Finite Group Databasebeta

← Group #14301715

Character table — Group #14301715

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size11222222244444444444444444444445588888888888888888888888101010101010101616161616161616161616162020202020202020202040404040406060606060606060120120120120
order122223666244456610101012121212151530303030303044461010121212202020203030303060606060606060604441212121210202020303060606060606022246666121246121212888888888888
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
χ511111111111-1-1111111-1-1-1-11111111111-1111-1-11-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1111-1-1-1-1111-1-11-1-1-1-111-11-1-1111111111-1-1-1-1
χ611111111111-1-1111111-1-1-1-11111111111-1111-1-11-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1111-1-1-1-1111-1-11-1-1-1-111-11-1-11-1-1-1-1-1-1-1-11111
χ711111111111-1-1111111-1-1-1-111111111-1-1-1111-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-1-1-111-111-11111-1-11-111-1iiii−i−i−i−i−i−iii
χ811111111111-1-1111111-1-1-1-111111111-1-1-1111-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-1-1-111-111-11111-1-11-111-1−i−i−i−iiiiiii−i−i
χ9111111111-1-11111111111111111111111-1-111-1-1-111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1111111-1-1-1-1-111-1-111-1-11-11-1
χ10111111111-1-11111111111111111111111-1-111-1-1-111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1111111-1-1-1-1-1-1-111-1-111-11-11
χ11111111111-1-111111111111111111111-1-1-1-111-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-111111ii−i−i−i−iiii−i−ii
χ12111111111-1-111111111111111111111-1-1-1-111-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-111111−i−iiiii−i−i−iii−i
χ13111111111-1-1-1-1111111-1-1-1-111111111111-11111-1-1-1-1-11111-1-1-1-1-1-1-1-11111111-111-1-1-11111-1-1-1-1-1-1-1-1-1-1111-111-111-1-111-1-1-11-11
χ14111111111-1-1-1-1111111-1-1-1-111111111111-11111-1-1-1-1-11111-1-1-1-1-1-1-1-11111111-111-1-1-11111-1-1-1-1-1-1-1-1-1-1111-111-1-1-111-1-1111-11-1
χ15111111111-1-1-1-1111111-1-1-1-111111111-1-11-11111-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11111-1-111111111-1-1-11-1-11ii−i−i−i−iii−iii−i
χ16111111111-1-1-1-1111111-1-1-1-111111111-1-11-11111-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11111-1-111111111-1-1-11-1-11−i−iiiii−i−ii−i−ii
χ1722222-1-1-1-122222-1-1222-1-1-1-1-1-1-1-1-1-1-1-1222-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1222-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-12-1-1-1-1000000000000
χ1822222-1-1-1-122222-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-2-22-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-211112222-1-1-1-1-1-1-1-1-2-2-2-2111111-21111000000000000
χ1922222-1-1-1-122-2-22-1-12221111-1-1-1-1-1-1-1-122-2-12211-1-2-2-2-2-1-1-1-111111111222-1-1-1-12-2-22-1-11111-1-12-2-221111-1-1-2-111-1000000000000
χ2022222-1-1-1-122-2-22-1-12221111-1-1-1-1-1-1-1-1-2-2-2-12211-1-2-2-2-2-1-1-1-111111111-2-2-211112-2-22-1-11111-1-1-222-2-1-1-1-11121-1-11000000000000
χ2122222-1-1-1-1-2-2222-1-1222-1-1-1-1-1-1-1-1-1-1-1-122-21221112222-1-1-1-1-1-1-1-1-1-1-1-1222-1-1-1-1-2-2-2-211111111-222-2-1-1-1-1-1-1-21111000000000000
χ2222222-1-1-1-1-2-2222-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-21221112222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-21111-2-2-2-2111111112-2-221111112-1-1-1-1000000000000
χ2322222-1-1-1-1-2-2-2-22-1-12221111-1-1-1-1-1-1-1-1222122-1-11-2-2-2-2-1-1-1-111111111222-1-1-1-1-222-211-1-1-1-111-2-2-2-21111-1-121-1-11000000000000
χ2422222-1-1-1-1-2-2-2-22-1-12221111-1-1-1-1-1-1-1-1-2-22122-1-11-2-2-2-2-1-1-1-111111111-2-2-21111-222-211-1-1-1-1112222-1-1-1-111-2-111-1000000000000
χ25222-2-22-2-22000022-2-2-22000022-2-2-2-22222002-2000000022-2-200000000-22-222-2-2000000000000000000002-200000002-2002-20000
χ26222-2-22-2-22000022-2-2-22000022-2-2-2-22222002-2000000022-2-200000000-22-222-2-2000000000000000000002-20000000-2200-220000
χ27222-2-22-2-22000022-2-2-22000022-2-2-2-222-2-2002-2000000022-2-2000000002-22-2-22200000000000000000000-2200000002i−2i00−2i2i0000
χ28222-2-22-2-22000022-2-2-22000022-2-2-2-222-2-2002-2000000022-2-2000000002-22-2-22200000000000000000000-220000000−2i2i002i−2i0000
χ2922-22-22-2-2200002-22-2-22000022-2-2-2-2222200-220000000-2-22200000000-2-2222-2-200000000000000000000-22000002-2002-2000000
χ3022-22-22-2-2200002-22-2-22000022-2-2-2-2222200-220000000-2-22200000000-2-2222-2-200000000000000000000-2200000-2200-22000000
χ3122-22-22-2-2200002-22-2-22000022-2-2-2-222-2-200-220000000-2-2220000000022-2-2-222000000000000000000002-2000002i−2i00−2i2i000000
χ3222-22-22-2-2200002-22-2-22000022-2-2-2-222-2-200-220000000-2-2220000000022-2-2-222000000000000000000002-200000−2i2i002i−2i000000
χ3322-2-2222222-2002-2-22220000222222222202-2-200-20000-2-2-2-2000000002-2-22222200-2220000-2-2-20020000-2-20-2002000000000000
χ3422-2-2222222-2002-2-2222000022222222-2-202-2-200-20000-2-2-2-200000000-222-2-2-2-2200-2220000-2-2200-20000220200-2000000000000
χ3522-2-222222-22002-2-2222000022222222220-2-2-20020000-2-2-2-2000000002-2-22222-2002-2-2000022200-20000-2-20200-2000000000000
χ3622-2-222222-22002-2-2222000022222222-2-20-2-2-20020000-2-2-2-200000000-222-2-2-2-2-2002-2-2000022-20020000220-2002000000000000
χ3722-2-22-1-1-1-12-200211222−i3−i3i3i3-1-1-1-1-1-1-1-1220-1-2-2−i3i3100001111−i3−i3−i3−i3i3i3i3i32-2-2-1-1-1-1200-2-1-1−i3−i3i3i311-2002−i3−i3i3i31101−i3i3-1000000000000
χ3822-2-22-1-1-1-12-200211222−i3−i3i3i3-1-1-1-1-1-1-1-1-2-20-1-2-2−i3i3100001111−i3−i3−i3−i3i3i3i3i3-2221111200-2-1-1−i3−i3i3i311200-2i3i3−i3−i3-1-10-1i3−i31000000000000
χ3922-2-22-1-1-1-12-200211222i3i3−i3−i3-1-1-1-1-1-1-1-1220-1-2-2i3−i3100001111i3i3i3i3−i3−i3−i3−i32-2-2-1-1-1-1200-2-1-1i3i3−i3−i311-2002i3i3−i3−i31101i3−i3-1000000000000
χ4022-2-22-1-1-1-12-200211222i3i3−i3−i3-1-1-1-1-1-1-1-1-2-20-1-2-2i3−i3100001111i3i3i3i3−i3−i3−i3−i3-2221111200-2-1-1i3i3−i3−i311200-2−i3−i3i3i3-1-10-1−i3i31000000000000
χ4122-2-22-1-1-1-1-2200211222−i3−i3i3i3-1-1-1-1-1-1-1-12201-2-2i3−i3-100001111−i3−i3−i3−i3i3i3i3i32-2-2-1-1-1-1-200211i3i3−i3−i3-1-1200-2−i3−i3i3i3110-1i3−i31000000000000
χ4222-2-22-1-1-1-1-2200211222−i3−i3i3i3-1-1-1-1-1-1-1-1-2-201-2-2i3−i3-100001111−i3−i3−i3−i3i3i3i3i3-2221111-200211i3i3−i3−i3-1-1-2002i3i3−i3−i3-1-101−i3i3-1000000000000
χ4322-2-22-1-1-1-1-2200211222i3i3−i3−i3-1-1-1-1-1-1-1-12201-2-2−i3i3-100001111i3i3i3i3−i3−i3−i3−i32-2-2-1-1-1-1-200211−i3−i3i3i3-1-1200-2i3i3−i3−i3110-1−i3i31000000000000
χ4422-2-22-1-1-1-1-2200211222i3i3−i3−i3-1-1-1-1-1-1-1-1-2-201-2-2−i3i3-100001111i3i3i3i3−i3−i3−i3−i3-2221111-200211−i3−i3i3i3-1-1-2002−i3−i3i3i3-1-101i3−i3-1000000000000
χ454444444444444-144-1-1-14444-1-1-1-1-1-1-1-10044-1-1444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000000
χ4644444444444-4-4-144-1-1-1-4-4-4-4-1-1-1-1-1-1-1-100-44-1-1-4-441111-1-1-1-1111111110000000-111-1-1-11111-1-1000000000000000000000000000
χ47444444444-4-444-144-1-1-14444-1-1-1-1-1-1-1-100-4-4-1-1-4-4-4-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000111111111111000000000000000000000000000
χ48444444444-4-4-4-4-144-1-1-1-4-4-4-4-1-1-1-1-1-1-1-1004-4-1-144-41111-1-1-1-11111111100000001-1-1111-1-1-1-111000000000000000000000000000
χ4944444-2-2-2-24444-1-2-2-1-1-1-2-2-2-21−i1521+i1521−i1521−i1521+i1521+i1521−i1521+i152004-2-1-1-2-2-2-1-1-1-11−i1521+i1521−i1521+i1521−i1521−i1521+i1521+i1521−i1521−i1521+i1521+i1520000000-1-1-1-11−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i152000000000000000000000000000
χ5044444-2-2-2-24444-1-2-2-1-1-1-2-2-2-21+i1521−i1521+i1521+i1521−i1521−i1521+i1521−i152004-2-1-1-2-2-2-1-1-1-11+i1521−i1521+i1521−i1521+i1521+i1521−i1521−i1521+i1521+i1521−i1521−i1520000000-1-1-1-11+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i152000000000000000000000000000
χ5144444-2-2-2-244-4-4-1-2-2-1-1-122221−i1521+i1521−i1521−i1521+i1521+i1521−i1521+i15200-4-2-1-122-211111−i1521+i1521−i1521+i152−1+i152−1+i152−1−i152−1−i152−1+i152−1+i152−1−i152−1−i1520000000-111-11−i1521+i152−1+i152−1−i152−1+i152−1−i1521−i1521+i152000000000000000000000000000
χ5244444-2-2-2-244-4-4-1-2-2-1-1-122221+i1521−i1521+i1521+i1521−i1521−i1521+i1521−i15200-4-2-1-122-211111+i1521−i1521+i1521−i152−1−i152−1−i152−1+i152−1+i152−1−i152−1−i152−1+i152−1+i1520000000-111-11+i1521−i152−1−i152−1+i152−1−i152−1+i1521+i1521−i152000000000000000000000000000
χ5344444-2-2-2-2-4-444-1-2-2-1-1-1-2-2-2-21−i1521+i1521−i1521−i1521+i1521+i1521−i1521+i15200-42-1-1222-1-1-1-11−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
χ5444444-2-2-2-2-4-444-1-2-2-1-1-1-2-2-2-21+i1521−i1521+i1521+i1521−i1521−i1521+i1521−i15200-42-1-1222-1-1-1-11+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
χ5544444-2-2-2-2-4-4-4-4-1-2-2-1-1-122221−i1521+i1521−i1521−i1521+i1521+i1521−i1521+i1520042-1-1-2-2211111−i1521+i1521−i1521+i152−1+i152−1+i152−1−i152−1−i152−1+i152−1+i152−1−i152−1−i15200000001-1-11−1+i152−1−i1521−i1521+i1521−i1521+i152−1+i152−1−i152000000000000000000000000000
χ5644444-2-2-2-2-4-4-4-4-1-2-2-1-1-122221+i1521−i1521+i1521+i1521−i1521−i1521+i1521−i1520042-1-1-2-2211111+i1521−i1521+i1521−i152−1−i152−1−i152−1+i152−1+i152−1−i152−1−i152−1+i152−1+i15200000001-1-11−1−i152−1+i1521+i1521−i1521+i1521−i152−1−i152−1+i152000000000000000000000000000
χ57444-4-4-222-200004-22-4-440000-2-22222-2-244004-40000000-2-22200000000-44-4-2-22200000000000000000000-2200000000000000000
χ58444-4-4-222-200004-22-4-440000-2-22222-2-2-4-4004-40000000-2-222000000004-4422-2-2000000000000000000002-200000000000000000
χ5944-44-4-222-2000042-2-4-440000-2-22222-2-24400-44000000022-2-200000000-4-44-2-222000000000000000000002-200000000000000000
χ6044-44-4-222-2000042-2-4-440000-2-22222-2-2-4-400-44000000022-2-20000000044-422-2-200000000000000000000-2200000000000000000
χ6144-4-4444444-400-1-4-4-1-1-10000-1-1-1-1-1-1-1-100041100-4−5−5551111−5−55555−5−50000000-1−551-1-1−555−511000000000000000000000000000
χ6244-4-4444444-400-1-4-4-1-1-10000-1-1-1-1-1-1-1-100041100-455−5−5111155−5−5−5−5550000000-15−51-1-15−5−5511000000000000000000000000000
χ6344-4-444444-4400-1-4-4-1-1-10000-1-1-1-1-1-1-1-1000-411004−5−5551111−5−55555−5−5000000015−5-1115−5−55-1-1000000000000000000000000000
χ6444-4-444444-4400-1-4-4-1-1-10000-1-1-1-1-1-1-1-1000-41100455−5−5111155−5−5−5−55500000001−55-111−555−5-1-1000000000000000000000000000
χ6544-4-44-2-2-2-24-400-122-1-1-1−2i3−2i32i32i31−i1521+i1521−i1521−i1521+i1521+i1521−i1521+i152000-211−2i32i3255−5−5−1+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+ζ460000000-15−511−i1521+i152ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46−1+i152−1−i152000000000000000000000000000
χ6644-4-44-2-2-2-24-400-122-1-1-1−2i3−2i32i32i31+i1521−i1521+i1521+i1521−i1521−i1521+i1521−i152000-211−2i32i32−5−555−1−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+ζ580000000-1−5511+i1521−i152ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58−1−i152−1+i152000000000000000000000000000
χ6744-4-44-2-2-2-24-400-122-1-1-12i32i3−2i3−2i31−i1521+i1521−i1521−i1521+i1521+i1521−i1521+i152000-2112i3−2i32−5−555−1+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−ζ460000000-1−5511−i1521+i152−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46−1+i152−1−i152000000000000000000000000000
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Here ζ is a primitive root of unity of order 60 (ζ60 = 1); i = ζ15.