Finite Group Databasebeta

← Group #14313188

Character table — Group #14313188

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1122244444444445588888888101010121216161616161616162020202020202424242424404040404040404040404040404048486060120120120120120
order12236224566610101044610101215303030412124410203030303060602441212124202020206888812242424242424242420202244444
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-111111-1-1-1-1
χ31111111111111111111111111111-1-111111111111111-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111-1-111111111111111-1-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111-1-111111111-1-1-11111111111-1-1-1-1-1-111111-1ii−i−i-1iiii−i−i−i−i11-1-1-1ii−i−i
χ6111111111111111-1-111111111-1-1-11111111111-1-1-1-1-1-111111-1−i−iii-1−i−i−i−iiiii11-1-1-1−i−iii
χ7111111111111111-1-111111111-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i-1iiii−i−i−i−i-1-1111−i−iii
χ8111111111111111-1-111111111-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−iii-1−i−i−i−iiiii-1-1111ii−i−i
χ9111111-1-111-1-111111111-1111111111-1-111-1-1-1-1-11-11-1-1-11111-1i−ii−i1ii−i−iii−i−i-1-111-1i−ii−i
χ10111111-1-111-1-111111111-1111111111-1-111-1-1-1-1-11-11-1-1-11111-1−ii−ii1−i−iii−i−iii-1-111-1−ii−ii
χ11111111-1-111-1-111111111-11111111-1-1-1-111-1-1-1-1-11-11-1-11-1-1-1-1-1i−ii−i1ii−i−iii−i−i11-1-11−ii−ii
χ12111111-1-111-1-111111111-11111111-1-1-1-111-1-1-1-1-11-11-1-11-1-1-1-1-1−ii−ii1−i−iii−i−iii11-1-11i−ii−i
χ13111111-1-111-1-1111-1-1111-11111-1-1-111-1-111-1-1-1-11-11-111-1111111-1-11-111-1-1-1-111-1-1-1-111-1-11
χ14111111-1-111-1-1111-1-1111-11111-1-1-111-1-111-1-1-1-11-11-111-111111-111-1-1-1-11111-1-1-1-1-1-11-111-1
χ15111111-1-111-1-1111-1-1111-11111-1-1-1-1-1-1-111-1-1-1-11-11-1111-1-1-1-111-1-11-111-1-1-1-1111111-1-111-1
χ16111111-1-111-1-1111-1-1111-11111-1-1-1-1-1-1-111-1-1-1-11-11-1111-1-1-1-11-111-1-1-1-11111-1-11111-11-1-11
χ1722222-22-2222222222-2-2-2-22222222002-2-2-222-2-2-2-2222200000-20000-200000000000000000
χ1822222-22-22222222-2-2-2-2-2-22222-2-2-2002-2-2-222-2-222-2-2-2-20000020000200000000000000000
χ1922222-2-2222-2-222222-2-2-22222222200-22-2-2-2-2222-2-22-2-20000020000-200000000000000000
χ2022222-2-2222-2-2222-2-2-2-2-222222-2-2-200-22-2-2-2-222-222-22200000-20000200000000000000000
χ21222-1-12222-1-1-122222-122-1-1-1-1-12-1-10022-1-1-1-1-1-1222-1-1-100000-12222-1-1-1-1-1-1-1-1-1000000000
χ22222-1-12222-1-1-122222-122-1-1-1-1-12-1-10022-1-1-1-1-1-1222-1-1-100000-1-2-2-2-2-111111111000000000
χ23222-1-12222-1-1-1222-2-2-122-1-1-1-1-1-2110022-1-1-1-1-1-1-2-2-21110000012i2i−2i−2i1−i−i−i−iiiii000000000
χ24222-1-12222-1-1-1222-2-2-122-1-1-1-1-1-2110022-1-1-1-1-1-1-2-2-2111000001−2i−2i2i2i1iiii−i−i−i−i000000000
χ25222-1-12-2-22-11122222-1221-1-1-1-12-1-100-2-2-1-11111-22-2-1110000012i−2i2i−2i-1−i−iii−i−iii000000000
χ26222-1-12-2-22-11122222-1221-1-1-1-12-1-100-2-2-1-11111-22-2-111000001−2i2i−2i2i-1ii−i−iii−i−i000000000
χ27222-1-12-2-22-111222-2-2-1221-1-1-1-1-21100-2-2-1-111112-221-1-100000-12-2-221-1-11111-1-1000000000
χ28222-1-12-2-22-111222-2-2-1221-1-1-1-1-21100-2-2-1-111112-221-1-100000-1-222-2111-1-1-1-111000000000
χ29222-1-1-22-22-1-1-1222221-2-21-1-1-1-12-1-1002-211-1-111-2-22-1-1-100000100001−i3i3−i3i3−i3i3−i3i3000000000
χ30222-1-1-22-22-1-1-1222221-2-21-1-1-1-12-1-1002-211-1-111-2-22-1-1-100000100001i3−i3i3−i3i3−i3i3−i3000000000
χ31222-1-1-22-22-1-1-1222-2-21-2-21-1-1-1-1-211002-211-1-11122-211100000-10000-13−33−3−33−33000000000
χ32222-1-1-22-22-1-1-1222-2-21-2-21-1-1-1-1-211002-211-1-11122-211100000-10000-1−33−333−33−3000000000
χ33222-1-1-2-222-111222221-2-2-1-1-1-1-12-1-100-221111-1-12-2-2-11100000-1000013−3−333−3−33000000000
χ34222-1-1-2-222-111222221-2-2-1-1-1-1-12-1-100-221111-1-12-2-2-11100000-100001−333−3−333−3000000000
χ35222-1-1-2-222-111222-2-21-2-2-1-1-1-1-1-21100-221111-1-1-2221-1-10000010000-1−i3i3i3−i3i3−i3−i3i3000000000
χ36222-1-1-2-222-111222-2-21-2-2-1-1-1-1-1-21100-221111-1-1-2221-1-10000010000-1i3−i3−i3i3−i3i3i3−i3000000000
χ3744444444-1444-1-1-1004-1-14-1-1-1-100044-1-1-1-1-1-1-1-10000004-1-1-1-100000000000000-1-10000000
χ3844444444-1444-1-1-1004-1-14-1-1-1-1000-4-4-1-1-1-1-1-1-1-1000000-4111100000000000000110000000
χ39444444-4-4-14-4-4-1-1-1004-1-1-4-1-1-1-10004411-1-11111000000-4-1-1-1-100000000000000110000000
χ40444444-4-4-14-4-4-1-1-1004-1-1-4-1-1-1-1000-4-411-1-111110000004111100000000000000-1-10000000
χ4144444-44-4-1444-1-1-100-411-4-1-1-1-100000-1111-1-1110000000−5−55500000000000000−550000000
χ4244444-44-4-1444-1-1-100-411-4-1-1-1-100000-1111-1-111000000055−5−5000000000000005−50000000
χ4344444-4-44-14-4-4-1-1-100-4114-1-1-1-1000001-11111-1-10000000−5−555000000000000005−50000000
χ4444444-4-44-14-4-4-1-1-100-4114-1-1-1-1000001-11111-1-1000000055−5−500000000000000−550000000
χ4544-4440004-400-4-444400004-4-44-4440000000000000-4000000000000000000000000000000
χ4644-4440004-400-4-44-4-400004-4-444-4-400000000000004000000000000000000000000000000
χ4744-4-2-200042−2i32i3-4-44440000-222-2-4-2-2000000−2i32i3000002−2i32i30000000000000000000000000000
χ4844-4-2-200042−2i32i3-4-44-4-40000-222-2422000000−2i32i300000-22i3−2i30000000000000000000000000000
χ4944-4-2-2000422i3−2i3-4-44440000-222-2-4-2-20000002i3−2i30000022i3−2i30000000000000000000000000000
χ5044-4-2-2000422i3−2i3-4-44-4-40000-222-24220000002i3−2i300000-2−2i32i30000000000000000000000000000
χ514-404-4000400000-44i−4i0000400-404i−4i2i−2i0000000000000002i−2i2i−2i00000000000000002-200000
χ524-404-4000400000-44i−4i0000400-404i−4i−2i2i000000000000000−2i2i−2i2i0000000000000000-2200000
χ534-404-4000400000-4−4i4i0000400-40−4i4i2i−2i0000000000000002i−2i2i−2i0000000000000000-2200000
χ544-404-4000400000-4−4i4i0000400-40−4i4i−2i2i000000000000000−2i2i−2i2i00000000000000002-200000
χ55888-4-4888-2-4-4-4-2-2-200-4-2-2-4111100000-2-21111110000000000000000000000000000000000
χ56888-4-48-8-8-2-444-2-2-200-4-2-241111000002211-1-1-1-10000000000000000000000000000000000
χ57888-4-4-88-8-2-4-4-4-2-2-2004224111100000-22-1-111-1-10000000000000000000000000000000000
χ58888-4-4-8-88-2-444-2-2-200422-41111000002-2-1-1-1-1110000000000000000000000000000000000
χ5988-888000-2-80022-2000−25250-222-20000000−252500000000000000000000000000000000000000
χ6088-888000-2-80022-200025−250-222-2000000025−2500000000000000000000000000000000000000
χ6188-8-4-4000-24−4i34i322-2000−252501-1-1100000005−5i3−i3−i15i150000000000000000000000000000000000
χ6288-8-4-4000-24−4i34i322-200025−2501-1-110000000−55i3−i3i15−i150000000000000000000000000000000000
χ6388-8-4-4000-244i3−4i322-2000−252501-1-1100000005−5−i3i3i15−i150000000000000000000000000000000000
χ6488-8-4-4000-244i3−4i322-200025−2501-1-110000000−55−i3i3−i15i150000000000000000000000000000000000
χ658-808-8000-2000−25252000000-2−252520004i−4i000000000000000−2ζ11−2ζ19−2ζ31−2ζ592ζ11+2ζ19+2ζ31+2ζ59−2ζ7−2ζ23−2ζ43−2ζ472ζ7+2ζ23+2ζ43+2ζ4700000000000000000000000
χ668-808-8000-2000−25252000000-2−25252000−4i4i0000000000000002ζ11+2ζ19+2ζ31+2ζ59−2ζ11−2ζ19−2ζ31−2ζ592ζ7+2ζ23+2ζ43+2ζ47−2ζ7−2ζ23−2ζ43−2ζ4700000000000000000000000
χ678-808-8000-200025−252000000-225−2520004i−4i000000000000000−2ζ7−2ζ23−2ζ43−2ζ472ζ7+2ζ23+2ζ43+2ζ47−2ζ11−2ζ19−2ζ31−2ζ592ζ11+2ζ19+2ζ31+2ζ5900000000000000000000000
χ688-808-8000-200025−252000000-225−252000−4i4i0000000000000002ζ7+2ζ23+2ζ43+2ζ47−2ζ7−2ζ23−2ζ43−2ζ472ζ11+2ζ19+2ζ31+2ζ59−2ζ11−2ζ19−2ζ31−2ζ5900000000000000000000000
χ698-80-44000800000-88i−8i0000-40040−4i4i00000000000000000000000000000000000000000000
χ708-80-44000800000-8−8i8i0000-400404i−4i00000000000000000000000000000000000000000000
χ7116-160-88000-4000−45454000000225−25-200000000000000000000000000000000000000000000000
χ7216-160-88000-400045−4540000002−2525-200000000000000000000000000000000000000000000000

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