211-1-111-1-1-2211-1-1000000000000
χ352222-2-2-1-2-2-11111-1-12222-2-2-2-22-1-111-1-1-1-1-1-111111111-1-1-2211-1-122-2-2-2-2-2-22222-1-1-1-1111111111111-1-1-1-1-1-1-1-122-2-222-2-1-111-1-111-2211-1-1000000000000
χ362222-2-2-1-2-2-11111-1-12222-2-2-2-22-1-111-1-1-1-1-1-111111111-1-1-2211-1-122-2-2-2-2-2-22222-1-1-1-1111111111111-1-1-1-1-1-1-1-1-2-222-2-2211-1-111-1-12-2-1-111000000000000
χ372-2-222-2200-222-2-2-22022-222-2-2-200002222-2-22222-2-2-2-2-2-2000000000000000000000000000000000000000000002i−2i2i−2i000002i−2i2i−2i0000001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000
χ382-2-222-2200-222-2-2-22022-222-2-2-200002222-2-22222-2-2-2-2-2-2000000000000000000000000000000000000000000002i−2i2i−2i000002i−2i2i−2i000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000
χ392-2-222-2200-222-2-2-22022-222-2-2-200002222-2-22222-2-2-2-2-2-200000000000000000000000000000000000000000000−2i2i−2i2i00000−2i2i−2i2i0000001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000
χ402-2-222-2200-222-2-2-22022-222-2-2-200002222-2-22222-2-2-2-2-2-200000000000000000000000000000000000000000000−2i2i−2i2i00000−2i2i−2i2i000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000
χ412-2-22-22200-2-2-222-22022-2-2-222-200002222-2-2-2-2-2-22222-2-2000000000000000000000000000000000000000000002i−2i−2i2i00000−2i2i2i−2i0000001−i−1+i−1+i1−i1+i−1−i−1−i1+i0000
χ422-2-22-22200-2-2-222-22022-2-2-222-200002222-2-2-2-2-2-22222-2-2000000000000000000000000000000000000000000002i−2i−2i2i00000−2i2i2i−2i000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i0000
χ432-2-22-22200-2-2-222-22022-2-2-222-200002222-2-2-2-2-2-22222-2-200000000000000000000000000000000000000000000−2i2i2i−2i000002i−2i−2i2i0000001+i−1−i−1−i1+i1−i−1+i−1+i1−i0000
χ442-2-22-22200-2-2-222-22022-2-2-222-200002222-2-2-2-2-2-22222-2-200000000000000000000000000000000000000000000−2i2i2i−2i000002i−2i−2i2i000000−1−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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χ11388-8-800-400-44i3−4i34i3−4i3440-22-2−252525−25200001−i151+i15−1+i15−1−i151−i151+i15−2ζ14+2ζ22−2ζ26+2ζ582ζ14−2ζ22+2ζ26−2ζ58−2ζ2+2ζ34−2ζ38+2ζ462ζ2−2ζ34+2ζ38−2ζ46−2ζ14+2ζ22−2ζ26+2ζ582ζ14−2ζ22+2ζ26−2ζ58−2ζ2+2ζ34−2ζ38+2ζ462ζ2−2ζ34+2ζ38−2ζ46−1+i15−1−i15000000000000000000000000000000000000000000000000000000000000000000000000000
χ11488-8-800-400-44i3−4i34i3−4i3440-22-225−25−2525200001+i151−i15−1−i15−1+i151+i151−i15−2ζ2+2ζ34−2ζ38+2ζ462ζ2−2ζ34+2ζ38−2ζ46−2ζ14+2ζ22−2ζ26+2ζ582ζ14−2ζ22+2ζ26−2ζ58−2ζ2+2ζ34−2ζ38+2ζ462ζ2−2ζ34+2ζ38−2ζ46−2ζ14+2ζ22−2ζ26+2ζ582ζ14−2ζ22+2ζ26−2ζ58−1−i15−1+i15000000000000000000000000000000000000000000000000000000000000000000000000000
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χ1208-8-88-88-400444-4-44-40-2-2222-2-2200001+i151−i151+i151−i15−1−i15−1+i15−1−i15−1−i15−1+i15−1+i151+i151+i151−i151−i15−1−i15−1+i15000000000000000000000000000000000000000000000000000000000000000000000000000

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