Finite Group Databasebeta

← Group #14303072

Character table — Group #14303072

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size1122222444444488888888810101010101012121616161616161616202020202020202424242424404040404040404040404040404848606060606060120120120
order1222236566610101041010121215303030444412122420203030606060608888121212210101010488121224242424242424241020248888288
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
χ911111111111111-111-1-1111111111111-1-111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1
χ1011111111111111-111-1-1111111111111-1-111-1-1-1-1-1-1-1-1111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-111
χ1111111111111111-111-1-11111111111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111
χ1211111111111111-111-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-111-1-11111-1-1-1-1-1-1-1-111111-1-1
χ1311111111111111-111-1-11111-1-1-1-1-1-111-1-111-1-1-1-1ii−i−i-1-1-1-1-1-1-1-11−ii11−i−iiiii−i−i11-1-1ii−i−i1−ii
χ1411111111111111-111-1-11111-1-1-1-1-1-111-1-111-1-1-1-1−i−iii-1-1-1-1-1-1-1-11i−i11ii−i−i−i−iii11-1-1−i−iii1i−i
χ1511111111111111-111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1ii−i−i-1-1-1111111−ii11−i−iiiii−i−i-1-111−i−iii-1i−i
χ1611111111111111-111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1−i−iii-1-1-1111111i−i11ii−i−i−i−iii-1-111ii−i−i-1−ii
χ1722222-1-12-1-1-1222222-1-1-1-1-1-12222-1-10022-1-1-1-1-1-12222-1-1-100000222-1-1-1-1-1-1-1-1-1-100000000000
χ1822222-1-12-1-1-1222222-1-1-1-1-1-12222-1-10022-1-1-1-1-1-1-2-2-2-2-1-1-1000002-2-2-1-11111111100000000000
χ1922222-1-12-1-1-1222222-1-1-1-1-1-1-2-2-2-2110022-1-1-1-1-1-12i2i−2i−2i11100000-22i−2i11−i−iii−i−iii00000000000
χ2022222-1-12-1-1-1222222-1-1-1-1-1-1-2-2-2-2110022-1-1-1-1-1-1−2i−2i2i2i11100000-2−2i2i11ii−i−iii−i−i00000000000
χ2122222-1-12-1-1-1222-22211-1-1-1-12222-1-100-2-2-1-111112222-1-1-100000-2-2-2111111-1-1-1-100000000000
χ2222222-1-12-1-1-1222-22211-1-1-1-12222-1-100-2-2-1-11111-2-2-2-2-1-1-100000-22211-1-1-1-1111100000000000
χ2322222-1-12-1-1-1222-22211-1-1-1-1-2-2-2-21100-2-2-1-111112i2i−2i−2i111000002−2i2i-1-1ii−i−i−i−iii00000000000
χ2422222-1-12-1-1-1222-22211-1-1-1-1-2-2-2-21100-2-2-1-11111−2i−2i2i2i1110000022i−2i-1-1−i−iiiii−i−i00000000000
χ25222-2-22222-2-2-2-2202-20022-2-222-2-22200002-200002i−2i2i−2i2-2-2000000000000002i−2i2i−2i00000000000
χ26222-2-22222-2-2-2-2202-20022-2-222-2-22200002-20000−2i2i−2i2i2-2-200000000000000−2i2i−2i2i00000000000
χ27222-2-22222-2-2-2-2202-20022-2-2-2-222-2-200002-200002-2-22-222000000000000002-2-2200000000000
χ28222-2-22222-2-2-2-2202-20022-2-2-2-222-2-200002-20000-222-2-22200000000000000-222-200000000000
χ29222-2-2-1-12-111-2-2202-23−3-1-11122-2-2-1-10000-1133−3−32i−2i2i−2i-111000000003−3−i3i3−i3i3−ii−ii00000000000
χ30222-2-2-1-12-111-2-2202-23−3-1-11122-2-2-1-10000-1133−3−3−2i2i−2i2i-111000000003−3i3−i3i3−i3i−ii−i00000000000
χ31222-2-2-1-12-111-2-2202-23−3-1-111-2-222110000-1133−3−32-2-221-1-100000000−33−333−3-111-100000000000
χ32222-2-2-1-12-111-2-2202-23−3-1-111-2-222110000-1133−3−3-222-21-1-100000000−333−3−331-1-1100000000000
χ33222-2-2-1-12-111-2-2202-2−33-1-11122-2-2-1-10000-11−3−3332i−2i2i−2i-11100000000−33i3−i3i3−i3−ii−ii00000000000
χ34222-2-2-1-12-111-2-2202-2−33-1-11122-2-2-1-10000-11−3−333−2i2i−2i2i-11100000000−33−i3i3−i3i3i−ii−i00000000000
χ35222-2-2-1-12-111-2-2202-2−33-1-111-2-222110000-11−3−3332-2-221-1-1000000003−33−3−33-111-100000000000
χ36222-2-2-1-12-111-2-2202-2−33-1-111-2-222110000-11−3−333-222-21-1-1000000003−3−333−31-1-1100000000000
χ3722-22-2222-22-2-2-220-220022-2-22-22-2-2-20000-220000000022-200000000000000000000002i−2i2i−2i000
χ3822-22-2222-22-2-2-220-220022-2-22-22-2-2-20000-220000000022-20000000000000000000000−2i2i−2i2i000
χ3922-22-2222-22-2-2-220-220022-2-2-22-22220000-2200000000-2-2200000000000000000000002-2-22000
χ4022-22-2222-22-2-2-220-220022-2-2-22-22220000-2200000000-2-220000000000000000000000-222-2000
χ4122-2-22222-2-222220-2-20022222-2-22-2-22-200-2-2000000002-220000000000000000002-2-220000000
χ4222-2-22222-2-222220-2-20022222-2-22-2-2-2200-2-2000000002-22000000000000000000-222-20000000
χ4322-2-22222-2-222220-2-2002222-222-2222-200-2-200000000-22-20000000000000000002-22-20000000
χ4422-2-22222-2-222220-2-2002222-222-222-2200-2-200000000-22-2000000000000000000-22-220000000
χ454444444-1444-1-1-14-1-144-1-1-1-100000044-1-1-1-1-1-1-1-100000004-1-1-1-10000000000000-1-1000000000
χ464444444-1444-1-1-14-1-144-1-1-1-1000000-4-4-1-1-1-1-1-1-1-10000000-41111000000000000011000000000
χ474444444-1444-1-1-1-4-1-1-4-4-1-1-1-10000004411-1-111110000000-411110000000000000-1-1000000000
χ484444444-1444-1-1-1-4-1-1-4-4-1-1-1-1000000-4-411-1-1111100000004-1-1-1-1000000000000011000000000
χ4944-44-4-2-242-22-4-440-4400-2-2224-44-42200002-200000000-2-2200000000000000000000000000000
χ5044-44-4-2-242-22-4-440-4400-2-222-44-44-2-200002-20000000022-200000000000000000000000000000
χ5144-4-4444-1-4-44-1-1-101100-1-1-1-10000004-4−5511−55−5500000000−5−5550000000000000-11000000000
χ5244-4-4444-1-4-44-1-1-101100-1-1-1-10000004-45−5115−55−50000000055−5−50000000000000-11000000000
χ5344-4-4444-1-4-44-1-1-101100-1-1-1-1000000-44−5511−55−550000000055−5−500000000000001-1000000000
χ5444-4-4444-1-4-44-1-1-101100-1-1-1-1000000-445−5115−55−500000000−5−55500000000000001-1000000000
χ5544-4-44-2-2422-24440-4-400-2-2-2-24-4-442200002200000000-22-200000000000000000000000000000
χ5644-4-44-2-2422-24440-4-400-2-2-2-2-444-4-2-2000022000000002-2200000000000000000000000000000
χ5788888-4-4-2-4-4-4-2-2-28-2-2-4-4111100000000-2-2111111000000000000000000000000000000000000
χ5888888-4-4-2-4-4-4-2-2-2-8-2-2441111000000002211-1-1-1-1000000000000000000000000000000000000
χ59888-8-888-28-8-822-20-2200-2-2220000000000-220000000000000000000000000000000000000000
χ60888-8-8-4-4-2-44422-20-2243−4311-1-100000000001-1−3−333000000000000000000000000000000000000
χ61888-8-8-4-4-2-44422-20-22−434311-1-100000000001-133−3−3000000000000000000000000000000000000
χ6288-88-888-2-88-822-202-200-2-22200000000002-20000000000000000000000000000000000000000
χ6388-88-8-4-4-24-4422-202-20011-1-10000000000-11−151515−15000000000000000000000000000000000000
χ6488-88-8-4-4-24-4422-202-20011-1-10000000000-1115−15−1515000000000000000000000000000000000000
χ6588-8-88-4-4-244-4-2-2-202200111100000000−2525-1-15−55−5000000000000000000000000000000000000
χ6688-8-88-4-4-244-4-2-2-20220011110000000025−25-1-1−55−55000000000000000000000000000000000000
χ678-80008-8800000-8000008-8000000000000000000000000000000000000000000000000000000
χ688-80008-8-2000−2525200000-22−25250000000000000000000000002ζ2+2ζ22−2ζ38−2ζ58−2ζ2−2ζ22+2ζ38+2ζ58−2ζ14+2ζ26−2ζ34+2ζ462ζ14−2ζ26+2ζ34−2ζ46000000000000000000000000
χ698-80008-8-2000−2525200000-22−2525000000000000000000000000−2ζ2−2ζ22+2ζ38+2ζ582ζ2+2ζ22−2ζ38−2ζ582ζ14−2ζ26+2ζ34−2ζ46−2ζ14+2ζ26−2ζ34+2ζ46000000000000000000000000
χ708-80008-8-200025−25200000-2225−25000000000000000000000000−2ζ14+2ζ26−2ζ34+2ζ462ζ14−2ζ26+2ζ34−2ζ46−2ζ2−2ζ22+2ζ38+2ζ582ζ2+2ζ22−2ζ38−2ζ58000000000000000000000000
χ718-80008-8-200025−25200000-2225−250000000000000000000000002ζ14−2ζ26+2ζ34−2ζ46−2ζ14+2ζ26−2ζ34+2ζ462ζ2+2ζ22−2ζ38−2ζ58−2ζ2−2ζ22+2ζ38+2ζ58000000000000000000000000
χ728-8000-44800000-800000-4400000043−430000000000000000000000000000000000000000000000
χ738-8000-44800000-800000-44000000−43430000000000000000000000000000000000000000000000
χ7416-16000-88-4000−45454000002-225−250000000000000000000000000000000000000000000000000000
χ7516-16000-88-400045−454000002-2−25250000000000000000000000000000000000000000000000000000

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