Finite Group Databasebeta

← Group #14302622

Character table — Group #14302622

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93
size11222222244444444445588888881010101010101010101010101010101010101016161616161616162020202020202020202020202020202020202020202020202020242448484848120120120120120120
order12234461212245666101212124410152020306060224444466121212121212121212121020303030606060244444446661212121212121212121212121212122810104040444888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-11-1-1
χ41111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111
χ51111111111111111111-1-11111111-1-1-1ii−i−i-1-1-1-1iiii−i−i−i−i11111111-1-1iii−i−i−i-1-1-1-1-1-1iiiiii−i−i−i−i−i−i111111-1i−i-1i−i
χ61111111111111111111-1-11111111-1-1-1ii−i−i-1-1-1-1iiii−i−i−i−i11111111-1-1iii−i−i−i-1-1-1-1-1-1iiiiii−i−i−i−i−i−i-1-1-1-1-1-11−ii1−ii
χ71111111111111111111-1-11111111-1-1-1−i−iii-1-1-1-1−i−i−i−iiiii11111111-1-1−i−i−iiii-1-1-1-1-1-1−i−i−i−i−i−iiiiiii111111-1−ii-1−ii
χ81111111111111111111-1-11111111-1-1-1−i−iii-1-1-1-1−i−i−i−iiiii11111111-1-1−i−i−iiii-1-1-1-1-1-1−i−i−i−i−i−iiiiiii-1-1-1-1-1-11i−i1i−i
χ9111111111-1-111-1-111-1-11111111111111111111111111111-1-11-1-11-1-1-1-11-1-11-1-11-1-11-1-111-1-1-1-111-1-1-1-11-111-1-11-1-1-111
χ10111111111-1-111-1-111-1-11111111111111111111111111111-1-11-1-11-1-1-1-11-1-11-1-11-1-11-1-111-1-1-1-111-1-1-1-1-11-1-111-1111-1-1
χ11111111111-1-111-1-111-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-1-111-1111-1-11-1-1-1-11111-1-111111-111-1-1111-1-1-1
χ12111111111-1-111-1-111-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-1-111-1111-1-11-1-1-1-11111-1-11111-11-1-111-1-1-1111
χ13111111111-1-111-1-111-1-1-1-11111111-1-1-1ii−i−i-1-1-1-1iiii−i−i−i−i-1-11-1-11-1-111i−i−i−iii-111-111ii−i−i−i−i−i−iiiii1-111-1-1-1−ii1i−i
χ14111111111-1-111-1-111-1-1-1-11111111-1-1-1ii−i−i-1-1-1-1iiii−i−i−i−i-1-11-1-11-1-111i−i−i−iii-111-111ii−i−i−i−i−i−iiiii-11-1-1111i−i-1−ii
χ15111111111-1-111-1-111-1-1-1-11111111-1-1-1−i−iii-1-1-1-1−i−i−i−iiiii-1-11-1-11-1-111−iiii−i−i-111-111−i−iiiiiii−i−i−i−i1-111-1-1-1i−i1−ii
χ16111111111-1-111-1-111-1-1-1-11111111-1-1-1−i−iii-1-1-1-1−i−i−i−iiiii-1-11-1-11-1-111−iiii−i−i-111-111−i−iiiiiii−i−i−i−i-11-1-1111−ii-1i−i
χ172222-2-22-2-20022002-2002222-2-22-2-2-2-220000-2-2220000000000200-2000002i−2i02i−2i-200200002i2i−2i−2i002i2i−2i−2i000000000000
χ182222-2-22-2-20022002-2002222-2-22-2-2-2-220000-2-2220000000000200-200000−2i2i0−2i2i-20020000−2i−2i2i2i00−2i−2i2i2i000000000000
χ192222-2-22-2-20022002-200-2-222-2-22-2-222-2000022-2-20000000000200-2000002-20-22200-2000022-2-200-2-222000000000000
χ202222-2-22-2-20022002-200-2-222-2-22-2-222-2000022-2-20000000000200-200000-2202-2200-20000-2-2220022-2-2000000000000
χ21222-122-1-1-1222-1-1-12-1-1-1222-122-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ22222-122-1-1-1222-1-1-12-1-1-1222-122-1-1-1222-2-2-2-2-1-1-1-11111111122-1-1-1-1-1-122-2-2-2-2-2-2-1-1-1-1-1-1111111111111000000000000
χ23222-122-1-1-1222-1-1-12-1-1-1-2-22-122-1-1-1-2-2-22i2i−2i−2i1111−i−i−i−iiiii22-1-1-1-1-1-1-2-22i2i2i−2i−2i−2i111111−i−i−i−i−i−iiiiiii000000000000
χ24222-122-1-1-1222-1-1-12-1-1-1-2-22-122-1-1-1-2-2-2−2i−2i2i2i1111iiii−i−i−i−i22-1-1-1-1-1-1-2-2−2i−2i−2i2i2i2i111111iiiiii−i−i−i−i−i−i000000000000
χ25222-122-1-1-1-2-22-1112-111222-122-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-111-111-2-22-2-22-2-2-111-111-1-11111-1-11111000000000000
χ26222-122-1-1-1-2-22-1112-111222-122-1-1-1222-2-2-2-2-1-1-1-111111111-2-2-111-111-2-2-222-222-111-11111-1-1-1-111-1-1-1-1000000000000
χ27222-122-1-1-1-2-22-1112-111-2-22-122-1-1-1-2-2-22i2i−2i−2i1111−i−i−i−iiiii-2-2-111-111222i−2i−2i−2i2i2i1-1-11-1-1−i−iiiiiii−i−i−i−i000000000000
χ28222-122-1-1-1-2-22-1112-111-2-22-122-1-1-1-2-2-2−2i−2i2i2i1111iiii−i−i−i−i-2-2-111-11122−2i2i2i2i−2i−2i1-1-11-1-1ii−i−i−i−i−i−iiiii000000000000
χ29222-1-2-2-111002-1−i3i321−i3i3222-1-2-2-111-2-22000011-1-133−3−333−3−300-1−i3i31−i3i30002i−2i02i−2i1−i3i3-1−i3i33−3−i−iii3−3−i−iii000000000000
χ30222-1-2-2-111002-1−i3i321−i3i3222-1-2-2-111-2-22000011-1-1−3−333−3−33300-1−i3i31−i3i3000−2i2i0−2i2i1−i3i3-1−i3i3−33ii−i−i−33ii−i−i000000000000
χ31222-1-2-2-111002-1−i3i321−i3i3-2-22-1-2-2-11122-20000-1-111−i3−i3i3i3i3i3−i3−i300-1−i3i31−i3i30002-20-22-1i3−i31i3−i3−i3i3-1-111i3−i311-1-1000000000000
χ32222-1-2-2-111002-1−i3i321−i3i3-2-22-1-2-2-11122-20000-1-111i3i3−i3−i3−i3−i3i3i300-1−i3i31−i3i3000-2202-2-1i3−i31i3−i3i3−i311-1-1−i3i3-1-111000000000000
χ33222-1-2-2-111002-1i3−i321i3−i3222-1-2-2-111-2-22000011-1-133−3−333−3−300-1i3−i31i3−i3000−2i2i0−2i2i1i3−i3-1i3−i33−3ii−i−i3−3ii−i−i000000000000
χ34222-1-2-2-111002-1i3−i321i3−i3222-1-2-2-111-2-22000011-1-1−3−333−3−33300-1i3−i31i3−i30002i−2i02i−2i1i3−i3-1i3−i3−33−i−iii−33−i−iii000000000000
χ35222-1-2-2-111002-1i3−i321i3−i3-2-22-1-2-2-11122-20000-1-111−i3−i3i3i3i3i3−i3−i300-1i3−i31i3−i3000-2202-2-1−i3i31−i3i3−i3i311-1-1i3−i3-1-111000000000000
χ36222-1-2-2-111002-1i3−i321i3−i3-2-22-1-2-2-11122-20000-1-111i3i3−i3−i3−i3−i3i3i300-1i3−i31i3−i30002-20-22-1−i3i31−i3i3i3−i3-1-111−i3i311-1-1000000000000
χ3722-222-2222002-2002-20022-222-22222-2-2222222222222222200-200-20000-200-200-200-200-2-20000-2-20000000000000000
χ3822-222-2222002-2002-20022-222-22222-2-2-2-2-2-22222-2-2-2-2-2-2-2-200-200-20000200200-200-200220000220000000000000000
χ3922-222-2222002-2002-200-2-2-222-2222-2222i2i−2i−2i-2-2-2-22i2i2i2i−2i−2i−2i−2i00-200-20000−2i002i00200200−2i−2i00002i2i0000000000000000
χ4022-222-2222002-2002-200-2-2-222-2222-222−2i−2i2i2i-2-2-2-2−2i−2i−2i−2i2i2i2i2i00-200-200002i00−2i002002002i2i0000−2i−2i0000000000000000
χ4122-22-222-2-22-22-22222-2-222-22-222-2-2-22-20000-2-222000000002-2-2222-2-2-220000002-2-2-222000000000000000000000000
χ4222-22-222-2-22-22-22222-2-2-2-2-22-222-2-22-22000022-2-2000000002-2-2222-2-22-2000000-2222-2-2000000000000000000000000
χ4322-22-222-2-2-222-2-2-2222222-22-222-2-2-22-20000-2-22200000000-22-2-2-22222-2000000222-2-2-2000000000000000000000000
χ4422-22-222-2-2-222-2-2-22222-2-2-22-222-2-22-22000022-2-200000000-22-2-2-2222-22000000-2-2-2222000000000000000000000000
χ4522-2-12-2-1-1-10021−i3i321i3−i322-2-12-2-1-1-12-2-22222-1-1-1-1-1-1-1-1-1-1-1-1001−i3i31i3−i300-200-2001i3−i31−i3i311−i3i3−i3i311−i3i3−i3i3000000000000
χ4622-2-12-2-1-1-10021−i3i321i3−i322-2-12-2-1-1-12-2-2-2-2-2-2-1-1-1-111111111001−i3i31i3−i3002002001i3−i31−i3i3-1-1i3−i3i3−i3-1-1i3−i3i3−i3000000000000
χ4722-2-12-2-1-1-10021−i3i321i3−i3-2-2-2-12-2-1-1-1-2222i2i−2i−2i1111−i−i−i−iiiii001−i3i31i3−i300−2i002i00-1−i3i3-1i3−i3ii3−33−3−i−i−33−33000000000000
χ4822-2-12-2-1-1-10021−i3i321i3−i3-2-2-2-12-2-1-1-1-222−2i−2i2i2i1111iiii−i−i−i−i001−i3i31i3−i3002i00−2i00-1−i3i3-1i3−i3−i−i−33−33ii3−33−3000000000000
χ4922-2-12-2-1-1-10021i3−i321−i3i322-2-12-2-1-1-12-2-22222-1-1-1-1-1-1-1-1-1-1-1-1001i3−i31−i3i300-200-2001−i3i31i3−i311i3−i3i3−i311i3−i3i3−i3000000000000
χ5022-2-12-2-1-1-10021i3−i321−i3i322-2-12-2-1-1-12-2-2-2-2-2-2-1-1-1-111111111001i3−i31−i3i3002002001−i3i31i3−i3-1-1−i3i3−i3i3-1-1−i3i3−i3i3000000000000
χ5122-2-12-2-1-1-10021i3−i321−i3i3-2-2-2-12-2-1-1-1-2222i2i−2i−2i1111−i−i−i−iiiii001i3−i31−i3i300−2i002i00-1i3−i3-1−i3i3ii−33−33−i−i3−33−3000000000000
χ5222-2-12-2-1-1-10021i3−i321−i3i3-2-2-2-12-2-1-1-1-222−2i−2i2i2i1111iiii−i−i−i−i001i3−i31−i3i3002i00−2i00-1i3−i3-1−i3i3−i−i3−33−3ii−33−33000000000000
χ5322-2-1-22-1112-221-1-12-11122-2-1-22-111-22-2000011-1-133−3−333−3−32-21-1-1-111-22000000-1111-1-1−333−3−33−333−3−33000000000000
χ5422-2-1-22-1112-221-1-12-11122-2-1-22-111-22-2000011-1-1−3−333−3−3332-21-1-1-111-22000000-1111-1-13−3−333−33−3−333−3000000000000
χ5522-2-1-22-1112-221-1-12-111-2-2-2-1-22-1112-220000-1-111−i3−i3i3i3i3i3−i3−i32-21-1-1-1112-20000001-1-1-111i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3000000000000
χ5622-2-1-22-1112-221-1-12-111-2-2-2-1-22-1112-220000-1-111i3i3−i3−i3−i3−i3i3i32-21-1-1-1112-20000001-1-1-111−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3000000000000
χ5722-2-1-22-111-2221112-1-1-122-2-1-22-111-22-2000011-1-133−3−333−3−3-22111-1-1-12-2000000-1-1-1111−33−333−3−33−333−3000000000000
χ5822-2-1-22-111-2221112-1-1-122-2-1-22-111-22-2000011-1-1−3−333−3−333-22111-1-1-12-2000000-1-1-11113−33−3−333−33−3−33000000000000
χ5922-2-1-22-111-2221112-1-1-1-2-2-2-1-22-1112-220000-1-111−i3−i3i3i3i3i3−i3−i3-22111-1-1-1-22000000111-1-1-1i3−i3i3−i3−i3i3−i3i3−i3i3i3−i3000000000000
χ6022-2-1-22-111-2221112-1-1-1-2-2-2-1-22-1112-220000-1-111i3i3−i3−i3−i3−i3i3i3-22111-1-1-1-22000000111-1-1-1−i3i3−i3i3i3−i3i3−i3i3−i3−i3i3000000000000
χ6144444444444-1444-144400-1-1-1-1-1-1-10000000000000000000-1-1-1-1-1-1-1-10000000000000000000000000044-1-1-1-1000000
χ6244444444444-1444-144400-1-1-1-1-1-1-10000000000000000000-1-1-1-1-1-1-1-100000000000000000000000000-4-41111000000
χ63444444444-4-4-14-4-4-14-4-400-1-1-1-1-1-1-1000000000000000000011-111-111000000000000000000000000004-4-1-111000000
χ64444444444-4-4-14-4-4-14-4-400-1-1-1-1-1-1-1000000000000000000011-111-11100000000000000000000000000-4411-1-1000000
χ6544-44-444-4-44-4-1-444-14-4-4001-11-1-1110000000000000000000-111-1-1-1110000000000000000000000000000−55−55000000
χ6644-44-444-4-44-4-1-444-14-4-4001-11-1-1110000000000000000000-111-1-1-11100000000000000000000000000005−55−5000000
χ6744-44-444-4-4-44-1-4-4-4-1444001-11-1-11100000000000000000001-1111-1-1-10000000000000000000000000000−555−5000000
χ6844-44-444-4-4-44-1-4-4-4-1444001-11-1-11100000000000000000001-1111-1-1-100000000000000000000000000005−5−55000000
χ694-40400-400004000-40004i−4i0400-4000002+2i−2−2i2−2i−2+2i004i−4i2+2i−2−2i2+2i−2−2i2−2i−2+2i2−2i−2+2i0000000000000000000000000000000000000000000000
χ704-40400-400004000-40004i−4i0400-400000−2−2i2+2i−2+2i2−2i004i−4i−2−2i2+2i−2−2i2+2i−2+2i2−2i−2+2i2−2i0000000000000000000000000000000000000000000000
χ714-40400-400004000-4000−4i4i0400-4000002−2i−2+2i2+2i−2−2i00−4i4i2−2i−2+2i2−2i−2+2i2+2i−2−2i2+2i−2−2i0000000000000000000000000000000000000000000000
χ724-40400-400004000-4000−4i4i0400-400000−2+2i2−2i−2−2i2+2i00−4i4i−2+2i2−2i−2+2i2−2i−2−2i2+2i−2−2i2+2i0000000000000000000000000000000000000000000000
χ734-40-200223−23004000-40004i−4i0-200223−230002+2i−2−2i2−2i−2+2i−2i32i3−2i2i−2ζ11+2ζ22−2ζ23+2ζ34+2ζ46−2ζ47+2ζ58−2ζ592ζ11−2ζ22+2ζ23−2ζ34−2ζ46+2ζ47−2ζ58+2ζ592ζ2−2ζ7+2ζ14−2ζ19+2ζ26−2ζ31+2ζ38−2ζ43−2ζ2+2ζ7−2ζ14+2ζ19−2ζ26+2ζ31−2ζ38+2ζ432ζ2+2ζ7+2ζ14+2ζ19+2ζ26+2ζ31+2ζ38+2ζ43−2ζ2−2ζ7−2ζ14−2ζ19−2ζ26−2ζ31−2ζ38−2ζ432ζ11+2ζ22+2ζ23+2ζ34+2ζ46+2ζ47+2ζ58+2ζ59−2ζ11−2ζ22−2ζ23−2ζ34−2ζ46−2ζ47−2ζ58−2ζ590000000000000000000000000000000000000000000000
χ744-40-200223−23004000-40004i−4i0-200223−23000−2−2i2+2i−2+2i2−2i−2i32i3−2i2i2ζ11−2ζ22+2ζ23−2ζ34−2ζ46+2ζ47−2ζ58+2ζ59−2ζ11+2ζ22−2ζ23+2ζ34+2ζ46−2ζ47+2ζ58−2ζ59−2ζ2+2ζ7−2ζ14+2ζ19−2ζ26+2ζ31−2ζ38+2ζ432ζ2−2ζ7+2ζ14−2ζ19+2ζ26−2ζ31+2ζ38−2ζ43−2ζ2−2ζ7−2ζ14−2ζ19−2ζ26−2ζ31−2ζ38−2ζ432ζ2+2ζ7+2ζ14+2ζ19+2ζ26+2ζ31+2ζ38+2ζ43−2ζ11−2ζ22−2ζ23−2ζ34−2ζ46−2ζ47−2ζ58−2ζ592ζ11+2ζ22+2ζ23+2ζ34+2ζ46+2ζ47+2ζ58+2ζ590000000000000000000000000000000000000000000000
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χ764-40-200223−23004000-4000−4i4i0-200223−23000−2+2i2−2i−2−2i2+2i2i3−2i32i−2i−2ζ2−2ζ7−2ζ14−2ζ19−2ζ26−2ζ31−2ζ38−2ζ432ζ2+2ζ7+2ζ14+2ζ19+2ζ26+2ζ31+2ζ38+2ζ43−2ζ11−2ζ22−2ζ23−2ζ34−2ζ46−2ζ47−2ζ58−2ζ592ζ11+2ζ22+2ζ23+2ζ34+2ζ46+2ζ47+2ζ58+2ζ592ζ11−2ζ22+2ζ23−2ζ34−2ζ46+2ζ47−2ζ58+2ζ59−2ζ11+2ζ22−2ζ23+2ζ34+2ζ46−2ζ47+2ζ58−2ζ59−2ζ2+2ζ7−2ζ14+2ζ19−2ζ26+2ζ31−2ζ38+2ζ432ζ2−2ζ7+2ζ14−2ζ19+2ζ26−2ζ31+2ζ38−2ζ430000000000000000000000000000000000000000000000
χ774-40-2002−2323004000-40004i−4i0-2002−23230002+2i−2−2i2−2i−2+2i2i3−2i3−2i2i2ζ2−2ζ7+2ζ14−2ζ19+2ζ26−2ζ31+2ζ38−2ζ43−2ζ2+2ζ7−2ζ14+2ζ19−2ζ26+2ζ31−2ζ38+2ζ43−2ζ11+2ζ22−2ζ23+2ζ34+2ζ46−2ζ47+2ζ58−2ζ592ζ11−2ζ22+2ζ23−2ζ34−2ζ46+2ζ47−2ζ58+2ζ592ζ11+2ζ22+2ζ23+2ζ34+2ζ46+2ζ47+2ζ58+2ζ59−2ζ11−2ζ22−2ζ23−2ζ34−2ζ46−2ζ47−2ζ58−2ζ592ζ2+2ζ7+2ζ14+2ζ19+2ζ26+2ζ31+2ζ38+2ζ43−2ζ2−2ζ7−2ζ14−2ζ19−2ζ26−2ζ31−2ζ38−2ζ430000000000000000000000000000000000000000000000
χ784-40-2002−2323004000-40004i−4i0-2002−2323000−2−2i2+2i−2+2i2−2i2i3−2i3−2i2i−2ζ2+2ζ7−2ζ14+2ζ19−2ζ26+2ζ31−2ζ38+2ζ432ζ2−2ζ7+2ζ14−2ζ19+2ζ26−2ζ31+2ζ38−2ζ432ζ11−2ζ22+2ζ23−2ζ34−2ζ46+2ζ47−2ζ58+2ζ59−2ζ11+2ζ22−2ζ23+2ζ34+2ζ46−2ζ47+2ζ58−2ζ59−2ζ11−2ζ22−2ζ23−2ζ34−2ζ46−2ζ47−2ζ58−2ζ592ζ11+2ζ22+2ζ23+2ζ34+2ζ46+2ζ47+2ζ58+2ζ59−2ζ2−2ζ7−2ζ14−2ζ19−2ζ26−2ζ31−2ζ38−2ζ432ζ2+2ζ7+2ζ14+2ζ19+2ζ26+2ζ31+2ζ38+2ζ430000000000000000000000000000000000000000000000
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χ804-40-2002−2323004000-4000−4i4i0-2002−2323000−2+2i2−2i−2−2i2+2i−2i32i32i−2i−2ζ11−2ζ22−2ζ23−2ζ34−2ζ46−2ζ47−2ζ58−2ζ592ζ11+2ζ22+2ζ23+2ζ34+2ζ46+2ζ47+2ζ58+2ζ59−2ζ2−2ζ7−2ζ14−2ζ19−2ζ26−2ζ31−2ζ38−2ζ432ζ2+2ζ7+2ζ14+2ζ19+2ζ26+2ζ31+2ζ38+2ζ43−2ζ2+2ζ7−2ζ14+2ζ19−2ζ26+2ζ31−2ζ38+2ζ432ζ2−2ζ7+2ζ14−2ζ19+2ζ26−2ζ31+2ζ38−2ζ432ζ11−2ζ22+2ζ23−2ζ34−2ζ46+2ζ47−2ζ58+2ζ59−2ζ11+2ζ22−2ζ23+2ζ34+2ζ46−2ζ47+2ζ58−2ζ590000000000000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 60 (ζ60 = 1); i = ζ15.