Finite Group Databasebeta

← Group #14279362

Character table — Group #14279362

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57
size112222244488888888816161616161616161620202020202040404040404040404040404040484848484880120120240240
order1223666451041012152020303030122020606060606060441212121228888242424242424242484040404062444
χ1111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-1-1-1-11-1-1-1-1
χ311111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ411111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111
χ51111111111111111111111111111-1-1-1-1-1-1-1ii−i−iiiii−i−i−i−i11111-1-1-1i−i
χ61111111111111111111111111111-1-1-1-1-1-1-1ii−i−iiiii−i−i−i−i-1-1-1-1-1-111−ii
χ71111111111111111111111111111-1-1-1-1-1-1-1−i−iii−i−i−i−iiiii11111-1-1-1−ii
χ81111111111111111111111111111-1-1-1-1-1-1-1−i−iii−i−i−i−iiiii-1-1-1-1-1-111i−i
χ92222222222-222222222-2-2-222-2-2-2-2222222-200000000000000000-20000
χ102222222222-222222222-2-2-222-2-2-2-2-2-2-2-2-2-220000000000000000020000
χ11222-1-1-1-122222-1-122-1-1-1-122-1-1-1-1-1-122-1-1-1-122222-1-1-1-1-1-1-1-100000-10000
χ12222-1-1-1-122222-1-122-1-1-1-122-1-1-1-1-1-122-1-1-1-12-2-2-2-21111111100000-10000
χ13222-1-1-1-122222-1-122-1-1-1-122-1-1-1-1-1-1-2-21111-22i2i−2i−2i−i−i−i−iiiii0000010000
χ14222-1-1-1-122222-1-122-1-1-1-122-1-1-1-1-1-1-2-21111-2−2i−2i2i2iiiii−i−i−i−i0000010000
χ15222-1-1-1-1222-22-1-122-1-1-11-2-2-1-1111122-1-1-1-1-20000−i3−i3i3i3−i3−i3i3i30000010000
χ16222-1-1-1-1222-22-1-122-1-1-11-2-2-1-1111122-1-1-1-1-20000i3i3−i3−i3i3i3−i3−i30000010000
χ17222-1-1-1-1222-22-1-122-1-1-11-2-2-1-11111-2-211112000033−3−3−3−33300000-10000
χ18222-1-1-1-1222-22-1-122-1-1-11-2-2-1-11111-2-2111120000−3−33333−3−300000-10000
χ1944444444-1-14-14-1-1-1-1-1-14-1-1-1-1-1-1-1-100000000000000000004-1-1-1-100000
χ2044444444-1-14-14-1-1-1-1-1-14-1-1-1-1-1-1-1-10000000000000000000-4111100000
χ2144444444-1-1-4-14-1-1-1-1-1-1-411-1-1111100000000000000000000−5−55500000
χ2244444444-1-1-4-14-1-1-1-1-1-1-411-1-111110000000000000000000055−5−500000
χ234444444-44404-44-4-4444000-4-4000000000000000000000000000000000
χ244444444-4-1-10-1-4-111-1-1-10−5511−5−55500000000000000000000ζ7+ζ11−ζ19−ζ23+ζ31−ζ43+ζ47−ζ59−ζ7−ζ11+ζ19+ζ23−ζ31+ζ43−ζ47+ζ59ζ7−ζ11+ζ19−ζ23−ζ31−ζ43+ζ47+ζ59−ζ7+ζ11−ζ19+ζ23+ζ31+ζ43−ζ47−ζ5900000
χ254444444-4-1-10-1-4-111-1-1-10−5511−5−55500000000000000000000−ζ7−ζ11+ζ19+ζ23−ζ31+ζ43−ζ47+ζ59ζ7+ζ11−ζ19−ζ23+ζ31−ζ43+ζ47−ζ59−ζ7+ζ11−ζ19+ζ23+ζ31+ζ43−ζ47−ζ59ζ7−ζ11+ζ19−ζ23−ζ31−ζ43+ζ47+ζ5900000
χ264444444-4-1-10-1-4-111-1-1-105−51155−5−500000000000000000000ζ7−ζ11+ζ19−ζ23−ζ31−ζ43+ζ47+ζ59−ζ7+ζ11−ζ19+ζ23+ζ31+ζ43−ζ47−ζ59−ζ7−ζ11+ζ19+ζ23−ζ31+ζ43−ζ47+ζ59ζ7+ζ11−ζ19−ζ23+ζ31−ζ43+ζ47−ζ5900000
χ274444444-4-1-10-1-4-111-1-1-105−51155−5−500000000000000000000−ζ7+ζ11−ζ19+ζ23+ζ31+ζ43−ζ47−ζ59ζ7−ζ11+ζ19−ζ23−ζ31−ζ43+ζ47+ζ59ζ7+ζ11−ζ19−ζ23+ζ31−ζ43+ζ47−ζ59−ζ7−ζ11+ζ19+ζ23−ζ31+ζ43−ζ47+ζ5900000
χ28444-2-2-2-2-444042-2-4-4-2-2-200022000000−2i3−2i32i32i300000000000000000000000
χ29444-2-2-2-2-444042-2-4-4-2-2-2000220000002i32i3−2i3−2i300000000000000000000000
χ3044-444-4-40440-40400-4-4400000000000000000000000000000000002-200
χ3144-444-4-40440-40400-4-440000000000000000000000000000000000-2200
χ324-404-40004-400040000-40000000002i−2i2i−2i2i−2i01+i−1−i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000
χ334-404-40004-400040000-40000000002i−2i2i−2i2i−2i0−1−i1+i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000
χ344-404-40004-400040000-4000000000−2i2i−2i2i−2i2i01−i−1+i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000
χ354-404-40004-400040000-4000000000−2i2i−2i2i−2i2i0−1+i1−i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000
χ364-40-22−2i32i304-4000-200−2i32i320000000002i−2i−2ζ11−2ζ23−2ζ47−2ζ592ζ11+2ζ23+2ζ47+2ζ59−2ζ7−2ζ19−2ζ31−2ζ432ζ7+2ζ19+2ζ31+2ζ4301+i−1−i1−i−1+iζ2−ζ11+ζ14−ζ23+ζ26+ζ38−ζ47−ζ59−ζ2+ζ11−ζ14+ζ23−ζ26−ζ38+ζ47+ζ59−ζ7−ζ19+ζ22−ζ31+ζ34−ζ43+ζ46+ζ58ζ7+ζ19−ζ22+ζ31−ζ34+ζ43−ζ46−ζ58ζ2+ζ11+ζ14+ζ23+ζ26+ζ38+ζ47+ζ59−ζ2−ζ11−ζ14−ζ23−ζ26−ζ38−ζ47−ζ59ζ7+ζ19+ζ22+ζ31+ζ34+ζ43+ζ46+ζ58−ζ7−ζ19−ζ22−ζ31−ζ34−ζ43−ζ46−ζ580000000000
χ374-40-22−2i32i304-4000-200−2i32i320000000002i−2i−2ζ11−2ζ23−2ζ47−2ζ592ζ11+2ζ23+2ζ47+2ζ59−2ζ7−2ζ19−2ζ31−2ζ432ζ7+2ζ19+2ζ31+2ζ430−1−i1+i−1+i1−i−ζ2+ζ11−ζ14+ζ23−ζ26−ζ38+ζ47+ζ59ζ2−ζ11+ζ14−ζ23+ζ26+ζ38−ζ47−ζ59ζ7+ζ19−ζ22+ζ31−ζ34+ζ43−ζ46−ζ58−ζ7−ζ19+ζ22−ζ31+ζ34−ζ43+ζ46+ζ58−ζ2−ζ11−ζ14−ζ23−ζ26−ζ38−ζ47−ζ59ζ2+ζ11+ζ14+ζ23+ζ26+ζ38+ζ47+ζ59−ζ7−ζ19−ζ22−ζ31−ζ34−ζ43−ζ46−ζ58ζ7+ζ19+ζ22+ζ31+ζ34+ζ43+ζ46+ζ580000000000
χ384-40-22−2i32i304-4000-200−2i32i32000000000−2i2i2ζ11+2ζ23+2ζ47+2ζ59−2ζ11−2ζ23−2ζ47−2ζ592ζ7+2ζ19+2ζ31+2ζ43−2ζ7−2ζ19−2ζ31−2ζ4301−i−1+i1+i−1−iζ2+ζ11+ζ14+ζ23+ζ26+ζ38+ζ47+ζ59−ζ2−ζ11−ζ14−ζ23−ζ26−ζ38−ζ47−ζ59ζ7+ζ19+ζ22+ζ31+ζ34+ζ43+ζ46+ζ58−ζ7−ζ19−ζ22−ζ31−ζ34−ζ43−ζ46−ζ58ζ2−ζ11+ζ14−ζ23+ζ26+ζ38−ζ47−ζ59−ζ2+ζ11−ζ14+ζ23−ζ26−ζ38+ζ47+ζ59−ζ7−ζ19+ζ22−ζ31+ζ34−ζ43+ζ46+ζ58ζ7+ζ19−ζ22+ζ31−ζ34+ζ43−ζ46−ζ580000000000
χ394-40-22−2i32i304-4000-200−2i32i32000000000−2i2i2ζ11+2ζ23+2ζ47+2ζ59−2ζ11−2ζ23−2ζ47−2ζ592ζ7+2ζ19+2ζ31+2ζ43−2ζ7−2ζ19−2ζ31−2ζ430−1+i1−i−1−i1+i−ζ2−ζ11−ζ14−ζ23−ζ26−ζ38−ζ47−ζ59ζ2+ζ11+ζ14+ζ23+ζ26+ζ38+ζ47+ζ59−ζ7−ζ19−ζ22−ζ31−ζ34−ζ43−ζ46−ζ58ζ7+ζ19+ζ22+ζ31+ζ34+ζ43+ζ46+ζ58−ζ2+ζ11−ζ14+ζ23−ζ26−ζ38+ζ47+ζ59ζ2−ζ11+ζ14−ζ23+ζ26+ζ38−ζ47−ζ59ζ7+ζ19−ζ22+ζ31−ζ34+ζ43−ζ46−ζ58−ζ7−ζ19+ζ22−ζ31+ζ34−ζ43+ζ46+ζ580000000000
χ404-40-222i3−2i304-4000-2002i3−2i320000000002i−2i−2ζ7−2ζ19−2ζ31−2ζ432ζ7+2ζ19+2ζ31+2ζ43−2ζ11−2ζ23−2ζ47−2ζ592ζ11+2ζ23+2ζ47+2ζ5901+i−1−i1−i−1+i−ζ7−ζ19+ζ22−ζ31+ζ34−ζ43+ζ46+ζ58ζ7+ζ19−ζ22+ζ31−ζ34+ζ43−ζ46−ζ58ζ2−ζ11+ζ14−ζ23+ζ26+ζ38−ζ47−ζ59−ζ2+ζ11−ζ14+ζ23−ζ26−ζ38+ζ47+ζ59ζ7+ζ19+ζ22+ζ31+ζ34+ζ43+ζ46+ζ58−ζ7−ζ19−ζ22−ζ31−ζ34−ζ43−ζ46−ζ58ζ2+ζ11+ζ14+ζ23+ζ26+ζ38+ζ47+ζ59−ζ2−ζ11−ζ14−ζ23−ζ26−ζ38−ζ47−ζ590000000000
χ414-40-222i3−2i304-4000-2002i3−2i320000000002i−2i−2ζ7−2ζ19−2ζ31−2ζ432ζ7+2ζ19+2ζ31+2ζ43−2ζ11−2ζ23−2ζ47−2ζ592ζ11+2ζ23+2ζ47+2ζ590−1−i1+i−1+i1−iζ7+ζ19−ζ22+ζ31−ζ34+ζ43−ζ46−ζ58−ζ7−ζ19+ζ22−ζ31+ζ34−ζ43+ζ46+ζ58−ζ2+ζ11−ζ14+ζ23−ζ26−ζ38+ζ47+ζ59ζ2−ζ11+ζ14−ζ23+ζ26+ζ38−ζ47−ζ59−ζ7−ζ19−ζ22−ζ31−ζ34−ζ43−ζ46−ζ58ζ7+ζ19+ζ22+ζ31+ζ34+ζ43+ζ46+ζ58−ζ2−ζ11−ζ14−ζ23−ζ26−ζ38−ζ47−ζ59ζ2+ζ11+ζ14+ζ23+ζ26+ζ38+ζ47+ζ590000000000
χ424-40-222i3−2i304-4000-2002i3−2i32000000000−2i2i2ζ7+2ζ19+2ζ31+2ζ43−2ζ7−2ζ19−2ζ31−2ζ432ζ11+2ζ23+2ζ47+2ζ59−2ζ11−2ζ23−2ζ47−2ζ5901−i−1+i1+i−1−iζ7+ζ19+ζ22+ζ31+ζ34+ζ43+ζ46+ζ58−ζ7−ζ19−ζ22−ζ31−ζ34−ζ43−ζ46−ζ58ζ2+ζ11+ζ14+ζ23+ζ26+ζ38+ζ47+ζ59−ζ2−ζ11−ζ14−ζ23−ζ26−ζ38−ζ47−ζ59−ζ7−ζ19+ζ22−ζ31+ζ34−ζ43+ζ46+ζ58ζ7+ζ19−ζ22+ζ31−ζ34+ζ43−ζ46−ζ58ζ2−ζ11+ζ14−ζ23+ζ26+ζ38−ζ47−ζ59−ζ2+ζ11−ζ14+ζ23−ζ26−ζ38+ζ47+ζ590000000000
χ434-40-222i3−2i304-4000-2002i3−2i32000000000−2i2i2ζ7+2ζ19+2ζ31+2ζ43−2ζ7−2ζ19−2ζ31−2ζ432ζ11+2ζ23+2ζ47+2ζ59−2ζ11−2ζ23−2ζ47−2ζ590−1+i1−i−1−i1+i−ζ7−ζ19−ζ22−ζ31−ζ34−ζ43−ζ46−ζ58ζ7+ζ19+ζ22+ζ31+ζ34+ζ43+ζ46+ζ58−ζ2−ζ11−ζ14−ζ23−ζ26−ζ38−ζ47−ζ59ζ2+ζ11+ζ14+ζ23+ζ26+ζ38+ζ47+ζ59ζ7+ζ19−ζ22+ζ31−ζ34+ζ43−ζ46−ζ58−ζ7−ζ19+ζ22−ζ31+ζ34−ζ43+ζ46+ζ58−ζ2+ζ11−ζ14+ζ23−ζ26−ζ38+ζ47+ζ59ζ2−ζ11+ζ14−ζ23+ζ26+ζ38−ζ47−ζ590000000000
χ44888-4-4-4-48-2-28-2-41-2-2111-4-2-211111100000000000000000000000000000
χ45888-4-4-4-48-2-2-8-2-41-2-211142211-1-1-1-100000000000000000000000000000
χ46888-4-4-4-4-8-2-20-241221110−2525-1-155−5−500000000000000000000000000000
χ47888-4-4-4-4-8-2-20-24122111025−25-1-1−5−55500000000000000000000000000000
χ4888-888-8-80-2-2020-2−252522-2000−2525000000000000000000000000000000000
χ4988-888-8-80-2-2020-225−2522-200025−25000000000000000000000000000000000
χ5088-8-4-4440880-80-40044-400000000000000000000000000000000000000
χ5188-8-4-4440-2-20201−2525-1-110005−5−ζ2+ζ14+ζ22−ζ26−ζ34+ζ38+ζ46−ζ58ζ2−ζ14−ζ22+ζ26+ζ34−ζ38−ζ46+ζ58ζ2+ζ14−ζ22−ζ26−ζ34−ζ38+ζ46+ζ58−ζ2−ζ14+ζ22+ζ26+ζ34+ζ38−ζ46−ζ5800000000000000000000000000000
χ5288-8-4-4440-2-20201−2525-1-110005−5ζ2−ζ14−ζ22+ζ26+ζ34−ζ38−ζ46+ζ58−ζ2+ζ14+ζ22−ζ26−ζ34+ζ38+ζ46−ζ58−ζ2−ζ14+ζ22+ζ26+ζ34+ζ38−ζ46−ζ58ζ2+ζ14−ζ22−ζ26−ζ34−ζ38+ζ46+ζ5800000000000000000000000000000
χ5388-8-4-4440-2-2020125−25-1-11000−55ζ2+ζ14−ζ22−ζ26−ζ34−ζ38+ζ46+ζ58−ζ2−ζ14+ζ22+ζ26+ζ34+ζ38−ζ46−ζ58ζ2−ζ14−ζ22+ζ26+ζ34−ζ38−ζ46+ζ58−ζ2+ζ14+ζ22−ζ26−ζ34+ζ38+ζ46−ζ5800000000000000000000000000000
χ5488-8-4-4440-2-2020125−25-1-11000−55−ζ2−ζ14+ζ22+ζ26+ζ34+ζ38−ζ46−ζ58ζ2+ζ14−ζ22−ζ26−ζ34−ζ38+ζ46+ζ58−ζ2+ζ14+ζ22−ζ26−ζ34+ζ38+ζ46−ζ58ζ2−ζ14−ζ22+ζ26+ζ34−ζ38−ζ46+ζ5800000000000000000000000000000
χ5516-16016-16000-44000-40000400000000000000000000000000000000000000
χ5616-160-88−8i38i30-440002002i3−2i3-200000000000000000000000000000000000000
χ5716-160-888i3−8i30-44000200−2i32i3-200000000000000000000000000000000000000

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