Finite Group Databasebeta

← Group #14299873

Character table — Group #14299873

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size11222222244444444444444444444445588888888888888888888888101010101010101616161616161616161616162020202020202020202040404040406060606060606060120120120120
order12234461212244456101212121212151520203030606060604468101220202020202424303060606060606060606060224661212102030304040606012012012012024446121212121268122424888888884488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-111111111111111111111111-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−ii−ii−i
χ41111111111111111111111111111111-1-111111111111111111111111-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−ii−ii
χ511111111111-1-11111-1-1-1-11111111111111-1111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111111-1-111-1-1-1-111-1-111-1-1-1-11-11-1-111111111-1-1-1-1
χ611111111111-1-11111-1-1-1-11111111111111-1111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111111-1-111-1-1-1-111-1-111-1-1-1-11-11-1-1-1-1-1-1-1-1-1-11111
χ711111111111-1-11111-1-1-1-11111111111-1-11-1111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-111-1-11111-11-111iiii−i−i−i−i−ii−ii
χ811111111111-1-11111-1-1-1-11111111111-1-11-1111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-111-1-11111-11-111−i−i−i−iiiiii−ii−i
χ9111111111-1-11111111111111111111111-1-11-111111-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1-111-1-111-1-1
χ10111111111-1-11111111111111111111111-1-11-111111-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-111-1-111-1-111
χ11111111111-1-111111111111111111111-1-1-1-11-111111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111ii−i−i−i−iiii−i−ii
χ12111111111-1-111111111111111111111-1-1-1-11-111111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111−i−iiiii−i−i−iii−i
χ13111111111-1-1-1-11111-1-1-1-1111111111111-111-11-1-1-1-1111111-1-1-1-1-1-1-1-11111111-1-1-1-111-1-11111-1-1-1-111-1-1-1-1-11-11111-1-111-1-1-1-111
χ14111111111-1-1-1-11111-1-1-1-1111111111111-111-11-1-1-1-1111111-1-1-1-1-1-1-1-11111111-1-1-1-111-1-11111-1-1-1-111-1-1-1-1-11-111-1-111-1-11111-1-1
χ15111111111-1-1-1-11111-1-1-1-11111111111-1-1-111-11-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-111111-11-1-1ii−i−i−i−iii−iii−i
χ16111111111-1-1-1-11111-1-1-1-11111111111-1-1-111-11-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-111111-11-1-1−i−iiiii−i−ii−i−ii
χ172222-2-22-2-20000222-2000022-2-222-2-2-2-2220020-200000022-2-200000000-2-22-2-2220000000000000000-22000000000002-2002-20000
χ182222-2-22-2-20000222-2000022-2-222-2-2-2-2220020-200000022-2-200000000-2-22-2-2220000000000000000-2200000000000-2200-220000
χ192222-2-22-2-20000222-2000022-2-222-2-2-2-2-2-20020-200000022-2-20000000022-222-2-200000000000000002-2000000000002i−2i00−2i2i0000
χ202222-2-22-2-20000222-2000022-2-222-2-2-2-2-2-20020-200000022-2-20000000022-222-2-200000000000000002-200000000000−2i2i002i−2i0000
χ21222-122-1-1-122222-12-1-1-1-1-1-1-122-1-1-1-1-1-122-122-122222-1-1-1-1-1-1-1-1-1-1-1-1-1-1222-1-1-1-122-1-122-1-1-1-1-1-12222-1-1-1-1-1-1-12-1-1-1000000000000
χ22222-122-1-1-122222-12-1-1-1-1-1-1-122-1-1-1-1-1-1-2-2-122-122222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2111122-1-122-1-1-1-1-1-1-2-2-2-21111111-2111000000000000
χ23222-122-1-1-122-2-22-12-11111-1-122-1-1-1-1-1-122-1-22-12-2-2-2-211-1-1-1-111111111222-1-1-1-122-1-1-2-2-1-1111122-2-2-1-11111-1-2-111000000000000
χ24222-122-1-1-122-2-22-12-11111-1-122-1-1-1-1-1-1-2-2-1-22-12-2-2-2-211-1-1-1-111111111-2-2-2111122-1-1-2-2-1-11111-2-22211-1-1-1-1121-1-1000000000000
χ25222-122-1-1-1-2-2222-12-1-1-1-1-1-1-122-1-1-1-1-1-1221-2212222211-1-1-1-1-1-1-1-1-1-1-1-1222-1-1-1-1-2-211-2-2111111-2-222-1-1-1-1-1-11-2111000000000000
χ26222-122-1-1-1-2-2222-12-1-1-1-1-1-1-122-1-1-1-1-1-1-2-21-2212222211-1-1-1-1-1-1-1-1-1-1-1-1-2-2-21111-2-211-2-211111122-2-2111111-12-1-1-1000000000000
χ27222-122-1-1-1-2-2-2-22-12-11111-1-122-1-1-1-1-1-12212212-2-2-2-2-1-1-1-1-1-111111111222-1-1-1-1-2-2112211-1-1-1-1-2-2-2-2-1-11111121-1-1000000000000
χ28222-122-1-1-1-2-2-2-22-12-11111-1-122-1-1-1-1-1-1-2-212212-2-2-2-2-1-1-1-1-1-111111111-2-2-21111-2-2112211-1-1-1-1222211-1-1-1-1-1-2-111000000000000
χ2922-222-22-2-22-2002-222000022-2-222-2-2-2-22220-2-22000000-2-22200000000-22-2-2-2222-22200-2-20000-22002-20000-20200000000000000
χ3022-222-22-2-22-2002-222000022-2-222-2-2-2-2-2-220-2-22000000-2-222000000002-2222-2-22-22200-2-200002-200-22000020-200000000000000
χ3122-222-22-2-2-22002-222000022-2-222-2-2-2-222-20-222000000-2-22200000000-22-2-2-222-22-2-2002200002-2002-2000020-200000000000000
χ3222-222-22-2-2-22002-222000022-2-222-2-2-2-2-2-2-20-222000000-2-222000000002-2222-2-2-22-2-200220000-2200-220000-20200000000000000
χ3322-22-2222200002-22-2000022222222222200-20-2000000-2-2-2-2000000002-2-222220000000000000000-2-20000000002-2002-2000000
χ3422-22-2222200002-22-2000022222222222200-20-2000000-2-2-2-2000000002-2-222220000000000000000-2-2000000000-2200-22000000
χ3522-22-2222200002-22-200002222222222-2-200-20-2000000-2-2-2-200000000-222-2-2-2-20000000000000000220000000002i−2i00−2i2i000000
χ3622-22-2222200002-22-200002222222222-2-200-20-2000000-2-2-2-200000000-222-2-2-2-2000000000000000022000000000−2i2i002i−2i000000
χ3722-2-12-2-1112-200212-133−3−3-1-1-2-2-1-1111122-10-21200003−311-1-13333−3−3−3−3-22-211-1-12-2-1-1001133−3−3-2200-1133−3−310-13−3000000000000
χ3822-2-12-2-1112-200212-133−3−3-1-1-2-2-1-11111-2-2-10-21200003−311-1-13333−3−3−3−32-22-1-1112-2-1-1001133−3−32-2001-1−3−333-101−33000000000000
χ3922-2-12-2-1112-200212-1−3−333-1-1-2-2-1-1111122-10-2120000−3311-1-1−3−3−3−33333-22-211-1-12-2-1-10011−3−333-2200-11−3−33310-1−33000000000000
χ4022-2-12-2-1112-200212-1−3−333-1-1-2-2-1-11111-2-2-10-2120000−3311-1-1−3−3−3−333332-22-1-1112-2-1-10011−3−3332-2001-133−3−3-1013−3000000000000
χ4122-2-12-2-111-2200212-133−3−3-1-1-2-2-1-111112210-2-120000−3311-1-13333−3−3−3−3-22-211-1-1-221100-1-1−3−3332-200-1133−3−3-101−33000000000000
χ4222-2-12-2-111-2200212-133−3−3-1-1-2-2-1-11111-2-210-2-120000−3311-1-13333−3−3−3−32-22-1-111-221100-1-1−3−333-22001-1−3−33310-13−3000000000000
χ4322-2-12-2-111-2200212-1−3−333-1-1-2-2-1-111112210-2-1200003−311-1-1−3−3−3−33333-22-211-1-1-221100-1-133−3−32-200-11−3−333-1013−3000000000000
χ4422-2-12-2-111-2200212-1−3−333-1-1-2-2-1-11111-2-210-2-1200003−311-1-1−3−3−3−333332-22-1-111-221100-1-133−3−3-22001-133−3−310-1−33000000000000
χ454444444444444-14-144444-1-1-1-1-1-1-1-1-1-10044-14-1-1-1-1-144-1-1-1-1-1-1-1-1-1-1-1-10000000-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000000
χ4644444444444-4-4-14-14-4-4-4-4-1-1-1-1-1-1-1-1-1-1004-4-14-11111-4-4-1-1-1-1111111110000000-1-1-1-111-1-11111000000000000000000000000000
χ47444444444-4-444-14-144444-1-1-1-1-1-1-1-1-1-100-4-4-1-4-1-1-1-1-1-4-4-1-1-1-1-1-1-1-1-1-1-1-10000000111111111111000000000000000000000000000
χ48444444444-4-4-4-4-14-14-4-4-4-4-1-1-1-1-1-1-1-1-1-100-44-1-4-1111144-1-1-1-11111111100000001111-1-111-1-1-1-1000000000000000000000000000
χ49444-244-2-2-24444-1-2-1-2-2-2-2-21−i1521+i152-1-11−i1521+i1521−i1521−i1521+i1521+i15200-24-1-2-1-1-1-1-1-2-21−i1521+i1521−i1521+i1521−i1521−i1521+i1521+i1521−i1521−i1521+i1521+i1520000000-1-11−i1521+i152-1-11−i1521+i1521−i1521+i1521−i1521+i152000000000000000000000000000
χ50444-244-2-2-24444-1-2-1-2-2-2-2-21+i1521−i152-1-11+i1521−i1521+i1521+i1521−i1521−i15200-24-1-2-1-1-1-1-1-2-21+i1521−i1521+i1521−i1521+i1521+i1521−i1521−i1521+i1521+i1521−i1521−i1520000000-1-11+i1521−i152-1-11+i1521−i1521+i1521−i1521+i1521−i152000000000000000000000000000
χ51444-244-2-2-244-4-4-1-2-1-222221−i1521+i152-1-11−i1521+i1521−i1521−i1521+i1521+i15200-2-4-1-2-11111221−i1521+i1521−i1521+i152−1+i152−1+i152−1−i152−1−i152−1+i152−1+i152−1−i152−1−i1520000000-1-11−i1521+i152111−i1521+i152−1+i152−1−i152−1+i152−1−i152000000000000000000000000000
χ52444-244-2-2-244-4-4-1-2-1-222221+i1521−i152-1-11+i1521−i1521+i1521+i1521−i1521−i15200-2-4-1-2-11111221+i1521−i1521+i1521−i152−1−i152−1−i152−1+i152−1+i152−1−i152−1−i152−1+i152−1+i1520000000-1-11+i1521−i152111+i1521−i152−1−i152−1+i152−1−i152−1+i152000000000000000000000000000
χ53444-244-2-2-2-4-444-1-2-1-2-2-2-2-21−i1521+i152-1-11−i1521+i1521−i1521−i1521+i1521+i152002-4-12-1-1-1-1-1221−i1521+i1521−i1521+i1521−i1521−i1521+i1521+i1521−i1521−i1521+i1521+i152000000011−1+i152−1−i15211−1+i152−1−i152−1+i152−1−i152−1+i152−1−i152000000000000000000000000000
χ54444-244-2-2-2-4-444-1-2-1-2-2-2-2-21+i1521−i152-1-11+i1521−i1521+i1521+i1521−i1521−i152002-4-12-1-1-1-1-1221+i1521−i1521+i1521−i1521+i1521+i1521−i1521−i1521+i1521+i1521−i1521−i152000000011−1−i152−1+i15211−1−i152−1+i152−1−i152−1+i152−1−i152−1+i152000000000000000000000000000
χ55444-244-2-2-2-4-4-4-4-1-2-1-222221−i1521+i152-1-11−i1521+i1521−i1521−i1521+i1521+i1520024-12-11111-2-21−i1521+i1521−i1521+i152−1+i152−1+i152−1−i152−1−i152−1+i152−1+i152−1−i152−1−i152000000011−1+i152−1−i152-1-1−1+i152−1−i1521−i1521+i1521−i1521+i152000000000000000000000000000
χ56444-244-2-2-2-4-4-4-4-1-2-1-222221+i1521−i152-1-11+i1521−i1521+i1521+i1521−i1521−i1520024-12-11111-2-21+i1521−i1521+i1521−i152−1−i152−1−i152−1+i152−1+i152−1−i152−1−i152−1+i152−1+i152000000011−1−i152−1+i152-1-1−1−i152−1+i1521+i1521−i1521+i1521−i152000000000000000000000000000
χ57444-2-4-4-22200004-2420000-2-2-4-4-2-22222440040-4000000-2-22200000000-4-4422-2-200000000000000002-2000000000000000000000
χ58444-2-4-4-22200004-2420000-2-2-4-4-2-22222-4-40040-4000000-2-2220000000044-4-2-2220000000000000000-22000000000000000000000
χ5944-444-44-4-44-400-1-4-140000-1-111-1-1111100401-4-1−i5−i5i5i50011-1-1−i5−i5i5i5i5i5−i5−i50000000-11-1-1−i5i511−i5i5i5−i5000000000000000000000000000
χ6044-444-44-4-44-400-1-4-140000-1-111-1-1111100401-4-1i5i5−i5−i50011-1-1i5i5−i5−i5−i5−i5i5i50000000-11-1-1i5−i511i5−i5−i5i5000000000000000000000000000
χ6144-444-44-4-4-4400-1-4-140000-1-111-1-1111100-4014-1−i5−i5i5i50011-1-1−i5−i5i5i5i5i5−i5−i500000001-111i5−i5-1-1i5−i5−i5i5000000000000000000000000000
χ6244-444-44-4-4-4400-1-4-140000-1-111-1-1111100-4014-1i5i5−i5−i50011-1-1i5i5−i5−i5−i5−i5i5i500000001-111−i5i5-1-1−i5i5i5−i5000000000000000000000000000
χ6344-4-24-4-2224-400-12-1-22323−23−231−i1521+i152111−i1521+i152−1+i152−1+i152−1−i152−1−i15200-2012-1i5i5−i5−i523−23−1+i152−1−i1521−i1521+i152ζ7−ζ11+ζ43−ζ59ζ7−ζ11+ζ43−ζ59ζ19−ζ23+ζ31−ζ47ζ19−ζ23+ζ31−ζ47−ζ7+ζ11−ζ43+ζ59−ζ7+ζ11−ζ43+ζ59−ζ19+ζ23−ζ31+ζ47−ζ19+ζ23−ζ31+ζ470000000-111−i1521+i152i5−i5−1+i152−1−i152ζ7−ζ11+ζ43−ζ59ζ19−ζ23+ζ31−ζ47−ζ7+ζ11−ζ43+ζ59−ζ19+ζ23−ζ31+ζ47000000000000000000000000000
χ6444-4-24-4-2224-400-12-1-22323−23−231+i1521−i152111+i1521−i152−1−i152−1−i152−1+i152−1+i15200-2012-1−i5−i5i5i523−23−1−i152−1+i1521+i1521−i152ζ19−ζ23+ζ31−ζ47ζ19−ζ23+ζ31−ζ47ζ7−ζ11+ζ43−ζ59ζ7−ζ11+ζ43−ζ59−ζ19+ζ23−ζ31+ζ47−ζ19+ζ23−ζ31+ζ47−ζ7+ζ11−ζ43+ζ59−ζ7+ζ11−ζ43+ζ590000000-111+i1521−i152−i5i5−1−i152−1+i152ζ19−ζ23+ζ31−ζ47ζ7−ζ11+ζ43−ζ59−ζ19+ζ23−ζ31+ζ47−ζ7+ζ11−ζ43+ζ59000000000000000000000000000
χ6544-4-24-4-2224-400-12-1-2−23−2323231−i1521+i152111−i1521+i152−1+i152−1+i152−1−i152−1−i15200-2012-1−i5−i5i5i5−2323−1+i152−1−i1521−i1521+i152−ζ7+ζ11−ζ43+ζ59−ζ7+ζ11−ζ43+ζ59−ζ19+ζ23−ζ31+ζ47−ζ19+ζ23−ζ31+ζ47ζ7−ζ11+ζ43−ζ59ζ7−ζ11+ζ43−ζ59ζ19−ζ23+ζ31−ζ47ζ19−ζ23+ζ31−ζ470000000-111−i1521+i152−i5i5−1+i152−1−i152−ζ7+ζ11−ζ43+ζ59−ζ19+ζ23−ζ31+ζ47ζ7−ζ11+ζ43−ζ59ζ19−ζ23+ζ31−ζ47000000000000000000000000000
χ6644-4-24-4-2224-400-12-1-2−23−2323231+i1521−i152111+i1521−i152−1−i152−1−i152−1+i152−1+i15200-2012-1i5i5−i5−i5−2323−1−i152−1+i1521+i1521−i152−ζ19+ζ23−ζ31+ζ47−ζ19+ζ23−ζ31+ζ47−ζ7+ζ11−ζ43+ζ59−ζ7+ζ11−ζ43+ζ59ζ19−ζ23+ζ31−ζ47ζ19−ζ23+ζ31−ζ47ζ7−ζ11+ζ43−ζ59ζ7−ζ11+ζ43−ζ590000000-111+i1521−i152i5−i5−1−i152−1+i152−ζ19+ζ23−ζ31+ζ47−ζ7+ζ11−ζ43+ζ59ζ19−ζ23+ζ31−ζ47ζ7−ζ11+ζ43−ζ59000000000000000000000000000
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Here ζ is a primitive root of unity of order 60 (ζ60 = 1); i = ζ15.