Finite Group Databasebeta

← Group #14297124

Character table — Group #14297124

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11112222224444444455556688888888888810101010101012121212121212161616161616202020202020202020202020202020202424242424243030404040404040404060606060606060120120
order1222344666445101010121244442212121520202020202030303022121212124441010101060606060606022444466121212121212121220202020202044668824242424222444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1111-1-1-1-1-1-1
χ31111111111111111111111-1-1111111111111111111-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1
χ41111111111111111111111-1-1111111111111111111-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111-1-1-1-111111111111111-1-1-1-1-1-11111111111111-1-1ii−i−i-1-1iiii−i−i−i−i111111-1-1-1-1i−iii−i−i-1-1-1ii−i−ii−i
χ6111111111111111111-1-1-1-111111111111111-1-1-1-1-1-11111111111111-1-1−i−iii-1-1−i−i−i−iiiii111111-1-1-1-1−ii−i−iii-1-1-1−i−iii−ii
χ7111111111111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1ii−i−i-1-1iiii−i−i−i−i-1-1-1-1-1-111-1-1i−iii−i−i111−i−iii−ii
χ8111111111111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1−i−iii-1-1−i−i−i−iiiii-1-1-1-1-1-111-1-1−ii−i−iii111ii−i−ii−i
χ91111111111-1-1111111111111-1-1111-1-1-1-11111111111-1-1111111-1-1-1-1-1-11111111111111111-1-1-1-111-1-1-1-1-1-1-1-11-1-11111-1-1
χ101111111111-1-1111111111111-1-1111-1-1-1-11111111111-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-111-1-11111111-1-1-1-1-1-111
χ111111111111-1-11111111111-1-1-1-1111-1-1-1-1111111111-111-1-1-1-111-1-1-1-1-1-111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111
χ121111111111-1-11111111111-1-1-1-1111-1-1-1-1111111111-111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1111111-1-1
χ131111111111-1-1111111-1-1-1-111-1-1111-1-1-1-1111-1-1-1-1-1-11-1-1111111-1-1-1-111ii−i−i-1-1iiii−i−i−i−i11-1-1-1-1-1-111−ii−i−iii-111ii−i−i−ii
χ141111111111-1-1111111-1-1-1-111-1-1111-1-1-1-1111-1-1-1-1-1-11-1-1111111-1-1-1-111−i−iii-1-1−i−i−i−iiiii11-1-1-1-1-1-111i−iii−i−i-111−i−iiii−i
χ151111111111-1-1111111-1-1-1-1-1-1-1-1111-1-1-1-1111-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111ii−i−i-1-1iiii−i−i−i−i-1-111111111−ii−i−iii1-1-1−i−iiii−i
χ161111111111-1-1111111-1-1-1-1-1-1-1-1111-1-1-1-1111-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111−i−iii-1-1−i−i−i−iiiii-1-111111111i−iii−i−i1-1-1ii−i−i−ii
χ1722222-2-2222002222-2-2222222002-2-20000222-2-22222-2002222-2-20000000000-2-200000000-2-200002200000000-200000000
χ1822222-2-2222002222-2-22222-2-2002-2-20000222-2-22222200-2-2-2-2-2-20000000000-2-200000000220000-2-200000000200000000
χ1922222-2-2222002222-2-2-2-2-2-222002-2-2000022222-2-2-2-2-2002222-2-200000000002200000000-2-20000-2-200000000200000000
χ2022222-2-2222002222-2-2-2-2-2-2-2-2002-2-2000022222-2-2-2-2200-2-2-2-2-2-2000000000022000000002200002200000000-200000000
χ212222-122-1-1-1222222-1-1222200-1-1-1222222-1-1-122-1-1-1-10000000-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-100000000-1-122-1-1-1-1000000000
χ222222-122-1-1-1222222-1-1222200-1-1-1222222-1-1-122-1-1-1-10000000-1-1-1-1-1-122-2-2-2-2-1-11111111100000000-1-1-2-21111000000000
χ232222-122-1-1-1222222-1-1-2-2-2-200-1-1-1222222-1-1-1-2-211110000000-1-1-1-1-1-1-2-22i2i−2i−2i11−i−i−i−iiiii00000000112i−2i−i−iii000000000
χ242222-122-1-1-1222222-1-1-2-2-2-200-1-1-1222222-1-1-1-2-211110000000-1-1-1-1-1-1-2-2−2i−2i2i2i11iiii−i−i−i−i0000000011−2i2iii−i−i000000000
χ252222-122-1-1-1-2-22222-1-122220011-122-2-2-2-2-1-1-122-1-1-1-10000000-1-11111-2-22222-1-1-1-1-1-1-1-1-1-10000000011-2-21111000000000
χ262222-122-1-1-1-2-22222-1-122220011-122-2-2-2-2-1-1-122-1-1-1-10000000-1-11111-2-2-2-2-2-2-1-111111111000000001122-1-1-1-1000000000
χ272222-122-1-1-1-2-22222-1-1-2-2-2-20011-122-2-2-2-2-1-1-1-2-211110000000-1-11111222i2i−2i−2i11−i−i−i−iiiii00000000-1-1−2i2iii−i−i000000000
χ282222-122-1-1-1-2-22222-1-1-2-2-2-20011-122-2-2-2-2-1-1-1-2-211110000000-1-1111122−2i−2i2i2i11iiii−i−i−i−i00000000-1-12i−2i−i−iii000000000
χ2922-2-22002-2-20022-2-2002i−2i2i−2i2-20020000002-2-2002i−2i2i−2i00022-2-2000000001+i−1−i1−i−1+i001+i1+i−1−i−1−i1−i1−i−1+i−1+i0000002i−2i000000000001+i−1−i1−i−1+i00
χ3022-2-22002-2-20022-2-2002i−2i2i−2i2-20020000002-2-2002i−2i2i−2i00022-2-200000000−1−i1+i−1+i1−i00−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000002i−2i00000000000−1−i1+i−1+i1−i00
χ3122-2-22002-2-20022-2-2002i−2i2i−2i-220020000002-2-2002i−2i2i−2i000-2-222000000001+i−1−i1−i−1+i001+i1+i−1−i−1−i1−i1−i−1+i−1+i000000−2i2i00000000000−1−i1+i−1+i1−i00
χ3222-2-22002-2-20022-2-2002i−2i2i−2i-220020000002-2-2002i−2i2i−2i000-2-22200000000−1−i1+i−1+i1−i00−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000−2i2i000000000001+i−1−i1−i−1+i00
χ3322-2-22002-2-20022-2-200−2i2i−2i2i2-20020000002-2-200−2i2i−2i2i00022-2-2000000001−i−1+i1+i−1−i001−i1−i−1+i−1+i1+i1+i−1−i−1−i000000−2i2i000000000001−i−1+i1+i−1−i00
χ3422-2-22002-2-20022-2-200−2i2i−2i2i2-20020000002-2-200−2i2i−2i2i00022-2-200000000−1+i1−i−1−i1+i00−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000−2i2i00000000000−1+i1−i−1−i1+i00
χ3522-2-22002-2-20022-2-200−2i2i−2i2i-220020000002-2-200−2i2i−2i2i000-2-222000000001−i−1+i1+i−1−i001−i1−i−1+i−1+i1+i1+i−1−i−1−i0000002i−2i00000000000−1+i1−i−1−i1+i00
χ3622-2-22002-2-20022-2-200−2i2i−2i2i-220020000002-2-200−2i2i−2i2i000-2-22200000000−1+i1−i−1−i1+i00−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000002i−2i000000000001−i−1+i1+i−1−i00
χ372-2-2222-2-2-22002-2-222-222-2-2000022-20000-2-22-22-2-22202-200002-200000000002-2000000000022-2-2000000000002-2000000
χ382-2-2222-2-2-22002-2-222-222-2-2000022-20000-2-22-22-2-2220-2200002-200000000002-20000000000-2-22200000000000-22000000
χ392-2-2222-2-2-22002-2-222-2-2-222000022-20000-2-222-222-2-202-200002-20000000000-22000000000022-2-200000000000-22000000
χ402-2-2222-2-2-22002-2-222-2-2-222000022-20000-2-222-222-2-20-2200002-20000000000-220000000000-2-222000000000002-2000000
χ412-2-222-22-2-222-22-2-22-2222-2-2002-22-2222-2-2-2-222-2-2-2220000000-2222-2-22-20000-2200000000000000002-2000000000000000
χ422-2-222-22-2-222-22-2-22-22-2-222002-22-2222-2-2-2-22-2222-2-20000000-2222-2-2-2200002-20000000000000000-22000000000000000
χ432-2-222-22-2-22-222-2-22-2222-2-200-222-22-2-222-2-222-2-2-2220000000-22-2-222-220000-220000000000000000-22000000000000000
χ442-2-222-22-2-22-222-2-22-22-2-22200-222-22-2-222-2-22-2222-2-20000000-22-2-2222-200002-200000000000000002-2000000000000000
χ452-2-22-1-2211-12-22-2-221-122-2-200-11-1-2222-2-211-12-211-1-100000001-1-1-1112-200001-1−i3i3−i3i3−i3i3−i3i300000000-1100−i3i3−i3i3000000000
χ462-2-22-1-2211-12-22-2-221-122-2-200-11-1-2222-2-211-12-211-1-100000001-1-1-1112-200001-1i3−i3i3−i3i3−i3i3−i300000000-1100i3−i3i3−i3000000000
χ472-2-22-1-2211-12-22-2-221-1-2-22200-11-1-2222-2-211-1-22-1-11100000001-1-1-111-220000-113−33−3−33−33000000001-1003−3−33000000000
χ482-2-22-1-2211-12-22-2-221-1-2-22200-11-1-2222-2-211-1-22-1-11100000001-1-1-111-220000-11−33−333−33−3000000001-100−333−3000000000
χ492-2-22-1-2211-1-222-2-221-122-2-2001-1-1-22-2-22211-12-211-1-100000001-111-1-1-2200001-1−i3i3−i3i3−i3i3−i3i3000000001-100i3−i3i3−i3000000000
χ502-2-22-1-2211-1-222-2-221-122-2-2001-1-1-22-2-22211-12-211-1-100000001-111-1-1-2200001-1i3−i3i3−i3i3−i3i3−i3000000001-100−i3i3−i3i3000000000
χ512-2-22-1-2211-1-222-2-221-1-2-222001-1-1-22-2-22211-1-22-1-11100000001-111-1-12-20000-113−33−3−33−3300000000-1100−333−3000000000
χ522-2-22-1-2211-1-222-2-221-1-2-222001-1-1-22-2-22211-1-22-1-11100000001-111-1-12-20000-11−33−333−33−300000000-11003−3−33000000000
χ53444444444444-1-1-1-14400004444-1-1-1-1-1-1-1-1-1-1000000444-1-1-1-1-1-1-1-1-1-10000000000000000-1-1-1-1-1-10000000000000000000
χ54444444444444-1-1-1-1440000-4-444-1-1-1-1-1-1-1-1-1-1000000-4-4-41111-1-1-1-1-1-100000000000000001111110000000000000000000
χ554444444444-4-4-1-1-1-144000044-4-4-1-1-11111-1-1-10000004-4-4-1-1-1-1-1-111110000000000000000-1-111110000000000000000000
χ564444444444-4-4-1-1-1-1440000-4-4-4-4-1-1-11111-1-1-1000000-4441111-1-11111000000000000000011-1-1-1-10000000000000000000
χ5744444-4-444400-1-1-1-1-4-400004400-111−55−55-1-1-1000000-400-1-1-1-111−55−55000000000000000011−55−550000000000000000000
χ5844444-4-444400-1-1-1-1-4-400004400-1115−55−5-1-1-1000000-400-1-1-1-1115−55−50000000000000000115−55−50000000000000000000
χ5944444-4-444400-1-1-1-1-4-40000-4-400-111−55−55-1-1-1000000400111111−55−550000000000000000-1-15−55−50000000000000000000
χ6044444-4-444400-1-1-1-1-4-40000-4-400-1115−55−5-1-1-10000004001111115−55−50000000000000000-1-1−55−550000000000000000000
χ614444-2-4-4-2-2-20044442244440000-2-4-40000-2-2-2-4-4-2-2-2-2000000022000000000022000000000000000000000000000000000
χ624444-2-4-4-2-2-200444422-4-4-4-40000-2-4-40000-2-2-24422220000000220000000000-2-2000000000000000000000000000000000
χ6344-4-4-200-2220044-4-4004i−4i4i−4i0000-2000000-22200−2i2i−2i2i0000000000000002+2i−2−2i2−2i−2+2i00−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000000000000000000000000
χ6444-4-4-200-2220044-4-4004i−4i4i−4i0000-2000000-22200−2i2i−2i2i000000000000000−2−2i2+2i−2+2i2−2i001+i1+i−1−i−1−i1−i1−i−1+i−1+i0000000000000000000000000
χ6544-4-4-200-2220044-4-400−4i4i−4i4i0000-2000000-222002i−2i2i−2i0000000000000002−2i−2+2i2+2i−2−2i00−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000000000000000000000000
χ6644-4-4-200-2220044-4-400−4i4i−4i4i0000-2000000-222002i−2i2i−2i000000000000000−2+2i2−2i−2−2i2+2i001−i1−i−1+i−1+i1+i1+i−1−i−1−i0000000000000000000000000
χ674-44-4400-44-4004-44-4004i−4i−4i4i00004000000-44-400−4i4i4i−4i000000000000000000000000000000000000000000000000000000
χ684-44-4400-44-4004-44-400−4i4i4i−4i00004000000-44-4004i−4i−4i4i000000000000000000000000000000000000000000000000000000
χ694-44-4-2002-22004-44-4004i−4i−4i4i0000-20000002-22002i−2i−2i2i000000000000000000000−ζ2−ζ7+ζ11−ζ14−ζ19+ζ22+ζ23−ζ26−ζ31+ζ34−ζ38−ζ43+ζ46+ζ47+ζ58+ζ59ζ2+ζ7−ζ11+ζ14+ζ19−ζ22−ζ23+ζ26+ζ31−ζ34+ζ38+ζ43−ζ46−ζ47−ζ58−ζ59ζ2+ζ7−ζ11+ζ14+ζ19−ζ22−ζ23+ζ26+ζ31−ζ34+ζ38+ζ43−ζ46−ζ47−ζ58−ζ59−ζ2−ζ7+ζ11−ζ14−ζ19+ζ22+ζ23−ζ26−ζ31+ζ34−ζ38−ζ43+ζ46+ζ47+ζ58+ζ59−ζ2+ζ7−ζ11−ζ14+ζ19+ζ22−ζ23−ζ26+ζ31+ζ34−ζ38+ζ43+ζ46−ζ47+ζ58−ζ59ζ2−ζ7+ζ11+ζ14−ζ19−ζ22+ζ23+ζ26−ζ31−ζ34+ζ38−ζ43−ζ46+ζ47−ζ58+ζ59ζ2−ζ7+ζ11+ζ14−ζ19−ζ22+ζ23+ζ26−ζ31−ζ34+ζ38−ζ43−ζ46+ζ47−ζ58+ζ59−ζ2+ζ7−ζ11−ζ14+ζ19+ζ22−ζ23−ζ26+ζ31+ζ34−ζ38+ζ43+ζ46−ζ47+ζ58−ζ590000000000000000000000000
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χ714-44-4-2002-22004-44-400−4i4i4i−4i0000-20000002-2200−2i2i2i−2i000000000000000000000−ζ2+ζ7−ζ11−ζ14+ζ19+ζ22−ζ23−ζ26+ζ31+ζ34−ζ38+ζ43+ζ46−ζ47+ζ58−ζ59ζ2−ζ7+ζ11+ζ14−ζ19−ζ22+ζ23+ζ26−ζ31−ζ34+ζ38−ζ43−ζ46+ζ47−ζ58+ζ59ζ2−ζ7+ζ11+ζ14−ζ19−ζ22+ζ23+ζ26−ζ31−ζ34+ζ38−ζ43−ζ46+ζ47−ζ58+ζ59−ζ2+ζ7−ζ11−ζ14+ζ19+ζ22−ζ23−ζ26+ζ31+ζ34−ζ38+ζ43+ζ46−ζ47+ζ58−ζ59−ζ2−ζ7+ζ11−ζ14−ζ19+ζ22+ζ23−ζ26−ζ31+ζ34−ζ38−ζ43+ζ46+ζ47+ζ58+ζ59ζ2+ζ7−ζ11+ζ14+ζ19−ζ22−ζ23+ζ26+ζ31−ζ34+ζ38+ζ43−ζ46−ζ47−ζ58−ζ59ζ2+ζ7−ζ11+ζ14+ζ19−ζ22−ζ23+ζ26+ζ31−ζ34+ζ38+ζ43−ζ46−ζ47−ζ58−ζ59−ζ2−ζ7+ζ11−ζ14−ζ19+ζ22+ζ23−ζ26−ζ31+ζ34−ζ38−ζ43+ζ46+ζ47+ζ58+ζ590000000000000000000000000
χ724-44-4-2002-22004-44-400−4i4i4i−4i0000-20000002-2200−2i2i2i−2i000000000000000000000ζ2−ζ7+ζ11+ζ14−ζ19−ζ22+ζ23+ζ26−ζ31−ζ34+ζ38−ζ43−ζ46+ζ47−ζ58+ζ59−ζ2+ζ7−ζ11−ζ14+ζ19+ζ22−ζ23−ζ26+ζ31+ζ34−ζ38+ζ43+ζ46−ζ47+ζ58−ζ59−ζ2+ζ7−ζ11−ζ14+ζ19+ζ22−ζ23−ζ26+ζ31+ζ34−ζ38+ζ43+ζ46−ζ47+ζ58−ζ59ζ2−ζ7+ζ11+ζ14−ζ19−ζ22+ζ23+ζ26−ζ31−ζ34+ζ38−ζ43−ζ46+ζ47−ζ58+ζ59ζ2+ζ7−ζ11+ζ14+ζ19−ζ22−ζ23+ζ26+ζ31−ζ34+ζ38+ζ43−ζ46−ζ47−ζ58−ζ59−ζ2−ζ7+ζ11−ζ14−ζ19+ζ22+ζ23−ζ26−ζ31+ζ34−ζ38−ζ43+ζ46+ζ47+ζ58+ζ59−ζ2−ζ7+ζ11−ζ14−ζ19+ζ22+ζ23−ζ26−ζ31+ζ34−ζ38−ζ43+ζ46+ζ47+ζ58+ζ59ζ2+ζ7−ζ11+ζ14+ζ19−ζ22−ζ23+ζ26+ζ31−ζ34+ζ38+ζ43−ζ46−ζ47−ζ58−ζ590000000000000000000000000
χ734-4-4444-4-4-4400-111-14-400000000-1-11−555−511-100000004-4−55−55-11−555−50000000000000000−55-1-1110000000000000000000
χ744-4-4444-4-4-4400-111-14-400000000-1-11−555−511-10000000-445−55−5-11−555−500000000000000005−511-1-10000000000000000000
χ754-4-4444-4-4-4400-111-14-400000000-1-115−5−5511-100000004-45−55−5-115−5−5500000000000000005−5-1-1110000000000000000000
χ764-4-4444-4-4-4400-111-14-400000000-1-115−5−5511-10000000-44−55−55-115−5−550000000000000000−5511-1-10000000000000000000
χ774-4-444-44-4-444-4-111-1-440000004-4-11-1-1-11111-1000000000−55−551-1-1-11100000000000000005−5−555−50000000000000000000
χ784-4-444-44-4-444-4-111-1-440000004-4-11-1-1-11111-10000000005−55−51-1-1-1110000000000000000−555−5−550000000000000000000
χ794-4-444-44-4-44-44-111-1-44000000-44-11-111-1-111-1000000000−55−551-111-1-100000000000000005−55−5−550000000000000000000
χ804-4-444-44-4-44-44-111-1-44000000-44-11-111-1-111-10000000005−55−51-111-1-10000000000000000−55−555−50000000000000000000
χ814-4-44-24-422-2004-4-44-2244-4-40000-24-4000022-2-4422-2-20000000-220000000000-22000000000000000000000000000000000
χ824-4-44-24-422-2004-4-44-22-4-4440000-24-4000022-24-4-2-2220000000-2200000000002-2000000000000000000000000000000000
χ838888-488-4-4-488-2-2-2-2-4-4000000-4-41-2-2-2-2-2-2111000000000000011111100000000000000000000000000000000000000000
χ848888-488-4-4-4-8-8-2-2-2-2-4-4000000441-2-22222111000000000000011-1-1-1-100000000000000000000000000000000000000000
χ858888-4-8-8-4-4-400-2-2-2-24400000000122−2525−25251110000000000000-1-15−55−500000000000000000000000000000000000000000
χ868888-4-8-8-4-4-400-2-2-2-2440000000012225−2525−251110000000000000-1-1−55−5500000000000000000000000000000000000000000
χ8788-8-88008-8-800-2-2220000008-800-2000000-222000000000-2-22200000000000000000000000000000000000000000000000
χ8888-8-88008-8-800-2-222000000-8800-2000000-22200000000022-2-200000000000000000000000000000000000000000000000
χ898-88-8800-88-800-22-220000000000-20000002-22000000000−252525−2500000000000000000000000000000000000000000000000
χ908-88-8800-88-800-22-220000000000-20000002-2200000000025−25−252500000000000000000000000000000000000000000000000
χ918-8-88-48-844-400-222-2-44000000001-22−252525−25-1-1100000000000001-15−5−5500000000000000000000000000000000000000000
χ928-8-88-48-844-400-222-2-44000000001-2225−25−2525-1-1100000000000001-1−555−500000000000000000000000000000000000000000
χ938-8-88-4-8844-48-8-222-24-4000000-4412-2-2-222-1-110000000000000-1111-1-100000000000000000000000000000000000000000
χ948-8-88-4-8844-4-88-222-24-40000004-412-222-2-2-1-110000000000000-11-1-11100000000000000000000000000000000000000000
χ951616-16-16-800-88800-4-444000000000020000002-2-2000000000000000000000000000000000000000000000000000000000000
χ9616-1616-16-8008-8800-44-4400000000002000000-22-2000000000000000000000000000000000000000000000000000000000000

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