Finite Group Databasebeta

← Group #14302551

Character table — Group #14302551

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size1122222444444488888888810101010101012121616161616161616202020202020202424242424404040404040404040404040404848606060606060120120120
order12234465610101012124121215202030303022441212442020606060606060444466128404040402446612121212121212122020444444888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-1111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11-1-1
χ311111111111111111111111111111-1-1111111111111111-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111-1-111111111-1-1-1-1111-1-1-1-1-11-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-111
χ511111111111111111111111-1-1-1-1-1-11111111111ii−i−i-1-1-111111-1i−i-1-1iiii−i−i−i−i11-1-1ii−i−i-1i−i
χ611111111111111111111111-1-1-1-1-1-11111111111−i−iii-1-1-111111-1−ii-1-1−i−i−i−iiiii11-1-1−i−iii-1−ii
χ711111111111111111111111-1-1-1-1-1-1-1-111111111ii−i−i-1-1-1-1-1-1-1-1-1i−i-1-1iiii−i−i−i−i-1-111−i−iii1−ii
χ811111111111111111111111-1-1-1-1-1-1-1-111111111−i−iii-1-1-1-1-1-1-1-1-1−ii-1-1−i−i−i−iiiii-1-111ii−i−i1i−i
χ911111111111111-1-1-111111111111111-1-111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1
χ1011111111111111-1-1-111111111111111-1-111-1-1-1-1-1-1-1-1111-1-1-1-1-1-111-1-1-1-111-1-1111111-1-1-1-1-111
χ1111111111111111-1-1-1111111111111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1111
χ1211111111111111-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-111-1-1-1-111-1-111-1-1-1-111111-1-1
χ1311111111111111-1-1-1111111-1-1-1-1-1-111-1-111-1-1-1-1ii−i−i-1-1-1-1-1-1-1-11−ii11ii−i−i−i−iii11-1-1ii−i−i1−ii
χ1411111111111111-1-1-1111111-1-1-1-1-1-111-1-111-1-1-1-1−i−iii-1-1-1-1-1-1-1-11i−i11−i−iiiii−i−i11-1-1−i−iii1i−i
χ1511111111111111-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1ii−i−i-1-1-1111111−ii11ii−i−i−i−iii-1-111−i−iii-1i−i
χ1611111111111111-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1−i−iii-1-1-1111111i−i11−i−iiiii−i−i-1-111ii−i−i-1−ii
χ172222-2-2222222-2-20002-2-222222-2-2-2-20000-2-200002-22-222-200000000002-2002-20000000000000
χ182222-2-2222222-2-20002-2-222222-2-2-2-20000-2-20000-22-2222-20000000000-2200-220000000000000
χ192222-2-2222222-2-20002-2-2222-2-222220000-2-200002i−2i−2i2i-2-2200000000002i−2i00−2i2i0000000000000
χ202222-2-2222222-2-20002-2-2222-2-222220000-2-20000−2i2i2i−2i-2-220000000000−2i2i002i−2i0000000000000
χ21222-122-12-1222-1-12-1-1-122-1-1-12222-1-10022-1-1-1-1-1-12222-1-1-100000222-1-1-1-1-1-1-1-1-1-100000000000
χ22222-122-12-1222-1-12-1-1-122-1-1-12222-1-10022-1-1-1-1-1-1-2-2-2-2-1-1-1000002-2-2-1-11111111100000000000
χ23222-122-12-1222-1-12-1-1-122-1-1-1-2-2-2-2110022-1-1-1-1-1-12i2i−2i−2i11100000-22i−2i11−i−i−i−iiiii00000000000
χ24222-122-12-1222-1-12-1-1-122-1-1-1-2-2-2-2110022-1-1-1-1-1-1−2i−2i2i2i11100000-2−2i2i11iiii−i−i−i−i00000000000
χ25222-122-12-1222-1-1-211-122-1-1-12222-1-100-2-2-1-111112222-1-1-100000-2-2-211-1-111-1-11100000000000
χ26222-122-12-1222-1-1-211-122-1-1-12222-1-100-2-2-1-11111-2-2-2-2-1-1-100000-2221111-1-111-1-100000000000
χ27222-122-12-1222-1-1-211-122-1-1-1-2-2-2-21100-2-2-1-111112i2i−2i−2i111000002−2i2i-1-1−i−iiiii−i−i00000000000
χ28222-122-12-1222-1-1-211-122-1-1-1-2-2-2-21100-2-2-1-11111−2i−2i2i2i1110000022i−2i-1-1ii−i−i−i−iii00000000000
χ29222-1-2-2-12-1222110−i3i3-1-2-2-1-1-122-2-211000011−i3−i3i3i32-22-2-1-1100000000−i3i3-11−i3i3-11−i3i300000000000
χ30222-1-2-2-12-1222110−i3i3-1-2-2-1-1-122-2-211000011−i3−i3i3i3-22-22-1-1100000000−i3i31-1i3−i31-1i3−i300000000000
χ31222-1-2-2-12-1222110−i3i3-1-2-2-1-1-1-2-222-1-1000011−i3−i3i3i32i−2i−2i2i11-100000000i3−i3−ii3−3i−i−3300000000000
χ32222-1-2-2-12-1222110−i3i3-1-2-2-1-1-1-2-222-1-1000011−i3−i3i3i3−2i2i2i−2i11-100000000i3−i3i−i−33−ii3−300000000000
χ33222-1-2-2-12-1222110i3−i3-1-2-2-1-1-122-2-211000011i3i3−i3−i32-22-2-1-1100000000i3−i3-11i3−i3-11i3−i300000000000
χ34222-1-2-2-12-1222110i3−i3-1-2-2-1-1-122-2-211000011i3i3−i3−i3-22-22-1-1100000000i3−i31-1−i3i31-1−i3i300000000000
χ35222-1-2-2-12-1222110i3−i3-1-2-2-1-1-1-2-222-1-1000011i3i3−i3−i32i−2i−2i2i11-100000000−i3i3−ii−33i−i3−300000000000
χ36222-1-2-2-12-1222110i3−i3-1-2-2-1-1-1-2-222-1-1000011i3i3−i3−i3−2i2i2i−2i11-100000000−i3i3i−i3−3−ii−3300000000000
χ3722-222-222-2-2-222-200022-2-2-222-22-22200002-2000000002-2-200000000000000000000002i−2i2i−2i000
χ3822-222-222-2-2-222-200022-2-2-222-22-22200002-2000000002-2-20000000000000000000000−2i2i−2i2i000
χ3922-222-222-2-2-222-200022-2-2-22-22-22-2-200002-200000000-22200000000000000000000002-2-22000
χ4022-222-222-2-2-222-200022-2-2-22-22-22-2-200002-200000000-2220000000000000000000000-222-2000
χ4122-22-2222-2-2-22-220002-22-2-222-2-22-2-22-200-22000000002-220000000000000000002-22-20000000
χ4222-22-2222-2-2-22-220002-22-2-222-2-22-2-2-2200-22000000002-22000000000000000000-22-220000000
χ4322-22-2222-2-2-22-220002-22-2-22-222-2222-200-2200000000-22-20000000000000000002-2-220000000
χ4422-22-2222-2-2-22-220002-22-2-22-222-222-2200-2200000000-22-2000000000000000000-222-20000000
χ454444444-14-1-1-144444-1-1-1-1-1-100000044-1-1-1-1-1-1-1-100000004-1-1-1-10000000000000-1-1000000000
χ464444444-14-1-1-144444-1-1-1-1-1-1000000-4-4-1-1-1-1-1-1-1-10000000-41111000000000000011000000000
χ474444444-14-1-1-144-4-4-4-1-1-1-1-1-10000004411-1-111110000000-411110000000000000-1-1000000000
χ484444444-14-1-1-144-4-4-4-1-1-1-1-1-1000000-4-411-1-1111100000004-1-1-1-1000000000000011000000000
χ4944-44-444-1-411-1-44000-11-111-10000004-4−551-1−55−5500000000−5−5550000000000000-11000000000
χ5044-44-444-1-411-1-44000-11-111-10000004-45−51-15−55−50000000055−5−50000000000000-11000000000
χ5144-44-444-1-411-1-44000-11-111-1000000-44−551-1−55−550000000055−5−500000000000001-1000000000
χ5244-44-444-1-411-1-44000-11-111-1000000-445−51-15−55−500000000−5−55500000000000001-1000000000
χ5344-4-24-4-242-4-44-22000-24-422-24-44-4-2-20000-2200000000-22200000000000000000000000000000
χ5444-4-24-4-242-4-44-22000-24-422-2-44-44220000-22000000002-2-200000000000000000000000000000
χ5544-4-2-44-242-4-442-2000-2-4422-24-4-442200002-200000000-22-200000000000000000000000000000
χ5644-4-2-44-242-4-442-2000-2-4422-2-444-4-2-200002-2000000002-2200000000000000000000000000000
χ578888-8-88-28-2-2-2-8-8000-222-2-2-20000000000220000000000000000000000000000000000000000
χ58888-488-4-2-4-2-2-2-4-48-4-41-2-211100000000-2-2111111000000000000000000000000000000000000
χ59888-488-4-2-4-2-2-2-4-4-8441-2-2111000000002211-1-1-1-1000000000000000000000000000000000000
χ60888-4-8-8-4-2-4-2-2-2440−4i34i31221110000000000-1-1i3i3−i3−i3000000000000000000000000000000000000
χ61888-4-8-8-4-2-4-2-2-24404i3−4i31221110000000000-1-1−i3−i3i3i3000000000000000000000000000000000000
χ6288-888-88-2-822-28-8000-2-2222-20000000000-220000000000000000000000000000000000000000
χ6388-8-48-8-4-2422-2-440001-22-1-1100000000001-1−i15i15i15−i15000000000000000000000000000000000000
χ6488-8-48-8-4-2422-2-440001-22-1-1100000000001-1i15−i15−i15i15000000000000000000000000000000000000
χ6588-8-4-88-4-2422-24-400012-2-1-1100000000−2525-115−55−5000000000000000000000000000000000000
χ6688-8-4-88-4-2422-24-400012-2-1-110000000025−25-11−55−55000000000000000000000000000000000000
χ678-80800-88000-80000080000-80000000000000000000000000000000000000000000000000000
χ688-80800-8-20−2525200000-200−25252000000000000000000000000−ζ7−ζ13+ζ23+ζ29+ζ31+ζ37−ζ47−ζ53−ζ61+ζ71+ζ77−ζ79−ζ101+ζ103+ζ109−ζ119ζ7+ζ13−ζ23−ζ29−ζ31−ζ37+ζ47+ζ53+ζ61−ζ71−ζ77+ζ79+ζ101−ζ103−ζ109+ζ119−ζ7−ζ13+ζ23−ζ29−ζ31+ζ37−ζ47−ζ53+ζ61−ζ71+ζ77+ζ79+ζ101+ζ103−ζ109+ζ119ζ7+ζ13−ζ23+ζ29+ζ31−ζ37+ζ47+ζ53−ζ61+ζ71−ζ77−ζ79−ζ101−ζ103+ζ109−ζ119000000000000000000000000
χ698-80800-8-20−2525200000-200−25252000000000000000000000000ζ7+ζ13−ζ23−ζ29−ζ31−ζ37+ζ47+ζ53+ζ61−ζ71−ζ77+ζ79+ζ101−ζ103−ζ109+ζ119−ζ7−ζ13+ζ23+ζ29+ζ31+ζ37−ζ47−ζ53−ζ61+ζ71+ζ77−ζ79−ζ101+ζ103+ζ109−ζ119ζ7+ζ13−ζ23+ζ29+ζ31−ζ37+ζ47+ζ53−ζ61+ζ71−ζ77−ζ79−ζ101−ζ103+ζ109−ζ119−ζ7−ζ13+ζ23−ζ29−ζ31+ζ37−ζ47−ζ53+ζ61−ζ71+ζ77+ζ79+ζ101+ζ103−ζ109+ζ119000000000000000000000000
χ708-80800-8-2025−25200000-20025−252000000000000000000000000−ζ7−ζ13+ζ23−ζ29−ζ31+ζ37−ζ47−ζ53+ζ61−ζ71+ζ77+ζ79+ζ101+ζ103−ζ109+ζ119ζ7+ζ13−ζ23+ζ29+ζ31−ζ37+ζ47+ζ53−ζ61+ζ71−ζ77−ζ79−ζ101−ζ103+ζ109−ζ119ζ7+ζ13−ζ23−ζ29−ζ31−ζ37+ζ47+ζ53+ζ61−ζ71−ζ77+ζ79+ζ101−ζ103−ζ109+ζ119−ζ7−ζ13+ζ23+ζ29+ζ31+ζ37−ζ47−ζ53−ζ61+ζ71+ζ77−ζ79−ζ101+ζ103+ζ109−ζ119000000000000000000000000
χ718-80800-8-2025−25200000-20025−252000000000000000000000000ζ7+ζ13−ζ23+ζ29+ζ31−ζ37+ζ47+ζ53−ζ61+ζ71−ζ77−ζ79−ζ101−ζ103+ζ109−ζ119−ζ7−ζ13+ζ23−ζ29−ζ31+ζ37−ζ47−ζ53+ζ61−ζ71+ζ77+ζ79+ζ101+ζ103−ζ109+ζ119−ζ7−ζ13+ζ23+ζ29+ζ31+ζ37−ζ47−ζ53−ζ61+ζ71+ζ77−ζ79−ζ101+ζ103+ζ109−ζ119ζ7+ζ13−ζ23−ζ29−ζ31−ζ37+ζ47+ζ53+ζ61−ζ71−ζ77+ζ79+ζ101−ζ103−ζ109+ζ119000000000000000000000000
χ728-80-40048000-800000-400004000043−430000000000000000000000000000000000000000000000
χ738-80-40048000-800000-4000040000−43430000000000000000000000000000000000000000000000
χ7416-160-8008-40−454540000020025−25-20000000000000000000000000000000000000000000000000000
χ7516-160-8008-4045−45400000200−2525-20000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 120 (ζ120 = 1); i = ζ30.