Finite Group Databasebeta

← Group #14512490

Character table — Group #14512490

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size112444444444668888101012161616161616161616161616161616161616202424242430306080808080120120120120120120120120
order1222510101010101010443666444661515303030303030303030303030303022020202022466121244448888
χ111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111-1-11111111111111111111-11111-1-1-1-1-1-1-1ii−i−iii−i−i
χ4111111111111111111-1-11111111111111111111-11111-1-1-1-1-1-1-1−i−iii−i−iii
χ5111-1111-1-1-1-1111111111-1-1-111111111-1-1-1-1-1-1-1-1-111-1-111-1-1-1111-11-11-11-1
χ6111-1111-1-1-1-1111111111-1-1-111111111-1-1-1-1-1-1-1-1-111-1-111-1-1-111-11-11-11-11
χ7111-1111-1-1-1-11111111-1-1-1-1-111111111-1-1-1-1-1-1-1-1111-1-1-1-1111-1-1i−i−iii−i−ii
χ8111-1111-1-1-1-11111111-1-1-1-1-111111111-1-1-1-1-1-1-1-1111-1-1-1-1111-1-1−iii−i−iii−i
χ922222222222222-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-100000000
χ1022222222222222-1-1-1-1-2-22-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-22222-2-2-2111100000000
χ11222-2222-2-2-2-2222-1-1-1-122-211-1-1-1-1-1-1-1-111111111-222-2-222-211-1-100000000
χ12222-2222-2-2-2-2222-1-1-1-1-2-2-211-1-1-1-1-1-1-1-111111111222-2-2-2-22-1-11100000000
χ1322-202-2-2000022-22-2-222-20002222-2-2-2-20000000002-2002-20002-200000000
χ1422-202-2-2000022-22-2-22-220002222-2-2-2-20000000002-200-22000-2200000000
χ1522-202-2-2000022-2-111-12-20−i3i3-1-1-1-11111−i3−i3−i3−i3i3i3i3i302-2002-20−i3i3-1100000000
χ1622-202-2-2000022-2-111-12-20i3−i3-1-1-1-11111i3i3i3i3−i3−i3−i3−i302-2002-20i3−i3-1100000000
χ1722-202-2-2000022-2-111-1-220−i3i3-1-1-1-11111−i3−i3−i3−i3i3i3i3i302-200-220i3−i31-100000000
χ1822-202-2-2000022-2-111-1-220i3−i3-1-1-1-11111i3i3i3i3−i3−i3−i3−i302-200-220−i3i31-100000000
χ19333333333333-1-1000033-10000000000000000003-1-1-1-1-1-1-100001111-1-1-1-1
χ20333333333333-1-1000033-10000000000000000003-1-1-1-1-1-1-10000-1-1-1-11111
χ21333333333333-1-10000-3-3-1000000000000000000-3-1-1-1-11110000ii−i−i−i−iii
χ22333333333333-1-10000-3-3-1000000000000000000-3-1-1-1-11110000−i−iiiii−i−i
χ23333-3333-3-3-3-33-1-10000331000000000000000000-3-1-111-1-1100001-11-1-11-11
χ24333-3333-3-3-3-33-1-10000331000000000000000000-3-1-111-1-110000-11-111-11-1
χ25333-3333-3-3-3-33-1-10000-3-310000000000000000003-1-11111-10000i−i−ii−iii−i
χ26333-3333-3-3-3-33-1-10000-3-310000000000000000003-1-11111-10000−iii−ii−i−ii
χ274444-1-1-1-1-1-1-1-144444400444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10-1-1-1-1000000000000000
χ284444-1-1-1-1-1-1-1-144-2-2-2-2004-2-21−i1521+i1521−i1521+i1521−i1521−i1521+i1521+i1521−i1521−i1521+i1521+i1521−i1521−i1521+i1521+i1520-1-1-1-1000000000000000
χ294444-1-1-1-1-1-1-1-144-2-2-2-2004-2-21+i1521−i1521+i1521−i1521+i1521+i1521−i1521−i1521+i1521+i1521−i1521−i1521+i1521+i1521−i1521−i1520-1-1-1-1000000000000000
χ30444-4-1-1-11111-144444400-4-4-4-1-1-1-1-1-1-1-1111111110-1-111000000000000000
χ31444-4-1-1-11111-144-2-2-2-200-4221−i1521+i1521−i1521+i1521−i1521−i1521+i1521+i152−1+i152−1+i152−1−i152−1−i152−1+i152−1+i152−1−i152−1−i1520-1-111000000000000000
χ32444-4-1-1-11111-144-2-2-2-200-4221+i1521−i1521+i1521−i1521+i1521+i1521−i1521−i152−1−i152−1−i152−1+i152−1+i152−1−i152−1−i152−1+i152−1+i1520-1-111000000000000000
χ3344-40-111−5−555-14-44-4-4400000-1-1-1-11111−5−55555−5−50-11−55000000000000000
χ3444-40-111−5−555-14-4-222-2000−2i32i31+i1521−i1521+i1521−i152−1−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+ζ580-11−55000000000000000
χ3544-40-111−5−555-14-4-222-20002i3−2i31−i1521+i1521−i1521+i152−1+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−ζ460-11−55000000000000000
χ3644-40-11155−5−5-14-44-4-4400000-1-1-1-1111155−5−5−5−5550-115−5000000000000000
χ3744-40-11155−5−5-14-4-222-2000−2i32i31−i1521+i1521−i1521+i152−1+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+ζ460-115−5000000000000000
χ3844-40-11155−5−5-14-4-222-20002i3−2i31+i1521−i1521+i1521−i152−1−i152−1−i152−1+i152−1+i152−ζ2+ζ34−ζ38+ζ46−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58−ζ14+ζ22−ζ26+ζ58ζ2−ζ34+ζ38−ζ46ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58ζ14−ζ22+ζ26−ζ580-115−5000000000000000
χ3966-606-6-600006-2200006-600000000000000000000-2200-220000000000000
χ4066-606-6-600006-220000-6600000000000000000000-22002-20000000000000
χ418-8008000000-8002−2i32i3-20000022-2-2−2i32i3−2i32i30000000000000000000000000000
χ428-8008000000-80022i3−2i3-20000022-2-22i3−2i32i3−2i30000000000000000000000000000
χ438-8008000000-800-400400000-4-44400000000000000000000000000000000
χ448-800-2−25252ζ2−2ζ14+2ζ22+2ζ26−2ζ34−2ζ38+2ζ46−2ζ58−2ζ2+2ζ14−2ζ22−2ζ26+2ζ34+2ζ38−2ζ46+2ζ582ζ2+2ζ14+2ζ22−2ζ26+2ζ34−2ζ38−2ζ46−2ζ58−2ζ2−2ζ14−2ζ22+2ζ26−2ζ34+2ζ38+2ζ46+2ζ582002−2i32i3-200000−1−i152−1+i1521+i1521−i152ζ2−ζ34+ζ38−ζ46−ζ2+ζ34−ζ38+ζ46ζ14−ζ22+ζ26−ζ58−ζ14+ζ22−ζ26+ζ58ζ2−ζ34−ζ38+ζ46−ζ2+ζ34+ζ38−ζ46ζ14+ζ22−ζ26−ζ58−ζ14−ζ22+ζ26+ζ58−ζ2−ζ34+ζ38+ζ46ζ2+ζ34−ζ38−ζ46ζ14−ζ22−ζ26+ζ58−ζ14+ζ22+ζ26−ζ5800000000000000000000
χ458-800-2−25252ζ2−2ζ14+2ζ22+2ζ26−2ζ34−2ζ38+2ζ46−2ζ58−2ζ2+2ζ14−2ζ22−2ζ26+2ζ34+2ζ38−2ζ46+2ζ582ζ2+2ζ14+2ζ22−2ζ26+2ζ34−2ζ38−2ζ46−2ζ58−2ζ2−2ζ14−2ζ22+2ζ26−2ζ34+2ζ38+2ζ46+2ζ5820022i3−2i3-200000−1+i152−1−i1521−i1521+i152−ζ14+ζ22−ζ26+ζ58ζ14−ζ22+ζ26−ζ58−ζ2+ζ34−ζ38+ζ46ζ2−ζ34+ζ38−ζ46−ζ14+ζ22+ζ26−ζ58ζ14−ζ22−ζ26+ζ58ζ2+ζ34−ζ38−ζ46−ζ2−ζ34+ζ38+ζ46−ζ14−ζ22+ζ26+ζ58ζ14+ζ22−ζ26−ζ58−ζ2+ζ34+ζ38−ζ46ζ2−ζ34−ζ38+ζ4600000000000000000000
χ468-800-2−25252ζ2−2ζ14+2ζ22+2ζ26−2ζ34−2ζ38+2ζ46−2ζ58−2ζ2+2ζ14−2ζ22−2ζ26+2ζ34+2ζ38−2ζ46+2ζ582ζ2+2ζ14+2ζ22−2ζ26+2ζ34−2ζ38−2ζ46−2ζ58−2ζ2−2ζ14−2ζ22+2ζ26−2ζ34+2ζ38+2ζ46+2ζ58200-40040000011-1-1−555−5−ζ2+ζ14−ζ22−ζ26+ζ34+ζ38−ζ46+ζ58ζ2−ζ14+ζ22+ζ26−ζ34−ζ38+ζ46−ζ58−ζ2−ζ14−ζ22+ζ26−ζ34+ζ38+ζ46+ζ58ζ2+ζ14+ζ22−ζ26+ζ34−ζ38−ζ46−ζ58ζ2+ζ14+ζ22−ζ26+ζ34−ζ38−ζ46−ζ58−ζ2−ζ14−ζ22+ζ26−ζ34+ζ38+ζ46+ζ58ζ2−ζ14+ζ22+ζ26−ζ34−ζ38+ζ46−ζ58−ζ2+ζ14−ζ22−ζ26+ζ34+ζ38−ζ46+ζ5800000000000000000000
χ478-800-2−2525−2ζ2+2ζ14−2ζ22−2ζ26+2ζ34+2ζ38−2ζ46+2ζ582ζ2−2ζ14+2ζ22+2ζ26−2ζ34−2ζ38+2ζ46−2ζ58−2ζ2−2ζ14−2ζ22+2ζ26−2ζ34+2ζ38+2ζ46+2ζ582ζ2+2ζ14+2ζ22−2ζ26+2ζ34−2ζ38−2ζ46−2ζ582002−2i32i3-200000−1−i152−1+i1521+i1521−i152ζ2−ζ34+ζ38−ζ46−ζ2+ζ34−ζ38+ζ46ζ14−ζ22+ζ26−ζ58−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34+ζ38−ζ46ζ2−ζ34−ζ38+ζ46−ζ14−ζ22+ζ26+ζ58ζ14+ζ22−ζ26−ζ58ζ2+ζ34−ζ38−ζ46−ζ2−ζ34+ζ38+ζ46−ζ14+ζ22+ζ26−ζ58ζ14−ζ22−ζ26+ζ5800000000000000000000
χ488-800-2−2525−2ζ2+2ζ14−2ζ22−2ζ26+2ζ34+2ζ38−2ζ46+2ζ582ζ2−2ζ14+2ζ22+2ζ26−2ζ34−2ζ38+2ζ46−2ζ58−2ζ2−2ζ14−2ζ22+2ζ26−2ζ34+2ζ38+2ζ46+2ζ582ζ2+2ζ14+2ζ22−2ζ26+2ζ34−2ζ38−2ζ46−2ζ5820022i3−2i3-200000−1+i152−1−i1521−i1521+i152−ζ14+ζ22−ζ26+ζ58ζ14−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−ζ58−ζ14−ζ22+ζ26+ζ58ζ2−ζ34−ζ38+ζ46−ζ2+ζ34+ζ38−ζ4600000000000000000000
χ498-800-2−2525−2ζ2+2ζ14−2ζ22−2ζ26+2ζ34+2ζ38−2ζ46+2ζ582ζ2−2ζ14+2ζ22+2ζ26−2ζ34−2ζ38+2ζ46−2ζ58−2ζ2−2ζ14−2ζ22+2ζ26−2ζ34+2ζ38+2ζ46+2ζ582ζ2+2ζ14+2ζ22−2ζ26+2ζ34−2ζ38−2ζ46−2ζ58200-40040000011-1-1−555−5ζ2−ζ14+ζ22+ζ26−ζ34−ζ38+ζ46−ζ58−ζ2+ζ14−ζ22−ζ26+ζ34+ζ38−ζ46+ζ58ζ2+ζ14+ζ22−ζ26+ζ34−ζ38−ζ46−ζ58−ζ2−ζ14−ζ22+ζ26−ζ34+ζ38+ζ46+ζ58−ζ2−ζ14−ζ22+ζ26−ζ34+ζ38+ζ46+ζ58ζ2+ζ14+ζ22−ζ26+ζ34−ζ38−ζ46−ζ58−ζ2+ζ14−ζ22−ζ26+ζ34+ζ38−ζ46+ζ58ζ2−ζ14+ζ22+ζ26−ζ34−ζ38+ζ46−ζ5800000000000000000000
χ508-800-225−252ζ2+2ζ14+2ζ22−2ζ26+2ζ34−2ζ38−2ζ46−2ζ58−2ζ2−2ζ14−2ζ22+2ζ26−2ζ34+2ζ38+2ζ46+2ζ58−2ζ2+2ζ14−2ζ22−2ζ26+2ζ34+2ζ38−2ζ46+2ζ582ζ2−2ζ14+2ζ22+2ζ26−2ζ34−2ζ38+2ζ46−2ζ582002−2i32i3-200000−1+i152−1−i1521−i1521+i152ζ14−ζ22+ζ26−ζ58−ζ14+ζ22−ζ26+ζ58ζ2−ζ34+ζ38−ζ46−ζ2+ζ34−ζ38+ζ46ζ14+ζ22−ζ26−ζ58−ζ14−ζ22+ζ26+ζ58−ζ2+ζ34+ζ38−ζ46ζ2−ζ34−ζ38+ζ46−ζ14+ζ22+ζ26−ζ58ζ14−ζ22−ζ26+ζ58−ζ2−ζ34+ζ38+ζ46ζ2+ζ34−ζ38−ζ4600000000000000000000
χ518-800-225−252ζ2+2ζ14+2ζ22−2ζ26+2ζ34−2ζ38−2ζ46−2ζ58−2ζ2−2ζ14−2ζ22+2ζ26−2ζ34+2ζ38+2ζ46+2ζ58−2ζ2+2ζ14−2ζ22−2ζ26+2ζ34+2ζ38−2ζ46+2ζ582ζ2−2ζ14+2ζ22+2ζ26−2ζ34−2ζ38+2ζ46−2ζ5820022i3−2i3-200000−1−i152−1+i1521+i1521−i152−ζ2+ζ34−ζ38+ζ46ζ2−ζ34+ζ38−ζ46−ζ14+ζ22−ζ26+ζ58ζ14−ζ22+ζ26−ζ58ζ2+ζ34−ζ38−ζ46−ζ2−ζ34+ζ38+ζ46ζ14−ζ22−ζ26+ζ58−ζ14+ζ22+ζ26−ζ58ζ2−ζ34−ζ38+ζ46−ζ2+ζ34+ζ38−ζ46−ζ14−ζ22+ζ26+ζ58ζ14+ζ22−ζ26−ζ5800000000000000000000
χ528-800-225−252ζ2+2ζ14+2ζ22−2ζ26+2ζ34−2ζ38−2ζ46−2ζ58−2ζ2−2ζ14−2ζ22+2ζ26−2ζ34+2ζ38+2ζ46+2ζ58−2ζ2+2ζ14−2ζ22−2ζ26+2ζ34+2ζ38−2ζ46+2ζ582ζ2−2ζ14+2ζ22+2ζ26−2ζ34−2ζ38+2ζ46−2ζ58200-40040000011-1-15−5−55−ζ2−ζ14−ζ22+ζ26−ζ34+ζ38+ζ46+ζ58ζ2+ζ14+ζ22−ζ26+ζ34−ζ38−ζ46−ζ58ζ2−ζ14+ζ22+ζ26−ζ34−ζ38+ζ46−ζ58−ζ2+ζ14−ζ22−ζ26+ζ34+ζ38−ζ46+ζ58−ζ2+ζ14−ζ22−ζ26+ζ34+ζ38−ζ46+ζ58ζ2−ζ14+ζ22+ζ26−ζ34−ζ38+ζ46−ζ58ζ2+ζ14+ζ22−ζ26+ζ34−ζ38−ζ46−ζ58−ζ2−ζ14−ζ22+ζ26−ζ34+ζ38+ζ46+ζ5800000000000000000000
χ538-800-225−25−2ζ2−2ζ14−2ζ22+2ζ26−2ζ34+2ζ38+2ζ46+2ζ582ζ2+2ζ14+2ζ22−2ζ26+2ζ34−2ζ38−2ζ46−2ζ582ζ2−2ζ14+2ζ22+2ζ26−2ζ34−2ζ38+2ζ46−2ζ58−2ζ2+2ζ14−2ζ22−2ζ26+2ζ34+2ζ38−2ζ46+2ζ582002−2i32i3-200000−1+i152−1−i1521−i1521+i152ζ14−ζ22+ζ26−ζ58−ζ14+ζ22−ζ26+ζ58ζ2−ζ34+ζ38−ζ46−ζ2+ζ34−ζ38+ζ46−ζ14−ζ22+ζ26+ζ58ζ14+ζ22−ζ26−ζ58ζ2−ζ34−ζ38+ζ46−ζ2+ζ34+ζ38−ζ46ζ14−ζ22−ζ26+ζ58−ζ14+ζ22+ζ26−ζ58ζ2+ζ34−ζ38−ζ46−ζ2−ζ34+ζ38+ζ4600000000000000000000
χ548-800-225−25−2ζ2−2ζ14−2ζ22+2ζ26−2ζ34+2ζ38+2ζ46+2ζ582ζ2+2ζ14+2ζ22−2ζ26+2ζ34−2ζ38−2ζ46−2ζ582ζ2−2ζ14+2ζ22+2ζ26−2ζ34−2ζ38+2ζ46−2ζ58−2ζ2+2ζ14−2ζ22−2ζ26+2ζ34+2ζ38−2ζ46+2ζ5820022i3−2i3-200000−1−i152−1+i1521+i1521−i152−ζ2+ζ34−ζ38+ζ46ζ2−ζ34+ζ38−ζ46−ζ14+ζ22−ζ26+ζ58ζ14−ζ22+ζ26−ζ58−ζ2−ζ34+ζ38+ζ46ζ2+ζ34−ζ38−ζ46−ζ14+ζ22+ζ26−ζ58ζ14−ζ22−ζ26+ζ58−ζ2+ζ34+ζ38−ζ46ζ2−ζ34−ζ38+ζ46ζ14+ζ22−ζ26−ζ58−ζ14−ζ22+ζ26+ζ5800000000000000000000
χ558-800-225−25−2ζ2−2ζ14−2ζ22+2ζ26−2ζ34+2ζ38+2ζ46+2ζ582ζ2+2ζ14+2ζ22−2ζ26+2ζ34−2ζ38−2ζ46−2ζ582ζ2−2ζ14+2ζ22+2ζ26−2ζ34−2ζ38+2ζ46−2ζ58−2ζ2+2ζ14−2ζ22−2ζ26+2ζ34+2ζ38−2ζ46+2ζ58200-40040000011-1-15−5−55ζ2+ζ14+ζ22−ζ26+ζ34−ζ38−ζ46−ζ58−ζ2−ζ14−ζ22+ζ26−ζ34+ζ38+ζ46+ζ58−ζ2+ζ14−ζ22−ζ26+ζ34+ζ38−ζ46+ζ58ζ2−ζ14+ζ22+ζ26−ζ34−ζ38+ζ46−ζ58ζ2−ζ14+ζ22+ζ26−ζ34−ζ38+ζ46−ζ58−ζ2+ζ14−ζ22−ζ26+ζ34+ζ38−ζ46+ζ58−ζ2−ζ14−ζ22+ζ26−ζ34+ζ38+ζ46+ζ58ζ2+ζ14+ζ22−ζ26+ζ34−ζ38−ζ46−ζ5800000000000000000000
χ5612121212-3-3-3-3-3-3-3-3-4-4000000-400000000000000000001111000000000000000
χ57121212-12-3-3-33333-3-4-40000004000000000000000000011-1-1000000000000000
χ581212-120-333−35−353535-3-44000000000000000000000000001-15−5000000000000000
χ591212-120-3333535−35−35-3-44000000000000000000000000001-1−55000000000000000

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