Finite Group Databasebeta

← Group #14313521

Character table — Group #14313521

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size1122244444488888888121216161616161616161620202424242424303040404040404040404048486080808080120120120120120
order122364561010102121520203030304461010303030306060224202020204444444661212202021212121224444
χ1111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-11111111-1-1-1-11-1-1-1-1
χ3111111111111111111111111111111-1-111111-1-1-1ii−i−i-1-1-1-111-1ii−i−i-1ii−i−i
χ4111111111111111111111111111111-1-111111-1-1-1−i−iii-1-1-1-111-1−i−iii-1−i−iii
χ51111111111111111111-1-111111111111-1-1-1-1-1-1-1111111111-1-1-11111-1-1-1-1-1
χ61111111111111111111-1-111111111111-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-11111
χ71111111111111111111-1-1111111111-1-1-1-1-1-1-111-1ii−i−i-1-1-1-1-1-11ii−i−i1−i−iii
χ81111111111111111111-1-1111111111-1-1-1-1-1-1-111-1−i−iii-1-1-1-1-1-11−i−iii1ii−i−i
χ911111111111-1111111111-1-1-1-1-1-1-11111-1-1-1-1-111-11-11-111-1-11111-11-1-11-11-1
χ1011111111111-1111111111-1-1-1-1-1-1-11111-1-1-1-1-111-1-11-1111-1-1111-11-11-1-11-11
χ1111111111111-1111111111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-11i−i−ii-1-11111-1i−i−ii1i−i−ii
χ1211111111111-1111111111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-11−iii−i-1-11111-1−iii−i1−iii−i
χ1311111111111-11111111-1-1-1-1-1-1-1-1-1111111111-1-1-11-11-111-1-1-1-1-11-11-11-11-11
χ1411111111111-11111111-1-1-1-1-1-1-1-1-1111111111-1-1-1-11-1111-1-1-1-1-1-11-1111-11-1
χ1511111111111-11111111-1-1-1-1-1-1-1-1-111-1-111111111i−i−ii-1-111-1-11i−i−ii-1−iii−i
χ1611111111111-11111111-1-1-1-1-1-1-1-1-111-1-111111111−iii−i-1-111-1-11−iii−i-1i−i−ii
χ1722222-2222220-22-2-22222-20000000-2-22-20000022000002-2002-2-2000000000
χ1822222-2222220-22-2-22222-20000000-2-2-2200000-2-200000-22002-22000000000
χ1922222-2222220-22-2-2222-220000000-2-22-200000-2-2000002-200-222000000000
χ2022222-2222220-22-2-2222-220000000-2-2-22000002200000-2200-22-2000000000
χ21222-1-122-12222-1-122-1-1-100-122-1-1-1-1-1-122000000022222-1-1-1-1000-1-1-1-100000
χ22222-1-122-12222-1-122-1-1-100-122-1-1-1-1-1-12200000002-2-2-2-2-1-1-1-1000111100000
χ23222-1-122-12222-1-122-1-1-100-122-1-1-1-1-1-1-2-20000000-22i2i−2i−2i1111000−i−iii00000
χ24222-1-122-12222-1-122-1-1-100-122-1-1-1-1-1-1-2-20000000-2−2i−2i2i2i1111000ii−i−i00000
χ25222-1-122-1222-2-1-122-1-1-1001-2-21111-1-1220000000-22-22-2-1-111000-11-1100000
χ26222-1-122-1222-2-1-122-1-1-1001-2-21111-1-1220000000-2-22-22-1-1110001-11-100000
χ27222-1-122-1222-2-1-122-1-1-1001-2-21111-1-1-2-2000000022i−2i−2i2i11-1-1000−iii−i00000
χ28222-1-122-1222-2-1-122-1-1-1001-2-21111-1-1-2-200000002−2i2i2i−2i11-1-1000i−i−ii00000
χ29444444-14-1-1-144-1-1-1-1-1-1444-1-1-1-1-1-1-1-1004-1-1-1-100000000000-1-10000000000
χ30444444-14-1-1-144-1-1-1-1-1-1-4-44-1-1-1-1-1-1-1-100-4111100000000000110000000000
χ31444444-14-1-1-1-44-1-1-1-1-1-144-4111111-1-100-4111100000000000-1-10000000000
χ32444444-14-1-1-1-44-1-1-1-1-1-1-4-4-4111111-1-1004-1-1-1-100000000000110000000000
χ3344444-4-14-1-1-10-4-111-1-1-14-40−55−5−55511000−5−55500000000000-110000000000
χ3444444-4-14-1-1-10-4-111-1-1-14-405−555−5−51100055−5−500000000000-110000000000
χ3544444-4-14-1-1-10-4-111-1-1-1-440−55−5−5551100055−5−5000000000001-10000000000
χ3644444-4-14-1-1-10-4-111-1-1-1-4405−555−5−511000−5−555000000000001-10000000000
χ37444-2-2-44-244402-2-4-4-2-2-2000000000224-4000000000000-2200000000000000
χ38444-2-2-44-244402-2-4-4-2-2-200000000022-440000000000002-200000000000000
χ3944-44404-4-4-4400400-4-440000000000000000004-4000000000000000000000
χ4044-44404-4-4-4400400-4-44000000000000000000-44000000000000000000000
χ41888-4-48-2-4-2-2-28-41-2-211100-4-2-2111111000000000000000000000000000000
χ42888-4-48-2-4-2-2-2-8-41-2-211100422-1-1-1-111000000000000000000000000000000
χ43888-4-4-8-2-4-2-2-204122111000−252555−5−5-1-1000000000000000000000000000000
χ44888-4-4-8-2-4-2-2-20412211100025−25−5−555-1-1000000000000000000000000000000
χ4588-8880-2-822-200-2−252522-2000000000−2525000000000000000000000000000000
χ4688-8880-2-822-200-225−2522-200000000025−25000000000000000000000000000000
χ4788-8-4-4084-8-8800-40044-400000000000000000000000000000000000000000
χ4888-8-4-40-2422-2001−2525-1-1100000ζ2+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+ζ585−5000000000000000000000000000000
χ4988-8-4-40-2422-2001−2525-1-1100000−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−ζ585−5000000000000000000000000000000
χ5088-8-4-40-2422-200125−25-1-1100000−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+ζ58−55000000000000000000000000000000
χ5188-8-4-40-2422-200125−25-1-1100000ζ2−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−ζ58−55000000000000000000000000000000
χ528-808-808000-80080000-800000000000000000000000000000000000000000
χ538-808-80-20−2525200-200−2525200000000000000−2ζ11+2ζ19−2ζ31+2ζ592ζ11−2ζ19+2ζ31−2ζ592ζ7−2ζ23−2ζ43+2ζ47−2ζ7+2ζ23+2ζ43−2ζ4700000000000000000000000
χ548-808-80-20−2525200-200−25252000000000000002ζ11−2ζ19+2ζ31−2ζ59−2ζ11+2ζ19−2ζ31+2ζ59−2ζ7+2ζ23+2ζ43−2ζ472ζ7−2ζ23−2ζ43+2ζ4700000000000000000000000
χ558-808-80-2025−25200-20025−252000000000000002ζ7−2ζ23−2ζ43+2ζ47−2ζ7+2ζ23+2ζ43−2ζ472ζ11−2ζ19+2ζ31−2ζ59−2ζ11+2ζ19−2ζ31+2ζ5900000000000000000000000
χ568-808-80-2025−25200-20025−25200000000000000−2ζ7+2ζ23+2ζ43−2ζ472ζ7−2ζ23−2ζ43+2ζ47−2ζ11+2ζ19−2ζ31+2ζ592ζ11−2ζ19+2ζ31−2ζ5900000000000000000000000
χ578-80-4408000-800-400004000000000000000000000000000−2i32i3000000000000
χ588-80-4408000-800-4000040000000000000000000000000002i3−2i3000000000000
χ5916-160-880-40−454540020025−25-200000000000000000000000000000000000000000
χ6016-160-880-4045−45400200−2525-200000000000000000000000000000000000000000

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