Finite Group Databasebeta

← Group #14302818

Character table — Group #14302818

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size1122222444444488888888810101010101012121616161616161616202020202020202424242424404040404040404040404040404848606060606060120120120
order122344656101010121241212152020303030224466222020606060606060688881212420202020444121212121212242424241010448888444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11-1-1
χ311111111111111111111111111111-1-1111111111111111-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111-1-1111111111-1-1-1-111-1-1-1-1-11-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-111
χ511111111111111111111111-1-1-1-1-1-11111111111-1ii−i−i-1-111111-1i−i-1-1ii−i−iii−i−i11-1-1ii−i−i-1i−i
χ611111111111111111111111-1-1-1-1-1-11111111111-1−i−iii-1-111111-1−ii-1-1−i−iii−i−iii11-1-1−i−iii-1−ii
χ711111111111111111111111-1-1-1-1-1-1-1-111111111-1ii−i−i-1-1-1-1-1-1-1-1i−i-1-1ii−i−iii−i−i-1-111−i−iii1−ii
χ811111111111111111111111-1-1-1-1-1-1-1-111111111-1−i−iii-1-1-1-1-1-1-1-1−ii-1-1−i−iii−i−iii-1-111ii−i−i1i−i
χ911111111111111-1-1-111111111111111-1-111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1
χ1011111111111111-1-1-111111111111111-1-111-1-1-1-11-1-1-1-111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-111
χ1111111111111111-1-1-1111111111111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111
χ1211111111111111-1-1-1111111111111-1-1-1-111-1-1-1-11-1-1-1-11111111-111-1-11111-1-1-1-1-1-1-1-111111-1-1
χ1311111111111111-1-1-1111111-1-1-1-1-1-111-1-111-1-1-1-1-1ii−i−i-1-1-1-1-1-1-11−ii11−i−iiiii−i−i11-1-1ii−i−i1−ii
χ1411111111111111-1-1-1111111-1-1-1-1-1-111-1-111-1-1-1-1-1−i−iii-1-1-1-1-1-1-11i−i11ii−i−i−i−iii11-1-1−i−iii1i−i
χ1511111111111111-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1ii−i−i-1-1111111−ii11−i−iiiii−i−i-1-111−i−iii-1i−i
χ1611111111111111-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1−i−iii-1-1111111i−i11ii−i−i−i−iii-1-111ii−i−i-1−ii
χ172222-2-2222222-2-20002-2-222222-2-2222-200-2-2000020000-2-20000000000000000002-22-20000000
χ182222-2-2222222-2-20002-2-222222-2-222-2200-2-2000020000-2-2000000000000000000-22-220000000
χ192222-2-2222222-2-20002-2-2222-2-222-2-22-200-2-20000-20000220000000000000000002-2-220000000
χ202222-2-2222222-2-20002-2-2222-2-222-2-2-2200-2-20000-2000022000000000000000000-222-20000000
χ21222-122-12-1222-1-12-1-1-122-1-1-12222-1-10022-1-1-1-1-1-1-12222-1-100000222-1-1-1-1-1-1-1-1-1-100000000000
χ22222-122-12-1222-1-12-1-1-122-1-1-12222-1-10022-1-1-1-1-1-1-1-2-2-2-2-1-1000002-2-2-1-11111111100000000000
χ23222-122-12-1222-1-12-1-1-122-1-1-1-2-2-2-2110022-1-1-1-1-1-112i2i−2i−2i1100000-22i−2i11−i−iii−i−iii00000000000
χ24222-122-12-1222-1-12-1-1-122-1-1-1-2-2-2-2110022-1-1-1-1-1-11−2i−2i2i2i1100000-2−2i2i11ii−i−iii−i−i00000000000
χ25222-122-12-1222-1-1-211-122-1-1-12222-1-100-2-2-1-11111-12222-1-100000-2-2-2111111-1-1-1-100000000000
χ26222-122-12-1222-1-1-211-122-1-1-12222-1-100-2-2-1-11111-1-2-2-2-2-1-100000-22211-1-1-1-1111100000000000
χ27222-122-12-1222-1-1-211-122-1-1-1-2-2-2-21100-2-2-1-1111112i2i−2i−2i11000002−2i2i-1-1ii−i−i−i−iii00000000000
χ28222-122-12-1222-1-1-211-122-1-1-1-2-2-2-21100-2-2-1-111111−2i−2i2i2i110000022i−2i-1-1−i−iiiii−i−i00000000000
χ2922-222-222-22-2-22-200022-2-2-222-22-22200002-20000-200002-200000000000000000000002i−2i2i−2i000
χ3022-222-222-22-2-22-200022-2-2-222-22-22200002-20000-200002-20000000000000000000000−2i2i−2i2i000
χ3122-222-222-22-2-22-200022-2-2-22-22-22-2-200002-2000020000-2200000000000000000000002-2-22000
χ3222-222-222-22-2-22-200022-2-2-22-22-22-2-200002-2000020000-220000000000000000000000-222-2000
χ3322-22-2222-22-2-2-220002-22-2-222-2-22220000-220000-22-22-2-22000000000000002-22-200000000000
χ3422-22-2222-22-2-2-220002-22-2-222-2-22220000-220000-2-22-22-2200000000000000-22-2200000000000
χ3522-22-2222-22-2-2-220002-22-2-22-222-2-2-20000-22000022i−2i−2i2i2-2000000000000002i−2i−2i2i00000000000
χ3622-22-2222-22-2-2-220002-22-2-22-222-2-2-20000-2200002−2i2i2i−2i2-200000000000000−2i2i2i−2i00000000000
χ3722-2-1-22-1212-2-21-10−i3i3-1-2211-12-2-22-1-100001-1−i3−i3i3i312-22-21-100000000−i3i3−i3i3−i3i3-11-1100000000000
χ3822-2-1-22-1212-2-21-10−i3i3-1-2211-12-2-22-1-100001-1−i3−i3i3i31-22-221-100000000−i3i3i3−i3i3−i31-11-100000000000
χ3922-2-1-22-1212-2-21-10−i3i3-1-2211-1-222-21100001-1−i3−i3i3i3-12i−2i−2i2i-1100000000i3−i33−3−33−iii−i00000000000
χ4022-2-1-22-1212-2-21-10−i3i3-1-2211-1-222-21100001-1−i3−i3i3i3-1−2i2i2i−2i-1100000000i3−i3−333−3i−i−ii00000000000
χ4122-2-1-22-1212-2-21-10i3−i3-1-2211-12-2-22-1-100001-1i3i3−i3−i312-22-21-100000000i3−i3i3−i3i3−i3-11-1100000000000
χ4222-2-1-22-1212-2-21-10i3−i3-1-2211-12-2-22-1-100001-1i3i3−i3−i31-22-221-100000000i3−i3−i3i3−i3i31-11-100000000000
χ4322-2-1-22-1212-2-21-10i3−i3-1-2211-1-222-21100001-1i3i3−i3−i3-12i−2i−2i2i-1100000000−i3i3−333−3−iii−i00000000000
χ4422-2-1-22-1212-2-21-10i3−i3-1-2211-1-222-21100001-1i3i3−i3−i3-1−2i2i2i−2i-1100000000−i3i33−3−33i−i−ii00000000000
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
χ494444-4-44-14-1-1-1-4-4000-111-1-1-10000004-4−5511−55−5500000000−5−5550000000000000-11000000000
χ504444-4-44-14-1-1-1-4-4000-111-1-1-10000004-45−5115−55−50000000055−5−50000000000000-11000000000
χ514444-4-44-14-1-1-1-4-4000-111-1-1-1000000-44−5511−55−550000000055−5−500000000000001-1000000000
χ524444-4-44-14-1-1-1-4-4000-111-1-1-1000000-445−5115−55−500000000−5−55500000000000001-1000000000
χ53444-2-4-4-24-244422000-2-4-4-2-2-244-4-4-2-20000220000-200002200000000000000000000000000000
χ54444-2-4-4-24-244422000-2-4-4-2-2-2-4-44422000022000020000-2-200000000000000000000000000000
χ5544-4-24-4-2424-4-4-22000-24-422-24-44-4-2-20000-22000020000-2200000000000000000000000000000
χ5644-4-24-4-2424-4-4-22000-24-422-2-44-44220000-220000-200002-200000000000000000000000000000
χ57888-488-4-2-4-2-2-2-4-48-4-41-2-211100000000-2-2111111000000000000000000000000000000000000
χ58888-488-4-2-4-2-2-2-4-4-8441-2-2111000000002211-1-1-1-1000000000000000000000000000000000000
χ59888-4-8-8-4-2-4-2-2-24400012211100000000−2525-1-15−55−5000000000000000000000000000000000000
χ60888-4-8-8-4-2-4-2-2-2440001221110000000025−25-1-1−55−55000000000000000000000000000000000000
χ6188-888-88-2-8-2228-8000-2-2222-20000000000-220000000000000000000000000000000000000000
χ6288-88-888-2-8-222-88000-22-222-200000000002-20000000000000000000000000000000000000000
χ6388-8-48-8-4-24-222-440001-22-1-1100000000001-1−i15i15i15−i15000000000000000000000000000000000000
χ6488-8-48-8-4-24-222-440001-22-1-1100000000001-1i15−i15−i15i15000000000000000000000000000000000000
χ6588-8-4-88-4-24-2224-40−4i34i312-2-1-110000000000-11i3i3−i3−i3000000000000000000000000000000000000
χ6688-8-4-88-4-24-2224-404i3−4i312-2-1-110000000000-11−i3−i3i3i3000000000000000000000000000000000000
χ678-80800-880-8000000080000-80000000000000000000000000000000000000000000000000000
χ688-80800-8-202−252500000-200−25252000000000000000000000000−2ζ11+2ζ19−2ζ31+2ζ592ζ11−2ζ19+2ζ31−2ζ592ζ7−2ζ23−2ζ43+2ζ47−2ζ7+2ζ23+2ζ43−2ζ47000000000000000000000000
χ698-80800-8-202−252500000-200−252520000000000000000000000002ζ11−2ζ19+2ζ31−2ζ59−2ζ11+2ζ19−2ζ31+2ζ59−2ζ7+2ζ23+2ζ43−2ζ472ζ7−2ζ23−2ζ43+2ζ47000000000000000000000000
χ708-80800-8-20225−2500000-20025−2520000000000000000000000002ζ7−2ζ23−2ζ43+2ζ47−2ζ7+2ζ23+2ζ43−2ζ472ζ11−2ζ19+2ζ31−2ζ59−2ζ11+2ζ19−2ζ31+2ζ59000000000000000000000000
χ718-80800-8-20225−2500000-20025−252000000000000000000000000−2ζ7+2ζ23+2ζ43−2ζ472ζ7−2ζ23−2ζ43+2ζ47−2ζ11+2ζ19−2ζ31+2ζ592ζ11−2ζ19+2ζ31−2ζ59000000000000000000000000
χ728-80-400480-80000000-4000040000−4i34i30000000000000000000000000000000000000000000000
χ738-80-400480-80000000-40000400004i3−4i30000000000000000000000000000000000000000000000
χ7416-160-8008-404−45450000020025−25-20000000000000000000000000000000000000000000000000000
χ7516-160-8008-40445−4500000200−2525-20000000000000000000000000000000000000000000000000000

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