Finite Group Databasebeta

← Group #14302576

Character table — Group #14302576

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size112222244444444444558888888888888888810101010101616161616161616161616161616161616162020202020303030304040404040404040606060606060120120120120
order1223446245610121215153030442666810122020242430306060606022412121010102030303030303040406060120120120120246612444446812121224244444444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111-11-1-1-11111-1-1111111111111-1-1111-1-1-1-1-1-111-1-1-1-1111111111-11-11-1-1-1-1111111-1-1-1-1
χ411111111111111111111-11-1-1-11111-1-1111111111111-1-1111-1-1-1-1-1-111-1-1-1-111111-1-1-1-1-11-11-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111-1-111111111111111111-1-1-1-1-1111111111111111111-1-1-1-1-1ii−i−i-1-1-1-1-1-1-1-1iii−i−i−ii−ii−i
χ6111111111111111111-1-111111111111111111-1-1-1-1-1111111111111111111-1-1-1-1-1−i−iii-1-1-1-1-1-1-1-1−i−i−iiii−ii−ii
χ7111111111111111111-1-1-11-1-1-11111-1-1111111-1-1-1-1-11-1-1111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1ii−i−i1-11-11111iii−i−i−i−ii−ii
χ8111111111111111111-1-1-11-1-1-11111-1-1111111-1-1-1-1-11-1-1111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1−i−iii1-11-11111−i−i−iiiii−ii−i
χ91111111-1-1111111111111-111-11-111-1-111111111111-111-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-111-1-11-1-11-1-1-1-111
χ101111111-1-1111111111111-111-11-111-1-111111111111-111-1-1-11111-1-1-1-1-1-1-1-1-1-1111-1-1-1-11-1-1-111-1-1-111-11111-1-1
χ111111111-1-111111111111-1-1-1-111-1111111111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111111-1-11-1-1-1111-1-11-1-111-1-1
χ121111111-1-111111111111-1-1-1-111-1111111111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1111-1-1-1-1-1-11-1-1-111-111-111-1-111
χ131111111-1-1111111111-1-11-111-11-111-1-1111111-1-1-1-1-1-111-1-1-11111-1-1-1-1-1-1-1-111-1-1-1ii−i−i-1111-1-111i−i−i−iii−iii−i
χ141111111-1-1111111111-1-11-111-11-111-1-1111111-1-1-1-1-1-111-1-1-11111-1-1-1-1-1-1-1-111-1-1-1−i−iii-1111-1-111−iiii−i−ii−i−ii
χ151111111-1-1111111111-1-1-1-1-1-111-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1ii−i−i11-1111-1-1i−i−i−iiii−i−ii
χ161111111-1-1111111111-1-1-1-1-1-111-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1−i−iii11-1111-1-1−iiii−i−i−iii−i
χ172222-2-2200222-2-22222220000020-2-20022-2-2-2-2-2-222200000000000000000000-2-2200000000000002i−2i02i−2i0000
χ182222-2-2200222-2-22222220000020-2-20022-2-2-2-2-2-222200000000000000000000-2-220000000000000−2i2i0−2i2i0000
χ192222-2-2200222-2-22222-2-20000020-2-20022-2-2-2-222-2-2-20000000000000000000022-200000000000002-20-220000
χ202222-2-2200222-2-22222-2-20000020-2-20022-2-2-2-222-2-2-20000000000000000000022-20000000000000-2202-20000
χ21222-122-1222-12-1-1-1-1-1-1222-1-1-122-122-1-1-1-1-1-1-1-1222-1-12222-1-1-1-1-1-122-1-1-1-1-1-122-1-1-100002-12-1-1-1-1-10000000000
χ22222-122-1222-12-1-1-1-1-1-122-2-111-22-12211-1-1-1-1-1-1222-1-12-2-22-1-11111-2-2-1-1111122-1-1-10000-2-1-2-111110000000000
χ23222-122-1222-12-1-1-1-1-1-1-2-22-1-1-122-122-1-1-1-1-1-1-1-1-2-2-2112222-1-1-1-1-1-122-1-1-1-1-1-1-2-21110000-21-2111110000000000
χ24222-122-1222-12-1-1-1-1-1-1-2-2-2-111-22-12211-1-1-1-1-1-1-2-2-2112-2-22-1-11111-2-2-1-11111-2-211100002121-1-1-1-10000000000
χ25222-122-1-2-22-12-1-1-1-1-1-12221-1-1-2212211-1-1-1-1-1-1222-1-1-222-211-1-1-1-1-2-2111111-2-2-1-1-1000021-21-1-1110000000000
χ26222-122-1-2-22-12-1-1-1-1-1-122-211122122-1-1-1-1-1-1-1-1222-1-1-2-2-2-21111112211-1-1-1-1-2-2-1-1-10000-212111-1-10000000000
χ27222-122-1-2-22-12-1-1-1-1-1-1-2-221-1-1-2212211-1-1-1-1-1-1-2-2-211-222-211-1-1-1-1-2-2111111221110000-2-12-111-1-10000000000
χ28222-122-1-2-22-12-1-1-1-1-1-1-2-2-211122122-1-1-1-1-1-1-1-1-2-2-211-2-2-2-21111112211-1-1-1-12211100002-1-2-1-1-1110000000000
χ2922-222-22002-222-222222200000-202-200-2-222-2-2-22-222000000000000000000002-2-2222200000000-200-2000000
χ3022-222-22002-222-222222200000-202-200-2-222-2-2-22-222000000000000000000002-2-2-2-2-2-2000000002002000000
χ3122-222-22002-222-22222-2-200000-202-200-2-222-2-22-22-2-200000000000000000000-2222i2i−2i−2i00000000−2i002i000000
χ3222-222-22002-222-22222-2-200000-202-200-2-222-2-22-22-2-200000000000000000000-222−2i−2i2i2i000000002i00−2i000000
χ3322-22-2222-22-22-2222222202000-2-2-2200-2-2-2-2222-2-222200-222000000-2-20000-22-22-200000-20200000000000000
χ3422-22-2222-22-22-222222-2-202000-2-2-2200-2-2-2-222-222-2-2200-222000000-2-200002-22-220000020-200000000000000
χ3522-22-222-222-22-222222220-2000-22-2200-2-2-2-2222-2-222-2002-2-20000002200002-2-22-20000020-200000000000000
χ3622-22-222-222-22-222222-2-20-2000-22-2200-2-2-2-222-222-2-2-2002-2-2000000220000-222-2200000-20200000000000000
χ3722-2-1-22-12-22121-1-1-1-1-1220-1−i3i30-21-22−i3i31111-1-12-2-2-1-1200-2-1-1−i3−i3i3i30011−i3−i3i3i3-221-110000010-1−i3i3−i3i30000000000
χ3822-2-1-22-12-22121-1-1-1-1-1220-1i3−i30-21-22i3−i31111-1-12-2-2-1-1200-2-1-1i3i3−i3−i30011i3i3−i3−i3-221-110000010-1i3−i3i3−i30000000000
χ3922-2-1-22-12-22121-1-1-1-1-1-2-20-1−i3i30-21-22−i3i31111-1-1-22211200-2-1-1−i3−i3i3i30011−i3−i3i3i32-2-11-100000-101i3−i3i3−i30000000000
χ4022-2-1-22-12-22121-1-1-1-1-1-2-20-1i3−i30-21-22i3−i31111-1-1-22211200-2-1-1i3i3−i3−i30011i3i3−i3−i32-2-11-100000-101−i3i3−i3i30000000000
χ4122-2-1-22-1-222121-1-1-1-1-12201−i3i30-2-1-22i3−i31111-1-12-2-2-1-1-200211−i3−i3i3i300-1-1i3i3−i3−i32-21-1100000-101−i3i3i3−i30000000000
χ4222-2-1-22-1-222121-1-1-1-1-12201i3−i30-2-1-22−i3i31111-1-12-2-2-1-1-200211i3i3−i3−i300-1-1−i3−i3i3i32-21-1100000-101i3−i3−i3i30000000000
χ4322-2-1-22-1-222121-1-1-1-1-1-2-201−i3i30-2-1-22i3−i31111-1-1-22211-200211−i3−i3i3i300-1-1i3i3−i3−i3-22-11-10000010-1i3−i3−i3i30000000000
χ4422-2-1-22-1-222121-1-1-1-1-1-2-201i3−i30-2-1-22−i3i31111-1-1-22211-200211i3i3−i3−i300-1-1−i3−i3i3i3-22-11-10000010-1−i3i3i3−i30000000000
χ45444444444-14-144-1-1-1-10044444-14-1-144-1-1-1-1-1-100000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000000
χ46444444444-14-144-1-1-1-100-44-4-4-4-14-1-1-4-4-1-1-1-1-1-100000-111-1-1-1111111-1-11111000000000000000000000000000
χ474444444-4-4-14-144-1-1-1-1004-444-4-1-4-1-1-4-4-1-1-1-1-1-1000001-1-1111-1-1-1-111111111000000000000000000000000000
χ484444444-4-4-14-144-1-1-1-100-4-4-4-44-1-4-1-144-1-1-1-1-1-1000001111111111-1-111-1-1-1-1000000000000000000000000000
χ49444-244-244-1-2-1-2-21−i1521+i1521−i1521+i152004-2-2-24-1-2-1-1-2-21−i1521+i1521−i1521+i1521−i1521+i15200000-1-1-1-11−i1521+i1521−i1521+i1521−i1521+i152-1-11−i1521+i1521−i1521+i1521−i1521+i152000000000000000000000000000
χ50444-244-244-1-2-1-2-21−i1521+i1521−i1521+i15200-4-222-4-1-2-1-1221−i1521+i1521−i1521+i1521−i1521+i15200000-111-11−i1521+i152−1+i152−1−i152−1+i152−1−i152111−i1521+i152−1+i152−1−i152−1+i152−1−i152000000000000000000000000000
χ51444-244-244-1-2-1-2-21+i1521−i1521+i1521−i152004-2-2-24-1-2-1-1-2-21+i1521−i1521+i1521−i1521+i1521−i15200000-1-1-1-11+i1521−i1521+i1521−i1521+i1521−i152-1-11+i1521−i1521+i1521−i1521+i1521−i152000000000000000000000000000
χ52444-244-244-1-2-1-2-21+i1521−i1521+i1521−i15200-4-222-4-1-2-1-1221+i1521−i1521+i1521−i1521+i1521−i15200000-111-11+i1521−i152−1−i152−1+i152−1−i152−1+i152111+i1521−i152−1−i152−1+i152−1−i152−1+i152000000000000000000000000000
χ53444-244-2-4-4-1-2-1-2-21−i1521+i1521−i1521+i1520042-2-2-4-12-1-1221−i1521+i1521−i1521+i1521−i1521+i152000001-1-11−1+i152−1−i1521−i1521+i1521−i1521+i15211−1+i152−1−i152−1+i152−1−i152−1+i152−1−i152000000000000000000000000000
χ54444-244-2-4-4-1-2-1-2-21−i1521+i1521−i1521+i15200-42224-12-1-1-2-21−i1521+i1521−i1521+i1521−i1521+i152000001111−1+i152−1−i152−1+i152−1−i152−1+i152−1−i152-1-1−1+i152−1−i1521−i1521+i1521−i1521+i152000000000000000000000000000
χ55444-244-2-4-4-1-2-1-2-21+i1521−i1521+i1521−i1520042-2-2-4-12-1-1221+i1521−i1521+i1521−i1521+i1521−i152000001-1-11−1−i152−1+i1521+i1521−i1521+i1521−i15211−1−i152−1+i152−1−i152−1+i152−1−i152−1+i152000000000000000000000000000
χ56444-244-2-4-4-1-2-1-2-21+i1521−i1521+i1521−i15200-42224-12-1-1-2-21+i1521−i1521+i1521−i1521+i1521−i152000001111−1−i152−1+i152−1−i152−1+i152−1−i152−1+i152-1-1−1−i152−1+i1521+i1521−i1521+i1521−i152000000000000000000000000000
χ57444-2-4-4-2004-2422-2-2-2-2440000040-4-400-2-22222-4-44-2-20000000000000000000022-20000000000000000000000
χ58444-2-4-4-2004-2422-2-2-2-2-4-40000040-4-400-2-2222244-42200000000000000000000-2-220000000000000000000000
χ5944-44-4444-4-1-4-1-44-1-1-1-100040001-41-1001111-1-100000-1−551-1-1−555−5−5511−555−5000000000000000000000000000
χ6044-44-4444-4-1-4-1-44-1-1-1-100040001-41-1001111-1-100000-15−51-1-15−5−555−5115−5−55000000000000000000000000000
χ6144-44-444-44-1-4-1-44-1-1-1-1000-4000141-1001111-1-1000001−55-111−555−55−5-1-15−5−55000000000000000000000000000
χ6244-44-444-44-1-4-1-44-1-1-1-1000-4000141-1001111-1-10000015−5-1115−5−55−55-1-1−555−5000000000000000000000000000
χ6344-4-24-4-200424-22-2-2-2-24400000-404-40022-2-222-44-4-2-200000000000000000000-2220000000000000000000000
χ6444-4-24-4-200424-22-2-2-2-2-4-400000-404-40022-2-2224-4422000000000000000000002-2-20000000000000000000000
χ6544-4-2-44-24-4-12-12-21−i1521+i1521−i1521+i152000-2−2i32i30121-1−2i32i3−1+i152−1−i152−1+i152−1−i1521−i1521+i15200000-15−511−i1521+i152ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ465−5−1+i152−1−i152ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46000000000000000000000000000
χ6644-4-2-44-24-4-12-12-21−i1521+i1521−i1521+i152000-22i3−2i30121-12i3−2i3−1+i152−1−i152−1+i152−1−i1521−i1521+i15200000-1−5511−i1521+i152−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46−55−1+i152−1−i152−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46000000000000000000000000000
χ6744-4-2-44-24-4-12-12-21+i1521−i1521+i1521−i152000-2−2i32i30121-1−2i32i3−1−i152−1+i152−1−i152−1+i1521+i1521−i15200000-1−5511+i1521−i152ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58−55−1−i152−1+i152ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58000000000000000000000000000
χ6844-4-2-44-24-4-12-12-21+i1521−i1521+i1521−i152000-22i3−2i30121-12i3−2i3−1−i152−1+i152−1−i152−1+i1521+i1521−i15200000-15−511+i1521−i152−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ585−5−1−i152−1+i152−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58000000000000000000000000000
χ6944-4-2-44-2-44-12-12-21−i1521+i1521−i1521+i1520002−2i32i301-21-12i3−2i3−1+i152−1−i152−1+i152−1−i1521−i1521+i1520000015−5-1−1+i152−1−i152ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46−551−i1521+i152−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46000000000000000000000000000
χ7044-4-2-44-2-44-12-12-21−i1521+i1521−i1521+i15200022i3−2i301-21-1−2i32i3−1+i152−1−i152−1+i152−1−i1521−i1521+i152000001−55-1−1+i152−1−i152−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ465−51−i1521+i152ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46000000000000000000000000000
χ7144-4-2-44-2-44-12-12-21+i1521−i1521+i1521−i1520002−2i32i301-21-12i3−2i3−1−i152−1+i152−1−i152−1+i1521+i1521−i152000001−55-1−1−i152−1+i152ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ585−51+i1521−i152−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58000000000000000000000000000
χ7244-4-2-44-2-44-12-12-21+i1521−i1521+i1521−i15200022i3−2i301-21-1−2i32i3−1−i152−1+i152−1−i152−1+i1521+i1521−i1520000015−5-1−1−i152−1+i152−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58−551+i1521−i152ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58000000000000000000000000000
χ734-40400-40040-40044-4-44i−4i000000000000000000004i−4i000000000000000000000002+2i−2−2i2−2i−2+2i000000000000000000
χ744-40400-40040-40044-4-44i−4i000000000000000000004i−4i00000000000000000000000−2−2i2+2i−2+2i2−2i000000000000000000
χ754-40400-40040-40044-4-4−4i4i00000000000000000000−4i4i000000000000000000000002−2i−2+2i2+2i−2−2i000000000000000000
χ764-40400-40040-40044-4-4−4i4i00000000000000000000−4i4i00000000000000000000000−2+2i2−2i−2−2i2+2i000000000000000000
χ778888-8-8800-28-2-8-8-2-2-2-20000000-202200-2-2222200000000000000000000000000000000000000000000000000
χ78888-4-8-8-400-2-4-2441−i151+i151−i151+i150000000-2022001−i151+i15−1+i15−1−i15−1+i15−1−i1500000000000000000000000000000000000000000000000000
χ79888-4-8-8-400-2-4-2441+i151−i151+i151−i150000000-2022001+i151−i15−1−i15−1+i15−1−i15−1+i1500000000000000000000000000000000000000000000000000
χ8088-888-8800-2-8-28-8-2-2-2-2000000020-220022-2-22200000000000000000000000000000000000000000000000000
χ8188-8-48-8-400-24-2-441−i151+i151−i151+i15000000020-2200−1+i15−1−i151−i151+i15−1+i15−1−i1500000000000000000000000000000000000000000000000000
χ8288-8-48-8-400-24-2-441+i151−i151+i151−i15000000020-2200−1−i15−1+i151+i151−i15−1−i15−1+i1500000000000000000000000000000000000000000000000000
χ838-80-40040080-800-4-4448i−8i00000000000000000000−4i4i000000000000000000000000000000000000000000000
χ848-80-40040080-800-4-444−8i8i000000000000000000004i−4i000000000000000000000000000000000000000000000
χ8516-1601600-1600-40400-4-444000000000000000000000000000000000000000000000000000000000000000000000
χ8616-160-800800-404002−2i152+2i15−2+2i15−2−2i15000000000000000000000000000000000000000000000000000000000000000000000
χ8716-160-800800-404002+2i152−2i15−2−2i15−2+2i15000000000000000000000000000000000000000000000000000000000000000000000

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