Finite Group Databasebeta

← Group #14284288

Character table — Group #14284288

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size1111222222444444444444444444448888888888888888888888881010101010101010101010101616161616161616161616162020202020204040404040406060606060606060120120120120
order1222223666445661010101212121215153030303030304410101212121220202020303030306060606060606060444444441212121220202020606060606060606012121212121224661212888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iii−i−i
χ4111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−iii
χ5111111111111111111111111111111-1-111-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1
χ6111111111111111111111111111111-1-111-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ7111111111111111111111111111111-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111iiii−i−i−i−i−i−iii
χ8111111111111111111111111111111-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111−i−i−i−iiiiiii−i−i
χ91111-1-111111-11-1-111111-1-1111111111-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-11111-1-111-1-1-11-1-111ii−i−iii−i−ii−ii−i
χ101111-1-111111-11-1-111111-1-1111111111-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-11111-1-111-1-1-11-1-111−i−iii−i−iii−ii−ii
χ111111-1-111111-11-1-111111-1-1111111111-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1111111-1-1111-111-1-111-1-1-1-1111-1-11
χ121111-1-111111-11-1-111111-1-1111111111-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1111111-1-1111-111-1-1-1-11111-1-1-111-1
χ131111-1-111111-11-1-111111-1-111111111-11-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-11111-1-1-1-1-1-111-1-11-111-1-1ii−i−iii−i−i−ii−ii
χ141111-1-111111-11-1-111111-1-111111111-11-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-11111-1-1-1-1-1-111-1-11-111-1-1−i−iii−i−iiii−ii−i
χ151111-1-111111-11-1-111111-1-111111111-11-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-111-1-111-11-1-11111-1-1-1-111-111-1
χ161111-1-111111-11-1-111111-1-111111111-11-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-111-1-111-11-1-111-1-11111-1-11-1-11
χ172222222222-2-2222222-2-2-2-22222222200220000-2-2-2-22222-2-2-2-2-2-2-2-222-2-222-2-2222200000000000022-2-2-2-2000000000000000000
χ182222222222-2-2222222-2-2-2-22222222200220000-2-2-2-22222-2-2-2-2-2-2-2-2-2-222-2-222-2-2-2-2000000000000-2-22222000000000000000000
χ19222222-1-1-1-1222-1-1222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1000000000000
χ20222222-1-1-1-1222-1-1222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211112222-1-1-1-1-1-1-1-1111111-2-21111000000000000
χ21222222-1-1-1-1222-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-2-22211112222-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-2-2-2-211111111-1-1-1-1-1-1-2-21111000000000000
χ22222222-1-1-1-1222-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-2-22211112222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111-2-2-2-21111111111111122-1-1-1-1000000000000
χ23222222-1-1-1-1-2-22-1-12221111-1-1-1-1-1-1-1-10022−i3i3−i3i3-2-2-2-2-1-1-1-11111111122-2-222-2-2-1-1-1-10000−i3−i3i3i3−i3−i3i3i3-1-1111100−i3i3−i3i3000000000000
χ24222222-1-1-1-1-2-22-1-12221111-1-1-1-1-1-1-1-10022−i3i3−i3i3-2-2-2-2-1-1-1-111111111-2-222-2-22211110000−i3−i3i3i3−i3−i3i3i311-1-1-1-100i3−i3i3−i3000000000000
χ25222222-1-1-1-1-2-22-1-12221111-1-1-1-1-1-1-1-10022i3−i3i3−i3-2-2-2-2-1-1-1-11111111122-2-222-2-2-1-1-1-10000i3i3−i3−i3i3i3−i3−i3-1-1111100i3−i3i3−i3000000000000
χ26222222-1-1-1-1-2-22-1-12221111-1-1-1-1-1-1-1-10022i3−i3i3−i3-2-2-2-2-1-1-1-111111111-2-222-2-22211110000i3i3−i3−i3i3i3−i3−i311-1-1-1-100−i3i3−i3i3000000000000
χ272222-2-22222-222-2-2222-2-2222222222200-2-20000-2-222-2-2-2-2-2-2-2-2222222-2-2-2-2222222000000000000-2-2-2-222000000000000000000
χ282222-2-22222-222-2-2222-2-2222222222200-2-20000-2-222-2-2-2-2-2-2-2-22222-2-22222-2-2-2-2-2-20000000000002222-2-2000000000000000000
χ292222-2-2-1-1-1-12-2211222-1-111-1-1-1-1-1-1-1-12-2-2-2-1-11122-2-21111-1-1-1-111112222-2-2-2-2-1-1-1-1-2-2221111-1-1-1-111-1-111-2211-1-1000000000000
χ302222-2-2-1-1-1-12-2211222-1-111-1-1-1-1-1-1-1-12-2-2-2-1-11122-2-21111-1-1-1-11111-2-2-2-222221111-2-2221111-1-1-1-1-1-111-1-12-2-1-111000000000000
χ312222-2-2-1-1-1-12-2211222-1-111-1-1-1-1-1-1-1-1-22-2-211-1-122-2-21111-1-1-1-111112222-2-2-2-2-1-1-1-122-2-2-1-1-1-1111111-1-1112-2-1-111000000000000
χ322222-2-2-1-1-1-12-2211222-1-111-1-1-1-1-1-1-1-1-22-2-211-1-122-2-21111-1-1-1-11111-2-2-2-22222111122-2-2-1-1-1-11111-1-111-1-1-2211-1-1000000000000
χ332222-2-2-1-1-1-1-2221122211-1-1-1-1-1-1-1-1-1-100-2-2−i3i3i3−i3-2-22211111111-1-1-1-122-2-2-2-222-1-1-1-10000i3i3−i3−i3−i3−i3i3i31111-1-100i3−i3−i3i3000000000000
χ342222-2-2-1-1-1-1-2221122211-1-1-1-1-1-1-1-1-1-100-2-2−i3i3i3−i3-2-22211111111-1-1-1-1-2-22222-2-211110000i3i3−i3−i3−i3−i3i3i3-1-1-1-11100−i3i3i3−i3000000000000
χ352222-2-2-1-1-1-1-2221122211-1-1-1-1-1-1-1-1-1-100-2-2i3−i3−i3i3-2-22211111111-1-1-1-122-2-2-2-222-1-1-1-10000−i3−i3i3i3i3i3−i3−i31111-1-100−i3i3i3−i3000000000000
χ362222-2-2-1-1-1-1-2221122211-1-1-1-1-1-1-1-1-1-100-2-2i3−i3−i3i3-2-22211111111-1-1-1-1-2-22222-2-211110000−i3−i3i3i3i3i3−i3−i3-1-1-1-11100i3−i3−i3i3000000000000
χ372-2-222-22-2-220022-22-2-200002222-2-2-2-2002-20000000022-2-2000000002i−2i002i−2i002i2i−2i−2i0000000000002i−2i00000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000
χ382-2-222-22-2-220022-22-2-200002222-2-2-2-2002-20000000022-2-2000000002i−2i002i−2i002i2i−2i−2i0000000000002i−2i0000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000
χ392-2-222-22-2-220022-22-2-200002222-2-2-2-2002-20000000022-2-200000000−2i2i00−2i2i00−2i−2i2i2i000000000000−2i2i00000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000
χ402-2-222-22-2-220022-22-2-200002222-2-2-2-2002-20000000022-2-200000000−2i2i00−2i2i00−2i−2i2i2i000000000000−2i2i0000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000
χ412-2-22-222-2-22002-222-2-200002222-2-2-2-200-2200000000-2-222000000002i−2i00−2i2i002i2i−2i−2i000000000000−2i2i00000000001−i−1+i−1+i1−i−1−i1+i1+i−1−i0000
χ422-2-22-222-2-22002-222-2-200002222-2-2-2-200-2200000000-2-222000000002i−2i00−2i2i002i2i−2i−2i000000000000−2i2i0000000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i0000
χ432-2-22-222-2-22002-222-2-200002222-2-2-2-200-2200000000-2-22200000000−2i2i002i−2i00−2i−2i2i2i0000000000002i−2i00000000001+i−1−i−1−i1+i−1+i1−i1−i−1+i0000
χ442-2-22-222-2-22002-222-2-200002222-2-2-2-200-2200000000-2-22200000000−2i2i002i−2i00−2i−2i2i2i0000000000002i−2i0000000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i0000
χ45444444444444-144-1-1-14444-1-1-1-1-1-1-1-144-1-14444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000
χ46444444444444-144-1-1-14444-1-1-1-1-1-1-1-1-4-4-1-1-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000111111111111000000000000000000000000
χ474444444444-4-4-144-1-1-1-4-4-4-4-1-1-1-1-1-1-1-100-1-100001111-1-1-1-111111111000000000000−55−55−55−55−55−55000000000000000000000000
χ484444444444-4-4-144-1-1-1-4-4-4-4-1-1-1-1-1-1-1-100-1-100001111-1-1-1-1111111110000000000005−55−55−55−55−55−5000000000000000000000000
χ49444444-2-2-2-244-1-2-2-1-1-1-2-2-2-21−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i15244-1-1-2-2-2-2-1-1-1-11−i1521+i1521−i1521+i1521−i1521−i1521+i1521+i1521−i1521−i1521+i1521+i152000000000000-1-1-1-11−i1521+i1521+i1521−i1521−i1521+i1521+i1521−i152000000000000000000000000
χ50444444-2-2-2-244-1-2-2-1-1-1-2-2-2-21−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i152-4-4-1-12222-1-1-1-11−i1521+i1521−i1521+i1521−i1521−i1521+i1521+i1521−i1521−i1521+i1521+i1520000000000001111−1+i152−1−i152−1−i152−1+i152−1+i152−1−i152−1−i152−1+i152000000000000000000000000
χ51444444-2-2-2-244-1-2-2-1-1-1-2-2-2-21+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i15244-1-1-2-2-2-2-1-1-1-11+i1521−i1521+i1521−i1521+i1521+i1521−i1521−i1521+i1521+i1521−i1521−i152000000000000-1-1-1-11+i1521−i1521−i1521+i1521+i1521−i1521−i1521+i152000000000000000000000000
χ52444444-2-2-2-244-1-2-2-1-1-1-2-2-2-21+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i152-4-4-1-12222-1-1-1-11+i1521−i1521+i1521−i1521+i1521+i1521−i1521−i1521+i1521+i1521−i1521−i1520000000000001111−1−i152−1+i152−1+i152−1−i152−1−i152−1+i152−1+i152−1−i152000000000000000000000000
χ53444444-2-2-2-2-4-4-1-2-2-1-1-122221−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i15200-1-1−2i32i3−2i32i311111−i1521+i1521−i1521+i152−1+i152−1+i152−1−i152−1−i152−1+i152−1+i152−1−i152−1−i1520000000000005−55−5ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58000000000000000000000000
χ54444444-2-2-2-2-4-4-1-2-2-1-1-122221−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i15200-1-12i3−2i32i3−2i311111−i1521+i1521−i1521+i152−1+i152−1+i152−1−i152−1−i152−1+i152−1+i152−1−i152−1−i152000000000000−55−55−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58000000000000000000000000
χ55444444-2-2-2-2-4-4-1-2-2-1-1-122221+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i15200-1-1−2i32i3−2i32i311111+i1521−i1521+i1521−i152−1−i152−1−i152−1+i152−1+i152−1−i152−1−i152−1+i152−1+i152000000000000−55−55ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46000000000000000000000000
χ56444444-2-2-2-2-4-4-1-2-2-1-1-122221+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i15200-1-12i3−2i32i3−2i311111+i1521−i1521+i1521−i152−1−i152−1−i152−1+i152−1+i152−1−i152−1−i152−1+i152−1+i1520000000000005−55−5−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46000000000000000000000000
χ574444-4-444444-4-1-4-4-1-1-144-4-4-1-1-1-1-1-1-1-14-41144-4-4-1-1111111-1-1-1-1111100000000000011-1-11111-1-1-1-1000000000000000000000000
χ584444-4-444444-4-1-4-4-1-1-144-4-4-1-1-1-1-1-1-1-1-4411-4-444-1-1111111-1-1-1-11111000000000000-1-111-1-1-1-11111000000000000000000000000
χ594444-4-44444-44-1-4-4-1-1-1-4-444-1-1-1-1-1-1-1-10011000011-1-111111111-1-1-1-1000000000000−555−5−55−555−55−5000000000000000000000000
χ604444-4-44444-44-1-4-4-1-1-1-4-444-1-1-1-1-1-1-1-10011000011-1-111111111-1-1-1-10000000000005−5−555−55−5−55−55000000000000000000000000
χ614444-4-4-2-2-2-24-4-122-1-1-1-2-2221−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1524-411-2-222-1-111−1+i152−1−i152−1+i152−1−i1521−i1521−i1521+i1521+i152−1+i152−1+i152−1−i152−1−i15200000000000011-1-1−1+i152−1−i152−1−i152−1+i1521−i1521+i1521+i1521−i152000000000000000000000000
χ624444-4-4-2-2-2-24-4-122-1-1-1-2-2221−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i152-441122-2-2-1-111−1+i152−1−i152−1+i152−1−i1521−i1521−i1521+i1521+i152−1+i152−1+i152−1−i152−1−i152000000000000-1-1111−i1521+i1521+i1521−i152−1+i152−1−i152−1−i152−1+i152000000000000000000000000
χ634444-4-4-2-2-2-24-4-122-1-1-1-2-2221+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1524-411-2-222-1-111−1−i152−1+i152−1−i152−1+i1521+i1521+i1521−i1521−i152−1−i152−1−i152−1+i152−1+i15200000000000011-1-1−1−i152−1+i152−1+i152−1−i1521+i1521−i1521−i1521+i152000000000000000000000000
χ644444-4-4-2-2-2-24-4-122-1-1-1-2-2221+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i152-441122-2-2-1-111−1−i152−1+i152−1−i152−1+i1521+i1521+i1521−i1521−i152−1−i152−1−i152−1+i152−1+i152000000000000-1-1111+i1521−i1521−i1521+i152−1−i152−1+i152−1+i152−1−i152000000000000000000000000
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Here ζ is a primitive root of unity of order 60 (ζ60 = 1); i = ζ15.