Finite Group Databasebeta

← Group #14303021

Character table — Group #14303021

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size11222224444444448888888810101010101016161616161616162020202020242424242424404040404040404040404040404048486060606060606060120120
order122223624566610101061010121530303022226610203030303060602466624101010104444612121212121212121220204444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111
χ31111111111111111111111111111111111111111111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1
χ5111111111111111111111111-1-1-1-1-1-111111111-1-1-1-1-1111111ii−i−i-1-1iiii−i−i−i−i11iiii−i−i−i−i-1-1
χ6111111111111111111111111-1-1-1-1-1-111111111-1-1-1-1-1111111−i−iii-1-1−i−i−i−iiiii11−i−i−i−iiiii-1-1
χ7111111111111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1ii−i−i-1-1iiii−i−i−i−i-1-1−i−i−i−iiiii11
χ8111111111111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1−i−iii-1-1−i−i−i−iiiii-1-1iiii−i−i−i−i11
χ91111111-1-11111111-111-11111111111-1-111-1-1-1-1-1-11111-111111-11-1-1-111-1-111-1-1-1-111-1-111-1-11-1
χ101111111-1-11111111-111-11111111111-1-111-1-1-1-1-1-11111-11111-11-11-1-1-1-111-1-111-1-1-1-111-1-1111-1
χ111111111-1-11111111-111-11111111111-1-111-1-1-1-1-1-1111-11-1-1-1-11-11-1-1-111-1-111-1-111-1-111-1-111-11
χ121111111-1-11111111-111-11111111111-1-111-1-1-1-1-1-1111-11-1-1-1-1-11-11-1-1-1-111-1-1111111-1-111-1-1-11
χ131111111-1-11111111-111-11111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-11-11111i−i−ii11ii−i−i−i−iii-1-1ii−i−i−i−iii-11
χ141111111-1-11111111-111-11111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-11-11111−iii−i11−i−iiiii−i−i-1-1−i−iiiii−i−i-11
χ151111111-1-11111111-111-11111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11-1-1-1-1i−i−ii11ii−i−i−i−iii11−i−iiiii−i−i1-1
χ161111111-1-11111111-111-11111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11-1-1-1-1−iii−i11−i−iiiii−i−i11ii−i−i−i−iii1-1
χ1722222-1-1222-1-1-1222-122-1-1-1-1-12222-1-122-1-1-1-1-1-122-1-1-10000002222-1-1-1-1-1-1-1-1-1-1000000000000
χ1822222-1-1222-1-1-1222-122-1-1-1-1-12222-1-122-1-1-1-1-1-122-1-1-1000000-2-2-2-2-1-111111111000000000000
χ1922222-1-1222-1-1-1222-122-1-1-1-1-1-2-2-2-21122-1-1-1-1-1-1-2-21110000002i2i−2i−2i11−i−i−i−iiiii000000000000
χ2022222-1-1222-1-1-1222-122-1-1-1-1-1-2-2-2-21122-1-1-1-1-1-1-2-2111000000−2i−2i2i2i11iiii−i−i−i−i000000000000
χ2122222-1-1-2-22-1-1-12221221-1-1-1-12222-1-1-2-2-1-11111-2-2-1-1-10000002-22-211-1-111-1-111000000000000
χ2222222-1-1-2-22-1-1-12221221-1-1-1-12222-1-1-2-2-1-11111-2-2-1-1-1000000-22-221111-1-111-1-1000000000000
χ2322222-1-1-2-22-1-1-12221221-1-1-1-1-2-2-2-211-2-2-1-11111221110000002i−2i−2i2i-1-1−i−iiiii−i−i000000000000
χ2422222-1-1-2-22-1-1-12221221-1-1-1-1-2-2-2-211-2-2-1-1111122111000000−2i2i2i−2i-1-1ii−i−i−i−iii000000000000
χ25222-2-2220022-2-22-2-202-202-2-2222-2-222002-2000000-22-20000000000000000000000002i−2i002i−2i00
χ26222-2-2220022-2-22-2-202-202-2-2222-2-222002-2000000-22-2000000000000000000000000−2i2i00−2i2i00
χ27222-2-2220022-2-22-2-202-202-2-22-2-222-2-2002-20000002-220000000000000000000000002-200-2200
χ28222-2-2220022-2-22-2-202-202-2-22-2-222-2-2002-20000002-22000000000000000000000000-22002-200
χ2922-22-222002-22-22-2-20-2202-2-222-22-22200-22000000-2-2200000000000000000000002i−2i002i−2i0000
χ3022-22-222002-22-22-2-20-2202-2-222-22-22200-22000000-2-220000000000000000000000−2i2i00−2i2i0000
χ3122-22-222002-22-22-2-20-2202-2-22-22-22-2-200-2200000022-200000000000000000000002-200-220000
χ3222-22-222002-22-22-2-20-2202-2-22-22-22-2-200-2200000022-20000000000000000000000-22002-20000
χ3322-2-22222-22-2-222222-2-2-222222-2-22222-2-2-222-2-22-22-2-200000000002-200000000000000000000
χ3422-2-22222-22-2-222222-2-2-22222-222-2-2-22-2-2-222-2-2-22-2220000000000-2200000000000000000000
χ3522-2-2222-222-2-22222-2-2-2222222-2-2222-22-2-2-2-222-222-2-20000000000-2200000000000000000000
χ3622-2-2222-222-2-22222-2-2-222222-222-2-2-2-22-2-2-2-2222-2-22200000000002-200000000000000000000
χ3722-2-22-1-12-2211-1222-1-2-21-1-1-1-12-2-22-1-12-211-1-1112-2-1110000000000-113−33−33−33−3000000000000
χ3822-2-22-1-12-2211-1222-1-2-21-1-1-1-12-2-22-1-12-211-1-1112-2-1110000000000-11−33−33−33−33000000000000
χ3922-2-22-1-12-2211-1222-1-2-21-1-1-1-1-222-2112-211-1-111-221-1-100000000001-1−i3i3−i3i3i3−i3i3−i3000000000000
χ4022-2-22-1-12-2211-1222-1-2-21-1-1-1-1-222-2112-211-1-111-221-1-100000000001-1i3−i3i3−i3−i3i3−i3i3000000000000
χ4122-2-22-1-1-22211-12221-2-2-1-1-1-1-12-2-22-1-1-221111-1-1-22-11100000000001-13−3−333−3−33000000000000
χ4222-2-22-1-1-22211-12221-2-2-1-1-1-1-12-2-22-1-1-221111-1-1-22-11100000000001-1−333−3−333−3000000000000
χ4322-2-22-1-1-22211-12221-2-2-1-1-1-1-1-222-211-221111-1-12-21-1-10000000000-11−i3i3i3−i3i3−i3−i3i3000000000000
χ4422-2-22-1-1-22211-12221-2-2-1-1-1-1-1-222-211-221111-1-12-21-1-10000000000-11i3−i3−i3i3−i3i3i3−i3000000000000
χ45444444444-1444-1-1-14-1-14-1-1-1-1000000-1-1-1-1-1-1-1-10000044-1-1-1-100000000000000-1-10000000000
χ46444444444-1444-1-1-14-1-14-1-1-1-1000000-1-1-1-1-1-1-1-100000-4-4111100000000000000110000000000
χ474444444-4-4-1444-1-1-1-4-1-1-4-1-1-1-100000011-1-11111000004-4-1-1-1-100000000000000110000000000
χ484444444-4-4-1444-1-1-1-4-1-1-4-1-1-1-100000011-1-1111100000-44111100000000000000-1-10000000000
χ49444-4-4-2-2004-2224-4-404-40-222-244-4-4-2-200-220000002-2200000000000000000000000000000000
χ50444-4-4-2-2004-2224-4-404-40-222-2-4-4442200-22000000-22-200000000000000000000000000000000
χ5144-44-4-2-20042-224-4-40-440-222-24-44-4-2-2002-200000022-200000000000000000000000000000000
χ5244-44-4-2-20042-224-4-40-440-222-2-44-4422002-2000000-2-2200000000000000000000000000000000
χ5344-4-44444-4-1-4-44-1-1-1411-4-1-1-1-1000000-1111-1-1110000000−5−55500000000000000−550000000000
χ5444-4-44444-4-1-4-44-1-1-1411-4-1-1-1-1000000-1111-1-111000000055−5−5000000000000005−50000000000
χ5544-4-4444-44-1-4-44-1-1-1-4114-1-1-1-10000001-11111-1-10000000−5−555000000000000005−50000000000
χ5644-4-4444-44-1-4-44-1-1-1-4114-1-1-1-10000001-11111-1-1000000055−5−500000000000000−550000000000
χ5788888-4-488-2-4-4-4-2-2-2-4-2-2-41111000000-2-21111110000000000000000000000000000000000000
χ5888888-4-4-8-8-2-4-4-4-2-2-24-2-2411110000002211-1-1-1-10000000000000000000000000000000000000
χ59888-8-88800-28-8-8-2220-220-222-200000000-2200000000000000000000000000000000000000000
χ60888-8-8-4-400-2-444-2220-2201-1-11000000001-1−i15i15−i15i150000000000000000000000000000000000000
χ61888-8-8-4-400-2-444-2220-2201-1-11000000001-1i15−i15i15−i150000000000000000000000000000000000000
χ6288-88-88800-2-88-8-22202-20-222-2000000002-200000000000000000000000000000000000000000
χ6388-88-8-4-400-24-44-22202-201-1-1100000000-11−i15i15i15−i150000000000000000000000000000000000000
χ6488-88-8-4-400-24-44-22202-201-1-1100000000-11i15−i15−i15i150000000000000000000000000000000000000
χ6588-8-88-4-48-8-244-4-2-2-2-42241111000000-22-1-111-1-10000000000000000000000000000000000000
χ6688-8-88-4-4-88-244-4-2-2-2422-411110000002-2-1-1-1-1110000000000000000000000000000000000000
χ678-80008-8008000-8000000800-8000000000000000000000000000000000000000000000000000
χ688-80008-800-20002−25250000-2−25252000000000000000000000−2ζ14+2ζ26−2ζ34+2ζ462ζ14−2ζ26+2ζ34−2ζ462ζ2+2ζ22−2ζ38−2ζ58−2ζ2−2ζ22+2ζ38+2ζ5800000000000000000000000000
χ698-80008-800-20002−25250000-2−252520000000000000000000002ζ14−2ζ26+2ζ34−2ζ46−2ζ14+2ζ26−2ζ34+2ζ46−2ζ2−2ζ22+2ζ38+2ζ582ζ2+2ζ22−2ζ38−2ζ5800000000000000000000000000
χ708-80008-800-2000225−250000-225−2520000000000000000000002ζ2+2ζ22−2ζ38−2ζ58−2ζ2−2ζ22+2ζ38+2ζ582ζ14−2ζ26+2ζ34−2ζ46−2ζ14+2ζ26−2ζ34+2ζ4600000000000000000000000000
χ718-80008-800-2000225−250000-225−252000000000000000000000−2ζ2−2ζ22+2ζ38+2ζ582ζ2+2ζ22−2ζ38−2ζ58−2ζ14+2ζ26−2ζ34+2ζ462ζ14−2ζ26+2ζ34−2ζ4600000000000000000000000000
χ728-8000-44008000-8000000-40040000−4i34i3000000000000000000000000000000000000000000000
χ738-8000-44008000-8000000-400400004i3−4i3000000000000000000000000000000000000000000000
χ7416-16000-8800-40004−45450000225−25-2000000000000000000000000000000000000000000000000000
χ7516-16000-8800-4000445−4500002−2525-2000000000000000000000000000000000000000000000000000

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