Finite Group Databasebeta

← Group #14302973

Character table — Group #14302973

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size1122222444444488888888810101010101012121616161616161616202020202020202424242424404040404040404040404040404848606060606060120120120
order12234465610101012122661520203030302244121244101030303030606044446612420202020488121212121212242424242020444444488
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-1-1ii−i−iii−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−iii−i−iii11-1-1−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-1-1ii−i−iii−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−iii−i−iii-1-111ii−i−i1i−i
χ911111111111111-1-1-111111111111111-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1
χ1011111111111111-1-1-111111111111111-1-1-1-1-1-111-1-1-1-1111-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-111
χ1111111111111111-1-1-1111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111
χ1211111111111111-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-111-1-1-1-1-1-11111-1-1-1-111111-1-1
χ1311111111111111-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-111ii−i−i-1-1-1-1-1-1-1-11−ii11ii−i−i−i−iii11-1-1ii−i−i1−ii
χ1411111111111111-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-111−i−iii-1-1-1-1-1-1-1-11i−i11−i−iiiii−i−i11-1-1−i−iii1i−i
χ1511111111111111-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111ii−i−i-1-1-1111111−ii11ii−i−i−i−iii-1-111−i−iii-1i−i
χ1611111111111111-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111−i−iii-1-1-1111111i−i11−i−iiiii−i−i-1-111ii−i−i-1−ii
χ172222-2-2222222-2-20002-2-222222-2-2-2-22-2000000-2-2000022-20000000000000000002-22-20000000
χ182222-2-2222222-2-20002-2-222222-2-2-2-2-22000000-2-2000022-2000000000000000000-22-220000000
χ192222-2-2222222-2-20002-2-2222-2-222222-2000000-2-20000-2-220000000000000000002-2-220000000
χ202222-2-2222222-2-20002-2-2222-2-22222-22000000-2-20000-2-22000000000000000000-222-20000000
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−iii−i−iii00000000000
χ24222-122-12-1222-1-12-1-1-122-1-1-1-2-2-2-2110022-1-1-1-1-1-1−2i−2i2i2i11100000-2−2i2i11ii−i−iii−i−i00000000000
χ25222-122-12-1222-1-1-211-122-1-1-12222-1-100-2-21111-1-12222-1-1-100000-2-2-211-1-1-1-1111100000000000
χ26222-122-12-1222-1-1-211-122-1-1-12222-1-100-2-21111-1-1-2-2-2-2-1-1-100000-222111111-1-1-1-100000000000
χ27222-122-12-1222-1-1-211-122-1-1-1-2-2-2-21100-2-21111-1-12i2i−2i−2i111000002−2i2i-1-1−i−iiiii−i−i00000000000
χ28222-122-12-1222-1-1-211-122-1-1-1-2-2-2-21100-2-21111-1-1−2i−2i2i2i1110000022i−2i-1-1ii−i−i−i−iii00000000000
χ2922-222-222-2-2-222-200022-2-2-222-22-222000000002-200002-2-200000000000000000000002i−2i2i−2i000
χ3022-222-222-2-2-222-200022-2-2-222-22-222000000002-200002-2-20000000000000000000000−2i2i−2i2i000
χ3122-222-222-2-2-222-200022-2-2-22-22-22-2-2000000002-20000-22200000000000000000000002-2-22000
χ3222-222-222-2-2-222-200022-2-2-22-22-22-2-2000000002-20000-2220000000000000000000000-222-2000
χ3322-22-2222-2-2-22-220002-22-2-222-2-22-2-200000000-222i−2i2i−2i2-2200000000002i−2i2i−2i000000000000000
χ3422-22-2222-2-2-22-220002-22-2-222-2-22-2-200000000-22−2i2i−2i2i2-220000000000−2i2i−2i2i000000000000000
χ3522-22-2222-2-2-22-220002-22-2-22-222-22200000000-222-2-22-22-200000000002-2-22000000000000000
χ3622-22-2222-2-2-22-220002-22-2-22-222-22200000000-22-222-2-22-20000000000-222-2000000000000000
χ3722-2-1-22-121-2-221-10−i3i3-1-2211-12-2-22110000−i3−i3i3i31-12i−2i2i−2i-11-100000000−i3i3−ii−ii3−33−300000000000
χ3822-2-1-22-121-2-221-10−i3i3-1-2211-12-2-22110000−i3−i3i3i31-1−2i2i−2i2i-11-100000000−i3i3i−ii−i−33−3300000000000
χ3922-2-1-22-121-2-221-10−i3i3-1-2211-1-222-2-1-10000−i3−i3i3i31-12-2-221-1100000000i3−i3-111-1−i3i3i3−i300000000000
χ4022-2-1-22-121-2-221-10−i3i3-1-2211-1-222-2-1-10000−i3−i3i3i31-1-222-21-1100000000i3−i31-1-11i3−i3−i3i300000000000
χ4122-2-1-22-121-2-221-10i3−i3-1-2211-12-2-22110000i3i3−i3−i31-12i−2i2i−2i-11-100000000i3−i3−ii−ii−33−3300000000000
χ4222-2-1-22-121-2-221-10i3−i3-1-2211-12-2-22110000i3i3−i3−i31-1−2i2i−2i2i-11-100000000i3−i3i−ii−i3−33−300000000000
χ4322-2-1-22-121-2-221-10i3−i3-1-2211-1-222-2-1-10000i3i3−i3−i31-12-2-221-1100000000−i3i3-111-1i3−i3−i3i300000000000
χ4422-2-1-22-121-2-221-10i3−i3-1-2211-1-222-2-1-10000i3i3−i3−i31-1-222-21-1100000000−i3i31-1-11−i3i3i3−i300000000000
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
χ474444444-14-1-1-144-4-4-4-1-1-1-1-1-100000044111111-1-10000000-411110000000000000-1-1000000000
χ484444444-14-1-1-144-4-4-4-1-1-1-1-1-1000000-4-4111111-1-100000004-1-1-1-1000000000000011000000000
χ494444-4-44-14-1-1-1-4-4000-111-1-1-10000004-4−55−55−551100000000−5−5550000000000000-11000000000
χ504444-4-44-14-1-1-1-4-4000-111-1-1-10000004-45−55−55−5110000000055−5−50000000000000-11000000000
χ514444-4-44-14-1-1-1-4-4000-111-1-1-1000000-44−55−55−55110000000055−5−500000000000001-1000000000
χ524444-4-44-14-1-1-1-4-4000-111-1-1-1000000-445−55−55−51100000000−5−55500000000000001-1000000000
χ53444-2-4-4-24-244422000-2-4-4-2-2-244-4-42200000000220000-2-2200000000000000000000000000000
χ54444-2-4-4-24-244422000-2-4-4-2-2-2-4-444-2-20000000022000022-200000000000000000000000000000
χ5544-4-24-4-242-4-44-22000-24-422-24-44-4-2-200000000-220000-22200000000000000000000000000000
χ5644-4-24-4-242-4-44-22000-24-422-2-44-442200000000-2200002-2-200000000000000000000000000000
χ57888-488-4-2-4-2-2-2-4-48-4-41-2-211100000000-2-2111111000000000000000000000000000000000000
χ58888-488-4-2-4-2-2-2-4-4-8441-2-21110000000022-1-1-1-111000000000000000000000000000000000000
χ59888-4-8-8-4-2-4-2-2-24400012211100000000−25255−55−5-1-1000000000000000000000000000000000000
χ60888-4-8-8-4-2-4-2-2-2440001221110000000025−25−55−55-1-1000000000000000000000000000000000000
χ6188-888-88-2-822-28-8000-2-2222-200000000000000-22000000000000000000000000000000000000
χ6288-88-888-2-822-2-88000-22-222-2000000000000002-2000000000000000000000000000000000000
χ6388-8-48-8-4-2422-2-440001-22-1-110000000000−i15i15i15−i151-1000000000000000000000000000000000000
χ6488-8-48-8-4-2422-2-440001-22-1-110000000000i15−i15−i15i151-1000000000000000000000000000000000000
χ6588-8-4-88-4-2422-24-40−4i34i312-2-1-110000000000i3i3−i3−i3-11000000000000000000000000000000000000
χ6688-8-4-88-4-2422-24-404i3−4i312-2-1-110000000000−i3−i3i3i3-11000000000000000000000000000000000000
χ678-80800-88000-80000080000-80000000000000000000000000000000000000000000000000000
χ688-80800-8-20−2525200000-200−25252000000000000000000000000−2ζ11+2ζ19−2ζ31+2ζ592ζ11−2ζ19+2ζ31−2ζ592ζ7−2ζ23−2ζ43+2ζ47−2ζ7+2ζ23+2ζ43−2ζ47000000000000000000000000
χ698-80800-8-20−2525200000-200−252520000000000000000000000002ζ11−2ζ19+2ζ31−2ζ59−2ζ11+2ζ19−2ζ31+2ζ59−2ζ7+2ζ23+2ζ43−2ζ472ζ7−2ζ23−2ζ43+2ζ47000000000000000000000000
χ708-80800-8-2025−25200000-20025−2520000000000000000000000002ζ7−2ζ23−2ζ43+2ζ47−2ζ7+2ζ23+2ζ43−2ζ472ζ11−2ζ19+2ζ31−2ζ59−2ζ11+2ζ19−2ζ31+2ζ59000000000000000000000000
χ718-80800-8-2025−25200000-20025−252000000000000000000000000−2ζ7+2ζ23+2ζ43−2ζ472ζ7−2ζ23−2ζ43+2ζ47−2ζ11+2ζ19−2ζ31+2ζ592ζ11−2ζ19+2ζ31−2ζ59000000000000000000000000
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 60 (ζ60 = 1); i = ζ15.