Finite Group Databasebeta

← Group #14313445

Character table — Group #14313445

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1122244444444445588888888101010121216161616161616162020202020202424242424404040404040404040404040404048486060120120120120120
order12236444561010101212441212152020303030412124420206060606060602226612220202020444466121212121212121210104444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111-1-1-1-1
χ31111111111111111111111111111-1-111111111111111-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111-1-111111111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111-1-111111111-1-1-11111111111-1-1-1-1-1-111111ii−i−i-1-1iiii−i−i−i−i11-1-1-1ii−i−i
χ6111111111111111-1-111111111-1-1-11111111111-1-1-1-1-1-111111−i−iii-1-1−i−i−i−iiiii11-1-1-1−i−iii
χ7111111111111111-1-111111111-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1ii−i−i-1-1iiii−i−i−i−i-1-1111−i−iii
χ8111111111111111-1-111111111-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1−i−iii-1-1−i−i−i−iiiii-1-1111ii−i−i
χ9111111-1-111111-1-1111-111111111111-1-111-1-1-1-11-1-1-1-11-11111i−ii−i1-1ii−i−iii−i−i-1-111-1i−ii−i
χ10111111-1-111111-1-1111-111111111111-1-111-1-1-1-11-1-1-1-11-11111−ii−ii1-1−i−iii−i−iii-1-111-1−ii−ii
χ11111111-1-111111-1-1111-1111111111-1-1-1-111-1-1-1-11-1-1-1-111-1-1-1-1i−ii−i1-1ii−i−iii−i−i11-1-11−ii−ii
χ12111111-1-111111-1-1111-1111111111-1-1-1-111-1-1-1-11-1-1-1-111-1-1-1-1−ii−ii1-1−i−iii−i−iii11-1-11i−ii−i
χ13111111-1-111111-1-1-1-11-1111111-1-1-111-1-111-1-1-1-1-11111-1-111111-1-11-1111-1-1-1-111-1-1-1-111-1-11
χ14111111-1-111111-1-1-1-11-1111111-1-1-111-1-111-1-1-1-1-11111-1-11111-111-1-11-1-11111-1-1-1-1-1-11-111-1
χ15111111-1-111111-1-1-1-11-1111111-1-1-1-1-1-1-111-1-1-1-1-11111-11-1-1-1-11-1-11-1111-1-1-1-1111111-1-111-1
χ16111111-1-111111-1-1-1-11-1111111-1-1-1-1-1-1-111-1-1-1-1-11111-11-1-1-1-1-111-1-11-1-11111-1-11111-11-1-11
χ1722222-22-2222222222-2-22-2-2222222002-2-2-222-2-2-22-2222000000000-2-200000000000000000
χ1822222-22-22222222-2-2-2-22-2-2222-2-2-2002-2-2-222-2-22-22-2-2-20000000002200000000000000000
χ1922222-2-2222222-2-222-222-2-222222200-22-2-2-2-222-2-22-2-22000000000-2200000000000000000
χ2022222-2-2222222-2-2-2-2-222-2-2222-2-2-200-22-2-2-2-22222-222-20000000002-200000000000000000
χ21222-1-12222-1222-1-122-1-1-122-1-1-12-1-10022-1-1-1-1-1-1222-1-1-1000002222-1-1-1-1-1-1-1-1-1-1000000000
χ22222-1-12222-1222-1-122-1-1-122-1-1-12-1-10022-1-1-1-1-1-1222-1-1-100000-2-2-2-2-1-111111111000000000
χ23222-1-12222-1222-1-1-2-2-1-1-122-1-1-1-2110022-1-1-1-1-1-1-2-2-2111000002i2i−2i−2i11−i−i−i−iiiii000000000
χ24222-1-12222-1222-1-1-2-2-1-1-122-1-1-1-2110022-1-1-1-1-1-1-2-2-211100000−2i−2i2i2i11iiii−i−i−i−i000000000
χ25222-1-12-2-22-12221122-11-122-1-1-12-1-100-2-2-1-111112-2-211-1000002i−2i2i−2i-11−i−iii−i−iii000000000
χ26222-1-12-2-22-12221122-11-122-1-1-12-1-100-2-2-1-111112-2-211-100000−2i2i−2i2i-11ii−i−iii−i−i000000000
χ27222-1-12-2-22-122211-2-2-11-122-1-1-1-21100-2-2-1-11111-222-1-11000002-2-221-1-1-11111-1-1000000000
χ28222-1-12-2-22-122211-2-2-11-122-1-1-1-21100-2-2-1-11111-222-1-1100000-222-21-111-1-1-1-111000000000
χ29222-1-1-22-22-1222-1-12211-1-2-2-1-1-12-1-1002-211-1-111-22-2-1-1-100000000011−i3i3−i3i3−i3i3−i3i3000000000
χ30222-1-1-22-22-1222-1-12211-1-2-2-1-1-12-1-1002-211-1-111-22-2-1-1-100000000011i3−i3i3−i3i3−i3i3−i3000000000
χ31222-1-1-22-22-1222-1-1-2-211-1-2-2-1-1-1-211002-211-1-1112-22111000000000-1-13−33−3−33−33000000000
χ32222-1-1-22-22-1222-1-1-2-211-1-2-2-1-1-1-211002-211-1-1112-22111000000000-1-1−33−333−33−3000000000
χ33222-1-1-2-222-122211221-1-1-2-2-1-1-12-1-100-221111-1-1-2-2211-10000000001-13−3−333−3−33000000000
χ34222-1-1-2-222-122211221-1-1-2-2-1-1-12-1-100-221111-1-1-2-2211-10000000001-1−333−3−333−3000000000
χ35222-1-1-2-222-122211-2-21-1-1-2-2-1-1-1-21100-221111-1-122-2-1-11000000000-11−i3i3i3−i3i3−i3−i3i3000000000
χ36222-1-1-2-222-122211-2-21-1-1-2-2-1-1-1-21100-221111-1-122-2-1-11000000000-11i3−i3−i3i3−i3i3i3−i3000000000
χ3744444444-14-1-1-1440044-1-1-1-1-1-100044-1-1-1-1-1-1-1-10000004-1-1-1-100000000000000-1-10000000
χ3844444444-14-1-1-1440044-1-1-1-1-1-1000-4-4-1-1-1-1-1-1-1-1000000-4111100000000000000110000000
χ39444444-4-4-14-1-1-1-4-4004-4-1-1-1-1-1-10004411-1-11111000000-4-1-1-1-100000000000000110000000
χ40444444-4-4-14-1-1-1-4-4004-4-1-1-1-1-1-1000-4-411-1-111110000004111100000000000000-1-10000000
χ4144444-44-4-14-1-1-14400-4-4-111-1-1-100000-1111-1-1110000000−5−55500000000000000−550000000
χ4244444-44-4-14-1-1-14400-4-4-111-1-1-100000-1111-1-111000000055−5−5000000000000005−50000000
χ4344444-4-44-14-1-1-1-4-400-44-111-1-1-1000001-11111-1-10000000−5−555000000000000005−50000000
χ4444444-4-44-14-1-1-1-4-400-44-111-1-1-1000001-11111-1-1000000055−5−500000000000000−550000000
χ4544-4440004-44-4-4004400400-4-44-444000000000000000-40000000000000000000000000000
χ4644-4440004-44-4-400-4-400400-4-444-4-400000000000000040000000000000000000000000000
χ4744-4-2-2000424-4-4−2i32i34400-20022-2-4-2-2000000−2i32i300000−2i32i320000000000000000000000000000
χ4844-4-2-2000424-4-4−2i32i3-4-400-20022-2422000000−2i32i3000002i3−2i3-20000000000000000000000000000
χ4944-4-2-2000424-4-42i3−2i34400-20022-2-4-2-20000002i3−2i3000002i3−2i320000000000000000000000000000
χ5044-4-2-2000424-4-42i3−2i3-4-400-20022-24220000002i3−2i300000−2i32i3-20000000000000000000000000000
χ514-404-400040-400004i−4i0040000-404i−4i2i−2i0000000000000002i−2i2i−2i00000000000000002-200000
χ524-404-400040-400004i−4i0040000-404i−4i−2i2i000000000000000−2i2i−2i2i0000000000000000-2200000
χ534-404-400040-40000−4i4i0040000-40−4i4i2i−2i0000000000000002i−2i2i−2i0000000000000000-2200000
χ544-404-400040-40000−4i4i0040000-40−4i4i−2i2i000000000000000−2i2i−2i2i00000000000000002-200000
χ55888-4-4888-2-4-2-2-2-4-400-4-41-2-211100000-2-21111110000000000000000000000000000000000
χ56888-4-48-8-8-2-4-2-2-24400-441-2-2111000002211-1-1-1-10000000000000000000000000000000000
χ57888-4-4-88-8-2-4-2-2-2-4-4004412211100000-22-1-111-1-10000000000000000000000000000000000
χ58888-4-4-8-88-2-4-2-2-244004-4122111000002-2-1-1-1-1110000000000000000000000000000000000
χ5988-888000-2-8-222000000-2−252522-20000000−252500000000000000000000000000000000000000
χ6088-888000-2-8-222000000-225−2522-2000000025−2500000000000000000000000000000000000000
χ6188-8-4-4000-24-222−4i34i300001−2525-1-1100000005−5i3−i3−i15i150000000000000000000000000000000000
χ6288-8-4-4000-24-222−4i34i30000125−25-1-110000000−55i3−i3i15−i150000000000000000000000000000000000
χ6388-8-4-4000-24-2224i3−4i300001−2525-1-1100000005−5−i3i3i15−i150000000000000000000000000000000000
χ6488-8-4-4000-24-2224i3−4i30000125−25-1-110000000−55−i3i3−i15i150000000000000000000000000000000000
χ658-808-8000-202−2525000000-200−252520004i−4i000000000000000−2ζ11−2ζ19−2ζ31−2ζ592ζ11+2ζ19+2ζ31+2ζ59−2ζ7−2ζ23−2ζ43−2ζ472ζ7+2ζ23+2ζ43+2ζ4700000000000000000000000
χ668-808-8000-202−2525000000-200−25252000−4i4i0000000000000002ζ11+2ζ19+2ζ31+2ζ59−2ζ11−2ζ19−2ζ31−2ζ592ζ7+2ζ23+2ζ43+2ζ47−2ζ7−2ζ23−2ζ43−2ζ4700000000000000000000000
χ678-808-8000-20225−25000000-20025−2520004i−4i000000000000000−2ζ7−2ζ23−2ζ43−2ζ472ζ7+2ζ23+2ζ43+2ζ47−2ζ11−2ζ19−2ζ31−2ζ592ζ11+2ζ19+2ζ31+2ζ5900000000000000000000000
χ688-808-8000-20225−25000000-20025−252000−4i4i0000000000000002ζ7+2ζ23+2ζ43+2ζ47−2ζ7−2ζ23−2ζ43−2ζ472ζ11+2ζ19+2ζ31+2ζ59−2ζ11−2ζ19−2ζ31−2ζ5900000000000000000000000
χ698-80-4400080-800008i−8i00-4000040−4i4i00000000000000000000000000000000000000000000
χ708-80-4400080-80000−8i8i00-40000404i−4i00000000000000000000000000000000000000000000
χ7116-160-88000-404−454500000020025−25-200000000000000000000000000000000000000000000000
χ7216-160-88000-40445−45000000200−2525-200000000000000000000000000000000000000000000000

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