Finite Group Databasebeta

← Group #14301625

Character table — Group #14301625

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size11222222244444444444444444444445588888888888888888888888101010101010101616161616161616161616162020202020202020202040404040406060606060606060120120120120
order12222366622245666666101010151530303030303022461010101010101212123030303030303030303030302226666102020203030606060606060222466666646121212444444444444
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−iii−i−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−i−iii
χ511111111111-1-111111111111111111111-1-1111111-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-111-1-111-1-11-11-1
χ611111111111-1-111111111111111111111-1-1111111-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-111-1-111-11-11
χ711111111111-1-1111111111111111111-1-1-1-1111111-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111ii−i−i−i−iiii−i−ii
χ811111111111-1-1111111111111111111-1-1-1-1111111-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111−i−iiiii−i−i−iii−i
χ9111111111-1-111111-1-1-1-11111111111111-1111-1-1-1-11-1-11111-1-1-1-1-1-1-1-1111111111-1-11111-1-1-1-1-1-11111-1-1-1-1-111-1-111111111-1-1-1-1
χ10111111111-1-111111-1-1-1-11111111111111-1111-1-1-1-11-1-11111-1-1-1-1-1-1-1-1111111111-1-11111-1-1-1-1-1-11111-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111
χ11111111111-1-111111-1-1-1-111111111111-1-1-1111-1-1-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1-1-111111-1-111iiii−i−i−i−i−i−iii
χ12111111111-1-111111-1-1-1-111111111111-1-1-1111-1-1-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1-1-111111-1-111−i−i−i−iiiiiii−i−i
χ13111111111-1-1-1-1111-1-1-1-111111111111111-111-1-1-1-1-1111111-1-1-1-1-1-1-1-11111111-1-111-1-1-1-11111-1-1-1-111-1-1-1-11-1-11111-1-111-1-1-11-11
χ14111111111-1-1-1-1111-1-1-1-111111111111111-111-1-1-1-1-1111111-1-1-1-1-1-1-1-11111111-1-111-1-1-1-11111-1-1-1-111-1-1-1-11-1-111-1-111-1-1111-11-1
χ15111111111-1-1-1-1111-1-1-1-111111111111-1-11-111-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-11111-111-1-1ii−i−i−i−iii−iii−i
χ16111111111-1-1-1-1111-1-1-1-111111111111-1-11-111-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-11111-111-1-1−i−iiiii−i−ii−i−ii
χ1722222-1-1-1-122222-1-1-1-1-1-1222-1-1-1-1-1-1-1-1222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-12-1-1-1-1000000000000
χ1822222-1-1-1-122222-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-2-22-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-211112222-1-1-1-1-1-1-1-1-2-2-2-2111111-21111000000000000
χ1922222-1-1-1-122-2-22-1-1-1-1-1-1222-1-1-1-1-1-1-1-122-21222222111-1-1-1-1-1-1-1-1-1-1-1-1222-1-1-1-1-2-2-2-21111111122-2-2-1-1-1-1-1-1-21111000000000000
χ2022222-1-1-1-122-2-22-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-2-2-21222222111-1-1-1-1-1-1-1-1-1-1-1-1-2-2-21111-2-2-2-211111111-2-2221111112-1-1-1-1000000000000
χ2122222-1-1-1-1-2-2222-1-11111222-1-1-1-1-1-1-1-122-2-122-2-2-2-2-111-1-1-1-111111111222-1-1-1-122-2-2-1-1-1-11111-2-222-1-11111-2-1-111000000000000
χ2222222-1-1-1-1-2-2222-1-11111222-1-1-1-1-1-1-1-1-2-2-2-122-2-2-2-2-111-1-1-1-111111111-2-2-2111122-2-2-1-1-1-1111122-2-211-1-1-1-1211-1-1000000000000
χ2322222-1-1-1-1-2-2-2-22-1-11111222-1-1-1-1-1-1-1-1222122-2-2-2-21-1-1-1-1-1-111111111222-1-1-1-1-2-2221111-1-1-1-1-2-2-2-2-1-11111211-1-1000000000000
χ2422222-1-1-1-1-2-2-2-22-1-11111222-1-1-1-1-1-1-1-1-2-22122-2-2-2-21-1-1-1-1-1-111111111-2-2-21111-2-2221111-1-1-1-1222211-1-1-1-1-2-1-111000000000000
χ25222-2-222-2-2000022-200002-2-22222-2-2-2-222002-2000000022-2-200000000-22-222-2-200000000000000002-2000000000002-2002-20000
χ26222-2-222-2-2000022-200002-2-22222-2-2-2-222002-2000000022-2-200000000-22-222-2-200000000000000002-200000000000-2200-220000
χ27222-2-222-2-2000022-200002-2-22222-2-2-2-2-2-2002-2000000022-2-2000000002-22-2-2220000000000000000-22000000000002i−2i00−2i2i0000
χ28222-2-222-2-2000022-200002-2-22222-2-2-2-2-2-2002-2000000022-2-2000000002-22-2-2220000000000000000-2200000000000−2i2i002i−2i0000
χ2922-22-222-2-200002-2200002-2-22222-2-2-2-22200-220000000-2-22200000000-2-2222-2-20000000000000000-220000000002-2002-2000000
χ3022-22-222-2-200002-2200002-2-22222-2-2-2-22200-220000000-2-22200000000-2-2222-2-20000000000000000-22000000000-2200-22000000
χ3122-22-222-2-200002-2200002-2-22222-2-2-2-2-2-200-220000000-2-2220000000022-2-2-22200000000000000002-20000000002i−2i00−2i2i000000
χ3222-22-222-2-200002-2200002-2-22222-2-2-2-2-2-200-220000000-2-2220000000022-2-2-22200000000000000002-2000000000−2i2i002i−2i000000
χ3322-2-222222002-22-2-20000222222222222202-2-20000-200-2-2-2-2000000002-2-222222-20022-2-20000002-2-2-2000002-200000000000000
χ3422-2-222222002-22-2-2000022222222222-2-202-2-20000-200-2-2-2-200000000-222-2-2-2-22-20022-2-2000000-222200000-2200000000000000
χ3522-2-22222200-222-2-2000022222222222220-2-2-20000200-2-2-2-2000000002-2-22222-2200-2-222000000-22-2-200000-2200000000000000
χ3622-2-22222200-222-2-2000022222222222-2-20-2-2-20000200-2-2-2-200000000-222-2-2-2-2-2200-2-2220000002-222000002-200000000000000
χ3722-2-22-1-1-1-1002-2211−i3−i3i3i3222-1-1-1-1-1-1-1-1220-1-2-200001−i3i31111−i3−i3−i3−i3i3i3i3i32-2-2-1-1-1-12-200-1-111−i3−i3i3i3002-211−i3−i3i3i30-11−i3i3000000000000
χ3822-2-22-1-1-1-1002-2211−i3−i3i3i3222-1-1-1-1-1-1-1-1-2-20-1-2-200001−i3i31111−i3−i3−i3−i3i3i3i3i3-22211112-200-1-111−i3−i3i3i300-22-1-1i3i3−i3−i301-1i3−i3000000000000
χ3922-2-22-1-1-1-1002-2211i3i3−i3−i3222-1-1-1-1-1-1-1-1220-1-2-200001i3−i31111i3i3i3i3−i3−i3−i3−i32-2-2-1-1-1-12-200-1-111i3i3−i3−i3002-211i3i3−i3−i30-11i3−i3000000000000
χ4022-2-22-1-1-1-1002-2211i3i3−i3−i3222-1-1-1-1-1-1-1-1-2-20-1-2-200001i3−i31111i3i3i3i3−i3−i3−i3−i3-22211112-200-1-111i3i3−i3−i300-22-1-1−i3−i3i3i301-1−i3i3000000000000
χ4122-2-22-1-1-1-100-22211−i3−i3i3i3222-1-1-1-1-1-1-1-12201-2-20000-1i3−i31111−i3−i3−i3−i3i3i3i3i32-2-2-1-1-1-1-220011-1-1i3i3−i3−i300-2211−i3−i3i3i301-1i3−i3000000000000
χ4222-2-22-1-1-1-100-22211−i3−i3i3i3222-1-1-1-1-1-1-1-1-2-201-2-20000-1i3−i31111−i3−i3−i3−i3i3i3i3i3-2221111-220011-1-1i3i3−i3−i3002-2-1-1i3i3−i3−i30-11−i3i3000000000000
χ4322-2-22-1-1-1-100-22211i3i3−i3−i3222-1-1-1-1-1-1-1-12201-2-20000-1−i3i31111i3i3i3i3−i3−i3−i3−i32-2-2-1-1-1-1-220011-1-1−i3−i3i3i300-2211i3i3−i3−i301-1−i3i3000000000000
χ4422-2-22-1-1-1-100-22211i3i3−i3−i3222-1-1-1-1-1-1-1-1-2-201-2-20000-1−i3i31111i3i3i3i3−i3−i3−i3−i3-2221111-220011-1-1−i3−i3i3i3002-2-1-1−i3−i3i3i30-11i3−i3000000000000
χ454444444444444-1444444-1-1-1-1-1-1-1-1-1-1-10044-1-1-1-1-1-1444-1-1-1-1-1-1-1-1-1-1-1-10000000-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000000
χ4644444444444-4-4-1444444-1-1-1-1-1-1-1-1-1-1-100-4-4-1-1-1-1-1-1-4-4-4-1-1-1-1-1-1-1-1-1-1-1-10000000111111111111000000000000000000000000000
χ47444444444-4-444-144-4-4-4-4-1-1-1-1-1-1-1-1-1-1-100-44-1-111114-4-4-1-1-1-1111111110000000-1-111-1-1-1-11111000000000000000000000000000
χ48444444444-4-4-4-4-144-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1004-4-1-11111-444-1-1-1-111111111000000011-1-11111-1-1-1-1000000000000000000000000000
χ4944444-2-2-2-24444-1-2-2-2-2-2-2-1-1-11−i1521+i1521−i1521+i1521−i1521−i1521+i1521+i152004-2-1-1-1-1-1-1-2-2-21−i1521+i1521−i1521+i1521−i1521−i1521+i1521+i1521−i1521−i1521+i1521+i1520000000-1-1-1-11−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i152000000000000000000000000000
χ5044444-2-2-2-24444-1-2-2-2-2-2-2-1-1-11+i1521−i1521+i1521−i1521+i1521+i1521−i1521−i152004-2-1-1-1-1-1-1-2-2-21+i1521−i1521+i1521−i1521+i1521+i1521−i1521−i1521+i1521+i1521−i1521−i1520000000-1-1-1-11+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i152000000000000000000000000000
χ5144444-2-2-2-244-4-4-1-2-2-2-2-2-2-1-1-11−i1521+i1521−i1521+i1521−i1521−i1521+i1521+i15200-42-1-1-1-1-1-12221−i1521+i1521−i1521+i1521−i1521−i1521+i1521+i1521−i1521−i1521+i1521+i15200000001111−1+i152−1−i152−1+i152−1−i152−1+i152−1−i152−1+i152−1−i152000000000000000000000000000
χ5244444-2-2-2-244-4-4-1-2-2-2-2-2-2-1-1-11+i1521−i1521+i1521−i1521+i1521+i1521−i1521−i15200-42-1-1-1-1-1-12221+i1521−i1521+i1521−i1521+i1521+i1521−i1521−i1521+i1521+i1521−i1521−i15200000001111−1−i152−1+i152−1−i152−1+i152−1−i152−1+i152−1−i152−1+i152000000000000000000000000000
χ5344444-2-2-2-2-4-444-1-2-22222-1-1-11−i1521+i1521−i1521+i1521−i1521−i1521+i1521+i15200-4-2-1-11111-2221−i1521+i1521−i1521+i152−1+i152−1+i152−1−i152−1−i152−1+i152−1+i152−1−i152−1−i1520000000-1-1111−i1521+i1521−i1521+i152−1+i152−1−i152−1+i152−1−i152000000000000000000000000000
χ5444444-2-2-2-2-4-444-1-2-22222-1-1-11+i1521−i1521+i1521−i1521+i1521+i1521−i1521−i15200-4-2-1-11111-2221+i1521−i1521+i1521−i152−1−i152−1−i152−1+i152−1+i152−1−i152−1−i152−1+i152−1+i1520000000-1-1111+i1521−i1521+i1521−i152−1−i152−1+i152−1−i152−1+i152000000000000000000000000000
χ5544444-2-2-2-2-4-4-4-4-1-2-22222-1-1-11−i1521+i1521−i1521+i1521−i1521−i1521+i1521+i1520042-1-111112-2-21−i1521+i1521−i1521+i152−1+i152−1+i152−1−i152−1−i152−1+i152−1+i152−1−i152−1−i152000000011-1-1−1+i152−1−i152−1+i152−1−i1521−i1521+i1521−i1521+i152000000000000000000000000000
χ5644444-2-2-2-2-4-4-4-4-1-2-22222-1-1-11+i1521−i1521+i1521−i1521+i1521+i1521−i1521−i1520042-1-111112-2-21+i1521−i1521+i1521−i152−1−i152−1−i152−1+i152−1+i152−1−i152−1−i152−1+i152−1+i152000000011-1-1−1−i152−1+i152−1−i152−1+i1521+i1521−i1521+i1521−i152000000000000000000000000000
χ57444-4-4-2-22200004-2200004-4-4-2-2-2-2222244004-40000000-2-22200000000-44-4-2-2220000000000000000-22000000000000000000000
χ58444-4-4-2-22200004-2200004-4-4-2-2-2-22222-4-4004-40000000-2-222000000004-4422-2-200000000000000002-2000000000000000000000
χ5944-44-4-2-222000042-200004-4-4-2-2-2-222224400-44000000022-2-200000000-4-44-2-22200000000000000002-2000000000000000000000
χ6044-44-4-2-222000042-200004-4-4-2-2-2-22222-4-400-44000000022-2-20000000044-422-2-20000000000000000-22000000000000000000000
χ6144-4-444444004-4-1-4-40000-1-1-1-1-1-1-1-1-1-1-1000411−5−555-4001111−5−55555−5−50000000-11−55-1-111−555−5000000000000000000000000000
χ6244-4-444444004-4-1-4-40000-1-1-1-1-1-1-1-1-1-1-100041155−5−5-400111155−5−5−5−5550000000-115−5-1-1115−5−55000000000000000000000000000
χ6344-4-44444400-44-1-4-40000-1-1-1-1-1-1-1-1-1-1-1000-411−5−5554001111−5−55555−5−500000001-15−511-1-15−5−55000000000000000000000000000
χ6444-4-44444400-44-1-4-40000-1-1-1-1-1-1-1-1-1-1-1000-41155−5−5400111155−5−5−5−55500000001-1−5511-1-1−555−5000000000000000000000000000
χ6544-4-44-2-2-2-2004-4-122−2i3−2i32i32i3-1-1-11−i1521+i1521−i1521+i1521−i1521−i1521+i1521+i152000-21155−5−52−2i32i3−1+i152−1−i152−1+i152−1−i152ζ14−ζ22+ζ26−ζ58ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46ζ2−ζ34+ζ38−ζ46−ζ14+ζ22−ζ26+ζ58−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46−ζ2+ζ34−ζ38+ζ460000000-115−51−i1521+i152−1+i152−1−i152ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46000000000000000000000000000
χ6644-4-44-2-2-2-2004-4-122−2i3−2i32i32i3-1-1-11+i1521−i1521+i1521−i1521+i1521+i1521−i1521−i152000-211−5−5552−2i32i3−1−i152−1+i152−1−i152−1+i152ζ2−ζ34+ζ38−ζ46ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58ζ14−ζ22+ζ26−ζ58−ζ2+ζ34−ζ38+ζ46−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58−ζ14+ζ22−ζ26+ζ580000000-11−551+i1521−i152−1−i152−1+i152ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58000000000000000000000000000
χ6744-4-44-2-2-2-2004-4-1222i32i3−2i3−2i3-1-1-11−i1521+i1521−i1521+i1521−i1521−i1521+i1521+i152000-211−5−55522i3−2i3−1+i152−1−i152−1+i152−1−i152−ζ14+ζ22−ζ26+ζ58−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46−ζ2+ζ34−ζ38+ζ46ζ14−ζ22+ζ26−ζ58ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46ζ2−ζ34+ζ38−ζ460000000-11−551−i1521+i152−1+i152−1−i152−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46000000000000000000000000000
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Here ζ is a primitive root of unity of order 60 (ζ60 = 1); i = ζ15.