Finite Group Databasebeta

← Group #14302031

Character table — Group #14302031

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size1111222222444444555588888888810101010101012121616161616161616202020202020202020202020202024242424244040404040404040404848606060606060120120120
order1222344666510101012124444412121520203030302212121212242020606060606060444466121212121212121241010202026688242424242020244444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-11-1-1
χ311111111111111111111111111111111111-1-11111111111111111111111-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-11111-111
χ511111111111111111111-1-1-111111111111111-1-111-1-1-1-111111111111111-11111-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1
χ611111111111111111111-1-1-111111111111111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-11111-1-1-1111111-1-111-1-1-1-1-111
χ711111111111111111111-1-1-1111111111111-1-1-1-111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111
χ811111111111111111111-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-111111111-1-111111-1-1
χ91111111111111111-1-1-1-1111111111-1-1-1-1-1-11111111111ii−i−i-1-1iiii−i−i−i−i11111-1-1-1i−iii−i−i11-1-1ii−i−i-1i−i
χ101111111111111111-1-1-1-1111111111-1-1-1-1-1-11111111111−i−iii-1-1−i−i−i−iiiii11111-1-1-1−ii−i−iii11-1-1−i−iii-1−ii
χ111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-111111111ii−i−i-1-1iiii−i−i−i−i-1-1-1-1-1-1-1-1i−iii−i−i-1-111−i−iii1−ii
χ121111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-111111111−i−iii-1-1−i−i−i−iiiii-1-1-1-1-1-1-1-1−ii−i−iii-1-111ii−i−i1i−i
χ131111111111111111-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-111-1-1-1-1ii−i−i-1-1iiii−i−i−i−i-11111111−ii−i−iii-1-1-1-1ii−i−i1−ii
χ141111111111111111-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-111-1-1-1-1−i−iii-1-1−i−i−i−iiiii-11111111i−iii−i−i-1-1-1-1−i−iii1i−i
χ151111111111111111-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1ii−i−i-1-1iiii−i−i−i−i1-1-1-1-1111−ii−i−iii1111−i−iii-1i−i
χ161111111111111111-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1−i−iii-1-1−i−i−i−iiiii1-1-1-1-1111i−iii−i−i1111ii−i−i-1−ii
χ1722222-2-22222222-2-222220002-2-2222-2-222222-200-2-200000000-2-200000000022-2-200000000000-220000000
χ1822222-2-22222222-2-222220002-2-2222-2-22222-2200-2-200000000-2-2000000000-2-222000000000002-20000000
χ1922222-2-22222222-2-2-2-2-2-20002-2-222222-2-2-2-22-200-2-2000000002200000000022-2-2000000000002-20000000
χ2022222-2-22222222-2-2-2-2-2-20002-2-222222-2-2-2-2-2200-2-20000000022000000000-2-22200000000000-220000000
χ212222-122-1-1-12222-1-122222-1-1-122-1-1-122-1-1-1-10022-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1000002-1-122-1-1-1-100000000000
χ222222-122-1-1-12222-1-122222-1-1-122-1-1-122-1-1-1-10022-1-1-1-1-1-1-2-2-2-2-1-111111111000002-1-1-2-2111100000000000
χ232222-122-1-1-12222-1-12222-211-122-1-1-122-1-1-1-100-2-2-1-111112222-1-1-1-1-1-1-1-1-1-100000-211-2-2111100000000000
χ242222-122-1-1-12222-1-12222-211-122-1-1-122-1-1-1-100-2-2-1-11111-2-2-2-2-1-11111111100000-21122-1-1-1-100000000000
χ252222-122-1-1-12222-1-1-2-2-2-22-1-1-122-1-1-1-2-211110022-1-1-1-1-1-12i2i−2i−2i11−i−i−i−iiiii00000-2112i−2i−i−iii00000000000
χ262222-122-1-1-12222-1-1-2-2-2-22-1-1-122-1-1-1-2-211110022-1-1-1-1-1-1−2i−2i2i2i11iiii−i−i−i−i00000-211−2i2iii−i−i00000000000
χ272222-122-1-1-12222-1-1-2-2-2-2-211-122-1-1-1-2-2111100-2-2-1-111112i2i−2i−2i11−i−i−i−iiiii000002-1-1−2i2iii−i−i00000000000
χ282222-122-1-1-12222-1-1-2-2-2-2-211-122-1-1-1-2-2111100-2-2-1-11111−2i−2i2i2i11iiii−i−i−i−i000002-1-12i−2i−i−iii00000000000
χ292-22-222-2-2-222-22-22-222-2-200022-2-2-222-2-2-22200002-2000000002-2000000000000000000000000002i−2i2i−2i000
χ302-22-222-2-2-222-22-22-222-2-200022-2-2-222-2-2-22200002-2000000002-200000000000000000000000000−2i2i−2i2i000
χ312-22-222-2-2-222-22-22-2-2-22200022-2-2-22-2222-2-200002-200000000-22000000000000000000000000002-2-22000
χ322-22-222-2-2-222-22-22-2-2-22200022-2-2-22-2222-2-200002-200000000-2200000000000000000000000000-222-2000
χ332-22-22-22-2-222-22-2-2222-2-20002-22-2-22-22-2-2220000-2200002-22-2-2222-2-222-2-20000000000000000000000000
χ342-22-22-22-2-222-22-2-2222-2-20002-22-2-22-22-2-2220000-220000-22-22-22-2-222-2-2220000000000000000000000000
χ352-22-22-22-2-222-22-2-22-2-2220002-22-2-222-222-2-20000-2200002i−2i−2i2i2-22i2i−2i−2i−2i−2i2i2i0000000000000000000000000
χ362-22-22-22-2-222-22-2-22-2-2220002-22-2-222-222-2-20000-220000−2i2i2i−2i2-2−2i−2i2i2i2i2i−2i−2i0000000000000000000000000
χ372-22-2-1-2211-12-22-21-122-2-20−i3i3-1-2211-1-2211-1-100001-1−i3−i3i3i32-22-21-1-1-111-1-111000000−i3i300−i3i3−i3i300000000000
χ382-22-2-1-2211-12-22-21-122-2-20−i3i3-1-2211-1-2211-1-100001-1−i3−i3i3i3-22-221-111-1-111-1-1000000−i3i300i3−i3i3−i300000000000
χ392-22-2-1-2211-12-22-21-122-2-20i3−i3-1-2211-1-2211-1-100001-1i3i3−i3−i32-22-21-1-1-111-1-111000000i3−i300i3−i3i3−i300000000000
χ402-22-2-1-2211-12-22-21-122-2-20i3−i3-1-2211-1-2211-1-100001-1i3i3−i3−i3-22-221-111-1-111-1-1000000i3−i300−i3i3−i3i300000000000
χ412-22-2-1-2211-12-22-21-1-2-2220−i3i3-1-2211-12-2-1-11100001-1−i3−i3i3i32i−2i−2i2i-11−i−iiiii−i−i000000i3−i3003−3−3300000000000
χ422-22-2-1-2211-12-22-21-1-2-2220−i3i3-1-2211-12-2-1-11100001-1−i3−i3i3i3−2i2i2i−2i-11ii−i−i−i−iii000000i3−i300−333−300000000000
χ432-22-2-1-2211-12-22-21-1-2-2220i3−i3-1-2211-12-2-1-11100001-1i3i3−i3−i32i−2i−2i2i-11−i−iiiii−i−i000000−i3i300−333−300000000000
χ442-22-2-1-2211-12-22-21-1-2-2220i3−i3-1-2211-12-2-1-11100001-1i3i3−i3−i3−2i2i2i−2i-11ii−i−i−i−iii000000−i3i3003−3−3300000000000
χ454444444444-1-1-1-1440000444-1-1-1-1-1-100000044-1-1-1-1-1-1-1-1000000000000004-1-1-1-1000000000-1-1000000000
χ464444444444-1-1-1-1440000444-1-1-1-1-1-1000000-4-4-1-1-1-1-1-1-1-100000000000000-4111100000000011000000000
χ474444444444-1-1-1-1440000-4-4-4-1-1-1-1-1-10000004411-1-1111100000000000000-4-1-1-1-100000000011000000000
χ484444444444-1-1-1-1440000-4-4-4-1-1-1-1-1-1000000-4-411-1-111110000000000000041111000000000-1-1000000000
χ4944444-4-4444-1-1-1-1-4-40000000-111-1-1-10000004-4−5511−55−55000000000000000-1-111000000000−55000000000
χ5044444-4-4444-1-1-1-1-4-40000000-111-1-1-10000004-45−5115−55−5000000000000000-1-1110000000005−5000000000
χ5144444-4-4444-1-1-1-1-4-40000000-111-1-1-1000000-44−5511−55−5500000000000000011-1-10000000005−5000000000
χ5244444-4-4444-1-1-1-1-4-40000000-111-1-1-1000000-445−5115−55−500000000000000011-1-1000000000−55000000000
χ534444-2-4-4-2-2-24444224444000-2-4-4-2-2-2-4-4-2-2-2-20000220000000022000000000000000000000000000000000
χ544444-2-4-4-2-2-2444422-4-4-4-4000-2-4-4-2-2-244222200002200000000-2-2000000000000000000000000000000000
χ5544-4-44004-4-44-4-44004i−4i4i−4i0004004-4-4004i−4i4i−4i0000000000000000000000000000000000000000000000000
χ5644-4-44004-4-44-4-4400−4i4i−4i4i0004004-4-400−4i4i−4i4i0000000000000000000000000000000000000000000000000
χ5744-4-4-200-2224-4-44004i−4i4i−4i000-200-22200−2i2i−2i2i0000000000000000−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+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+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−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
χ5844-4-4-200-2224-4-44004i−4i4i−4i000-200-22200−2i2i−2i2i0000000000000000ζ2−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+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−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−ζ59−ζ2−ζ7+ζ11−ζ14−ζ19+ζ22+ζ23−ζ26−ζ31+ζ34−ζ38−ζ43+ζ46+ζ47+ζ58+ζ590000000000000000000000000
χ5944-4-4-200-2224-4-4400−4i4i−4i4i000-200-222002i−2i2i−2i0000000000000000−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−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−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+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
χ6044-4-4-200-2224-4-4400−4i4i−4i4i000-200-222002i−2i2i−2i0000000000000000ζ2+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−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+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+ζ59−ζ2+ζ7−ζ11−ζ14+ζ19+ζ22−ζ23−ζ26+ζ31+ζ34−ζ38+ζ43+ζ46−ζ47+ζ58−ζ590000000000000000000000000
χ614-44-4-24-422-24-44-4-2244-4-4000-24-422-24-422-2-20000-2200000000-22000000000000000000000000000000000
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χ728888-4-8-8-4-4-4-2-2-2-24400000001221110000000025−25-1-1−55−55000000000000000000000000000000000000000
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χ758-88-888-8-8-88-22-228-80000000-2-2222-20000000000-220000000000000000000000000000000000000000000
χ768-88-88-88-8-88-22-22-880000000-22-222-200000000002-20000000000000000000000000000000000000000000
χ778-88-8-48-844-4-22-22-4400000001-22-1-1100000000001-1−i15i15i15−i15000000000000000000000000000000000000000
χ788-88-8-48-844-4-22-22-4400000001-22-1-1100000000001-1i15−i15−i15i15000000000000000000000000000000000000000
χ798-88-8-4-8844-4-22-224-400000−4i34i312-2-1-110000000000-11i3i3−i3−i3000000000000000000000000000000000000000
χ808-88-8-4-8844-4-22-224-4000004i3−4i312-2-1-110000000000-11−i3−i3i3i3000000000000000000000000000000000000000
χ818-8-88800-88-8-2-222000000000-2002-220000000000000000000000000000000−25250000000000000000000000
χ828-8-88800-88-8-2-222000000000-2002-22000000000000000000000000000000025−250000000000000000000000
χ831616-16-16-800-888-444-40000000002002-2-20000000000000000000000000000000000000000000000000000000
χ8416-16-1616-8008-88-4-444000000000200-22-20000000000000000000000000000000000000000000000000000000

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