Finite Group Databasebeta

← Group #14297414

Character table — Group #14297414

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size112222222444444444444888888888888888888888810101010121212122020202020202424242424242424404040404040404040404040404060606060120120120120
order12234461212245610101012202020206101012152020303030303030306060606060606060224422442466121210101010202020206888812242424242424242444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-111111111-1ii−i−i-1iiii−i−i−i−i-1-1-1-1ii−i−i
χ61111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-111111111-1−i−iii-1−i−i−i−iiiii-1-1-1-1−i−iii
χ71111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i-1iiii−i−i−i−i1111−i−iii
χ81111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii-1−i−i−i−iiiii1111ii−i−i
χ9111111111-1-1111111-1-1-1-1-1-1-1-111111-1-1-1-111111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-11-11-1-111-1-111-1-111-1-11-11-1
χ10111111111-1-1111111-1-1-1-1-1-1-1-111111-1-1-1-111111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-11-11-1-1-111-1-11111-1-1-11-11
χ11111111111-1-1111111-1-1-1-1-1-1-1-111111-1-1-1-111111-1-1-1-11111-1-111-1-11111-1-1-1-11111-11-11-1-111-1-111-1-1-1-111-11-11
χ12111111111-1-1111111-1-1-1-1-1-1-1-111111-1-1-1-111111-1-1-1-11111-1-111-1-11111-1-1-1-11111-1-11-11-1-1-111-1-111-1-1111-11-1
χ13111111111-1-1111111-1-1-1-1-1-1-1-111111-1-1-1-111111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11i−i−ii1ii−i−i−i−iii-1-111i−i−ii
χ14111111111-1-1111111-1-1-1-1-1-1-1-111111-1-1-1-111111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11−iii−i1−i−iiiii−i−i-1-111−iii−i
χ15111111111-1-1111111-1-1-1-1-1-1-1-111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111i−i−ii1ii−i−i−i−iii11-1-1−iii−i
χ16111111111-1-1111111-1-1-1-1-1-1-1-111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111−iii−i1−i−iiiii−i−i11-1-1i−i−ii
χ172222-2-22-2-22-222222-2-2-2-2-2222-22-2-22222222-2-2-2-2-2-2-2-222-2-20000-2222-2-200000000-2000020000000000000000
χ182222-2-22-2-22-222222-2-2-2-2-2222-22-2-22222222-2-2-2-2-2-2-2-2-2-22200002-2-2-2220000000020000-20000000000000000
χ192222-2-22-2-2-2222222-22222-2-2-222-2-222-2-2-2-22-2-2-2-2222222-2-200002-222-2-20000000020000-20000000000000000
χ202222-2-22-2-2-2222222-22222-2-2-222-2-222-2-2-2-22-2-2-2-22222-2-2220000-22-2-22200000000-2000020000000000000000
χ21222-122-1-1-1222-1222-12222-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222000022-1-1-1-100000000-12222-1-1-1-1-1-1-1-1-100000000
χ22222-122-1-1-1222-1222-12222-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222000022-1-1-1-100000000-1-2-2-2-2-11111111100000000
χ23222-122-1-1-1222-1222-12222-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-20000-2-211110000000012i2i−2i−2i1−i−i−i−iiiii00000000
χ24222-122-1-1-1222-1222-12222-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-20000-2-21111000000001−2i−2i2i2i1iiii−i−i−i−i00000000
χ25222-122-1-1-1-2-22-1222-1-2-2-2-21-2-21-122-1-11111-1-1-1-1-1111122220000-2-2-1-1-1-10000000012-22-21-1-111-1-11100000000
χ26222-122-1-1-1-2-22-1222-1-2-2-2-21-2-21-122-1-11111-1-1-1-1-1111122220000-2-2-1-1-1-1000000001-22-22111-1-111-1-100000000
χ27222-122-1-1-1-2-22-1222-1-2-2-2-21-2-21-122-1-11111-1-1-1-1-11111-2-2-2-2000022111100000000-12i−2i−2i2i-1−i−iiiii−i−i00000000
χ28222-122-1-1-1-2-22-1222-1-2-2-2-21-2-21-122-1-11111-1-1-1-1-11111-2-2-2-2000022111100000000-1−2i2i2i−2i-1ii−i−i−i−iii00000000
χ29222-1-2-2-1112-22-12221-2-2-2-2-1221-1-2-2-1-1-1-1-1-1-11111111122-2-20000-22-1-1110000000010000-13−33−33−33−300000000
χ30222-1-2-2-1112-22-12221-2-2-2-2-1221-1-2-2-1-1-1-1-1-1-11111111122-2-20000-22-1-1110000000010000-1−33−33−33−3300000000
χ31222-1-2-2-1112-22-12221-2-2-2-2-1221-1-2-2-1-1-1-1-1-1-111111111-2-22200002-211-1-100000000-100001−i3i3−i3i3i3−i3i3−i300000000
χ32222-1-2-2-1112-22-12221-2-2-2-2-1221-1-2-2-1-1-1-1-1-1-111111111-2-22200002-211-1-100000000-100001i3−i3i3−i3−i3i3−i3i300000000
χ33222-1-2-2-111-222-1222122221-2-2-1-1-2-2-1-11111-11111-1-1-1-122-2-200002-2-1-11100000000-1000013−3−333−3−3300000000
χ34222-1-2-2-111-222-1222122221-2-2-1-1-2-2-1-11111-11111-1-1-1-122-2-200002-2-1-11100000000-100001−333−3−333−300000000
χ35222-1-2-2-111-222-1222122221-2-2-1-1-2-2-1-11111-11111-1-1-1-1-2-2220000-2211-1-10000000010000-1−i3i3i3−i3i3−i3−i3i300000000
χ36222-1-2-2-111-222-1222122221-2-2-1-1-2-2-1-11111-11111-1-1-1-1-2-2220000-2211-1-10000000010000-1i3−i3−i3i3−i3i3i3−i300000000
χ3722-222-2222002-2-2-22-20000000022-2-2-20000222-2-200002-22-2002-2002-22-2000022-2-200000000000000002-20000
χ3822-222-2222002-2-2-22-20000000022-2-2-20000222-2-200002-22-200-22002-22-20000-2-2220000000000000000-220000
χ3922-222-2222002-2-2-22-20000000022-2-2-20000222-2-20000-22-22002-200-22-22000022-2-20000000000000000-220000
χ4022-222-2222002-2-2-22-20000000022-2-2-20000222-2-20000-22-2200-2200-22-220000-2-22200000000000000002-20000
χ4122-22-222-2-2002-2-2-222000000002-22-2-200002-2-22200002-2-222-200002-2-2222-2-20000000000000000002-2000000
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χ4544444444444-14-1-1-14-1-1-1-14-1-14-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100004444000000-1-1-1-1-1-1-1-10000000000000000000000
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χ48444444444-4-4-14-1-1-141111-411-4-1-1-1-1-11111-1-1-1-1-111110000-4-4440000001111-1-1-1-10000000000000000000000
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χ514444-4-44-4-4-44-14-1-1-1-4-1-1-1-1-4114-111-1-11111-11111-1-1-1-100000000000000−55−555−55−50000000000000000000000
χ524444-4-44-4-4-44-14-1-1-1-4-1-1-1-1-4114-111-1-11111-11111-1-1-1-1000000000000005−55−5−55−550000000000000000000000
χ5344-444-444400-1-411-1-4−5−5550−550-1-1111−5−555-1-1-111−5−5550000004-4000000−555−5-1-1110000000000000000000000
χ5444-444-444400-1-411-1-4−5−5550−550-1-1111−5−555-1-1-111−5−555000000-440000005−5−5511-1-10000000000000000000000
χ5544-444-444400-1-411-1-455−5−505−50-1-111155−5−5-1-1-11155−5−50000004-40000005−5−55-1-1110000000000000000000000
χ5644-444-444400-1-411-1-455−5−505−50-1-111155−5−5-1-1-11155−5−5000000-44000000−555−511-1-10000000000000000000000
χ5744-44-444-4-400-1-411-14−5−55505−50-11-11155−5−5-111-1-1−5−55500004-400000000-1-1115−5−550000000000000000000000
χ5844-44-444-4-400-1-411-14−5−55505−50-11-11155−5−5-111-1-1−5−5550000-440000000011-1-1−555−50000000000000000000000
χ5944-44-444-4-400-1-411-1455−5−50−550-11-111−5−555-111-1-155−5−500004-400000000-1-111−555−50000000000000000000000
χ6044-44-444-4-400-1-411-1455−5−50−550-11-111−5−555-111-1-155−5−50000-440000000011-1-15−5−550000000000000000000000
χ6144-4-24-4-2-2-20042-4-44200000000-24-4220000-2-2-22200004-44-4000000-22-22000000000000000000000000000000
χ6244-4-24-4-2-2-20042-4-44200000000-24-4220000-2-2-2220000-44-440000002-22-2000000000000000000000000000000
χ6344-4-2-44-2220042-4-44-200000000-2-44220000-222-2-200004-4-44000000-222-2000000000000000000000000000000
χ6444-4-2-44-2220042-4-44-200000000-2-44220000-222-2-20000-444-40000002-2-22000000000000000000000000000000
χ65888-488-4-4-488-2-4-2-2-2-4-2-2-2-2-4-2-2-41-2-211111111111111100000000000000000000000000000000000000000000
χ66888-488-4-4-4-8-8-2-4-2-2-2-4222242241-2-211-1-1-1-111111-1-1-1-100000000000000000000000000000000000000000000
χ67888-4-8-8-4448-8-2-4-2-2-242222-4-2-241221111111-1-1-1-1-1-1-1-100000000000000000000000000000000000000000000
χ68888-4-8-8-444-88-2-4-2-2-24-2-2-2-2422-412211-1-1-1-11-1-1-1-1111100000000000000000000000000000000000000000000
χ6988-8-48-8-4-4-400-2422-24−25−2525250−252501-22-1-155−5−5111-1-155−5−500000000000000000000000000000000000000000000
χ7088-8-48-8-4-4-400-2422-242525−25−25025−2501-22-1-1−5−555111-1-1−5−55500000000000000000000000000000000000000000000
χ7188-8-4-88-44400-2422-2-4−25−252525025−25012-2-1-1−5−5551-1-11155−5−500000000000000000000000000000000000000000000
χ7288-8-4-88-44400-2422-2-42525−25−250−2525012-2-1-155−5−51-1-111−5−55500000000000000000000000000000000000000000000
χ738-80800-800008000-8000000000800000000-80000000000000000000000000000000000000000000000000000
χ748-80800-80000-20−2525202ζ7+2ζ11−2ζ19−2ζ23+2ζ31−2ζ43+2ζ47−2ζ59−2ζ7−2ζ11+2ζ19+2ζ23−2ζ31+2ζ43−2ζ47+2ζ592ζ7−2ζ11+2ζ19−2ζ23−2ζ31−2ζ43+2ζ47+2ζ59−2ζ7+2ζ11−2ζ19+2ζ23+2ζ31+2ζ43−2ζ47−2ζ590000-200−25250000200002ζ7+2ζ11−2ζ19−2ζ23+2ζ31−2ζ43+2ζ47−2ζ59−2ζ7−2ζ11+2ζ19+2ζ23−2ζ31+2ζ43−2ζ47+2ζ592ζ7−2ζ11+2ζ19−2ζ23−2ζ31−2ζ43+2ζ47+2ζ59−2ζ7+2ζ11−2ζ19+2ζ23+2ζ31+2ζ43−2ζ47−2ζ5900000000000000000000000000000000000000000000
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χ818-80-400443−4300-2025−25202ζ7−2ζ11+2ζ19−2ζ23−2ζ31−2ζ43+2ζ47+2ζ59−2ζ7+2ζ11−2ζ19+2ζ23+2ζ31+2ζ43−2ζ47−2ζ59−2ζ7−2ζ11+2ζ19+2ζ23−2ζ31+2ζ43−2ζ47+2ζ592ζ7+2ζ11−2ζ19−2ζ23+2ζ31−2ζ43+2ζ47−2ζ590000100−55−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+ζ58-1−3315−15−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+ζ5900000000000000000000000000000000000000000000
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χ838-80-4004−4343008000-8000000000-4000000004−434300000000000000000000000000000000000000000000000000
χ848-80-4004−434300-20−2525202ζ7+2ζ11−2ζ19−2ζ23+2ζ31−2ζ43+2ζ47−2ζ59−2ζ7−2ζ11+2ζ19+2ζ23−2ζ31+2ζ43−2ζ47+2ζ592ζ7−2ζ11+2ζ19−2ζ23−2ζ31−2ζ43+2ζ47+2ζ59−2ζ7+2ζ11−2ζ19+2ζ23+2ζ31+2ζ43−2ζ47−2ζ5900001005−5ζ2−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+ζ58-13−315−15−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+ζ5900000000000000000000000000000000000000000000
χ858-80-4004−434300-20−252520−2ζ7−2ζ11+2ζ19+2ζ23−2ζ31+2ζ43−2ζ47+2ζ592ζ7+2ζ11−2ζ19−2ζ23+2ζ31−2ζ43+2ζ47−2ζ59−2ζ7+2ζ11−2ζ19+2ζ23+2ζ31+2ζ43−2ζ47−2ζ592ζ7−2ζ11+2ζ19−2ζ23−2ζ31−2ζ43+2ζ47+2ζ5900001005−5−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−ζ58-13−315−15ζ7+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−ζ5900000000000000000000000000000000000000000000
χ868-80-4004−434300-2025−25202ζ7−2ζ11+2ζ19−2ζ23−2ζ31−2ζ43+2ζ47+2ζ59−2ζ7+2ζ11−2ζ19+2ζ23+2ζ31+2ζ43−2ζ47−2ζ59−2ζ7−2ζ11+2ζ19+2ζ23−2ζ31+2ζ43−2ζ47+2ζ592ζ7+2ζ11−2ζ19−2ζ23+2ζ31−2ζ43+2ζ47−2ζ590000100−55ζ2+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−ζ58-13−3−1515−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+ζ5900000000000000000000000000000000000000000000
χ878-80-4004−434300-2025−2520−2ζ7+2ζ11−2ζ19+2ζ23+2ζ31+2ζ43−2ζ47−2ζ592ζ7−2ζ11+2ζ19−2ζ23−2ζ31−2ζ43+2ζ47+2ζ592ζ7+2ζ11−2ζ19−2ζ23+2ζ31−2ζ43+2ζ47−2ζ59−2ζ7−2ζ11+2ζ19+2ζ23−2ζ31+2ζ43−2ζ47+2ζ590000100−55−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+ζ58-13−3−1515ζ7−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−ζ5900000000000000000000000000000000000000000000

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