Finite Group Databasebeta

← Group #72230996

Character table — Group #72230996

Order 2400.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size1122244444444444446688888888888888888888888888888824242424242424242424242425255050505050505075757575100100100100100150150150150
order123465555551010101010101222151515151515202020202020303030303030606060606060606060606060101010101010101010101010224444466444412121212122244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-11-1-1-1-111-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1ii−i−i-1-1ii−i−i-1ii−i−i-1-1i−i
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1−i−iii-1-1−i−iii-1−i−iii-1-1−ii
χ5111111111111111111-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-111111-1-1-1-1
χ6111111111111111111-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-11111111-1-1-1-1-1-111
χ7111111111111111111-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i-1-1−i−iii-1ii−i−i11−ii
χ8111111111111111111-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii-1-1ii−i−i-1−i−iii11i−i
χ9111-11111111111111-11-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-11-11-1111111-11-11-11-1-1-1
χ10111-11111111111111-11-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-11-1111-1-1-1-1-1-11-111-111
χ11111-11111111111111-11-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11i−i−ii-1-1ii−i−i1i−i−ii-11−ii
χ12111-11111111111111-11-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11−iii−i-1-1−i−iii1−iii−i-11i−i
χ13111-11111111111111-1-11111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-11-111-1-1-1-1-11-11-1-1111
χ14111-11111111111111-1-11111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11-11111111-1-11-11-11-1-1
χ15111-11111111111111-1-11111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11i−i−ii-1-1−i−iii1i−i−ii1-1i−i
χ16111-11111111111111-1-11111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11−iii−i-1-1ii−i−i1−iii−i1-1−ii
χ1722-12-1222222222222-100-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000002222222-1-10000-1-1-1-1-10000
χ1822-12-1222222222222-100-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000222-2-2-2-2-1-10000-111110000
χ1922-12-1222222222222-100-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000-2-2-22i2i−2i−2i1100001−i−iii0000
χ2022-12-1222222222222-100-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000-2-2-2−2i−2i2i2i1100001ii−i−i0000
χ2122-1-2-1222222222222100-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1-1-1-111111111111100000000000022-22-22-2-1-100001-11-110000
χ2222-1-2-1222222222222100-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1-1-1-111111111111100000000000022-2-22-22-1-1000011-11-10000
χ2322-1-2-1222222222222100-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1-1-1-1111111111111000000000000-2-222i−2i−2i2i110000-1−iii−i0000
χ2422-1-2-1222222222222100-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1-1-1-1111111111111000000000000-2-22−2i2i2i−2i110000-1i−i−ii0000
χ252-220-2222222-2-2-2-2-2-2000222222000000-2-2-2-2-2-20000000000000000000000002-2000002-22i−2i2i−2i000000000
χ262-220-2222222-2-2-2-2-2-2000222222000000-2-2-2-2-2-20000000000000000000000002-2000002-2−2i2i−2i2i000000000
χ272-220-2222222-2-2-2-2-2-2000222222000000-2-2-2-2-2-2000000000000000000000000-2200000-222-2-22000000000
χ282-220-2222222-2-2-2-2-2-2000222222000000-2-2-2-2-2-2000000000000000000000000-2200000-22-222-2000000000
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χ3144444-14-1-1-1-1-14-1-1-1-1444-14-1-1-1-1-14-1-1-1-1-14-1-1-1-1-1-144-1-1-1-1-1-1-1-1-14-1-1-1-1-14-1-1-1-10000000000000000000000
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χ3444444-1-1−1−53+523−52−1+5-1-1−1−53+523−52−1+54-4-4-1-1−1−53+523−52−1+5-1-1−1−53+523−52−1+5-1-1−1−53+523−52−1+5-1-1-1-1−1−5−1−53+523+523−523−52−1+5−1+5111+5−3−52−3+521−5111+5−3−52−3+521−50000000000000000000000
χ3544444-1-13+52−1+5−1−53−52-1-13+52−1+5−1−53−52444-1-13+52−1+5−1−53−52-1-13+52−1+5−1−53−52-1-13+52−1+5−1−53−52-1-1-1-13+523+52−1+5−1+5−1−5−1−53−523−52-1-13+52−1+5−1−53−52-1-13+52−1+5−1−53−520000000000000000000000
χ3644444-1-13+52−1+5−1−53−52-1-13+52−1+5−1−53−524-4-4-1-13+52−1+5−1−53−52-1-13+52−1+5−1−53−52-1-13+52−1+5−1−53−52-1-1-1-13+523+52−1+5−1+5−1−5−1−53−523−5211−3−521−51+5−3+5211−3−521−51+5−3+520000000000000000000000
χ3744444-1-13−52−1−5−1+53+52-1-13−52−1−5−1+53+52444-1-13−52−1−5−1+53+52-1-13−52−1−5−1+53+52-1-13−52−1−5−1+53+52-1-1-1-13−523−52−1−5−1−5−1+5−1+53+523+52-1-13−52−1−5−1+53+52-1-13−52−1−5−1+53+520000000000000000000000
χ3844444-1-13−52−1−5−1+53+52-1-13−52−1−5−1+53+524-4-4-1-13−52−1−5−1+53+52-1-13−52−1−5−1+53+52-1-13−52−1−5−1+53+52-1-1-1-13−523−52−1−5−1−5−1+5−1+53+523+5211−3+521+51−5−3−5211−3+521+51−5−3−520000000000000000000000
χ3944444-1-1−1+53−523+52−1−5-1-1−1+53−523+52−1−5444-1-1−1+53−523+52−1−5-1-1−1+53−523+52−1−5-1-1−1+53−523+52−1−5-1-1-1-1−1+5−1+53−523−523+523+52−1−5−1−5-1-1−1+53−523+52−1−5-1-1−1+53−523+52−1−50000000000000000000000
χ4044444-1-1−1+53−523+52−1−5-1-1−1+53−523+52−1−54-4-4-1-1−1+53−523+52−1−5-1-1−1+53−523+52−1−5-1-1−1+53−523+52−1−5-1-1-1-1−1+5−1+53−523−523+523+52−1−5−1−5111−5−3+52−3−521+5111−5−3+52−3−521+50000000000000000000000
χ41444-444-1-1-1-1-14-1-1-1-1-1-44-44-1-1-1-1-1-4111114-1-1-1-1-1-4-411111111114-1-1-1-1-1-4111110000000000000000000000
χ42444-444-1-1-1-1-14-1-1-1-1-1-4-444-1-1-1-1-1-4111114-1-1-1-1-1-4-41111111111-4111114-1-1-1-1-10000000000000000000000
χ43444-44-14-1-1-1-1-14-1-1-1-1-44-4-14-1-1-1-11-41111-14-1-1-1-111-4-411111111-14-1-1-1-11-411110000000000000000000000
χ44444-44-14-1-1-1-1-14-1-1-1-1-4-44-14-1-1-1-11-41111-14-1-1-1-111-4-4111111111-41111-14-1-1-1-10000000000000000000000
χ45444-44-1-1−1−53+523−52−1+5-1-1−1−53+523−52−1+5-44-4-1-1−1−53+523−52−1+5111+5−3−52−3+521−5-1-1−1−53+523−52−1+511111+51+5−3−52−3−52−3+52−3+521−51−5-1-1−1−53+523−52−1+5111+5−3−52−3+521−50000000000000000000000
χ46444-44-1-1−1−53+523−52−1+5-1-1−1−53+523−52−1+5-4-44-1-1−1−53+523−52−1+5111+5−3−52−3+521−5-1-1−1−53+523−52−1+511111+51+5−3−52−3−52−3+52−3+521−51−5111+5−3−52−3+521−5-1-1−1−53+523−52−1+50000000000000000000000
χ47444-44-1-13+52−1+5−1−53−52-1-13+52−1+5−1−53−52-44-4-1-13+52−1+5−1−53−5211−3−521−51+5−3+52-1-13+52−1+5−1−53−521111−3−52−3−521−51−51+51+5−3+52−3+52-1-13+52−1+5−1−53−5211−3−521−51+5−3+520000000000000000000000
χ48444-44-1-13+52−1+5−1−53−52-1-13+52−1+5−1−53−52-4-44-1-13+52−1+5−1−53−5211−3−521−51+5−3+52-1-13+52−1+5−1−53−521111−3−52−3−521−51−51+51+5−3+52−3+5211−3−521−51+5−3+52-1-13+52−1+5−1−53−520000000000000000000000
χ49444-44-1-13−52−1−5−1+53+52-1-13−52−1−5−1+53+52-44-4-1-13−52−1−5−1+53+5211−3+521+51−5−3−52-1-13−52−1−5−1+53+521111−3+52−3+521+51+51−51−5−3−52−3−52-1-13−52−1−5−1+53+5211−3+521+51−5−3−520000000000000000000000
χ50444-44-1-13−52−1−5−1+53+52-1-13−52−1−5−1+53+52-4-44-1-13−52−1−5−1+53+5211−3+521+51−5−3−52-1-13−52−1−5−1+53+521111−3+52−3+521+51+51−51−5−3−52−3−5211−3+521+51−5−3−52-1-13−52−1−5−1+53+520000000000000000000000
χ51444-44-1-1−1+53−523+52−1−5-1-1−1+53−523+52−1−5-44-4-1-1−1+53−523+52−1−5111−5−3+52−3−521+5-1-1−1+53−523+52−1−511111−51−5−3+52−3+52−3−52−3−521+51+5-1-1−1+53−523+52−1−5111−5−3+52−3−521+50000000000000000000000
χ52444-44-1-1−1+53−523+52−1−5-1-1−1+53−523+52−1−5-4-44-1-1−1+53−523+52−1−5111−5−3+52−3−521+5-1-1−1+53−523+52−1−511111−51−5−3+52−3+52−3−52−3−521+51+5111−5−3+52−3−521+5-1-1−1+53−523+52−1−50000000000000000000000
χ534-4-202444444-4-4-4-4-4-4000-2-2-2-2-2-20000002222220000000000000000000000004-400000-220000000000000
χ544-4-202444444-4-4-4-4-4-4000-2-2-2-2-2-2000000222222000000000000000000000000-44000002-20000000000000
χ5588-48-48-2-2-2-2-28-2-2-2-2-2-400-4111118-2-2-2-2-2-411111-4-411111111110000000000000000000000000000000000
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χ5888-48-4-2-23+5−2+25−2−253−5-2-23+5−2+25−2−253−5-40011−3−521−51+5−3+52-2-23+5−2+25−2−253−511−3−521−51+5−3+521111−3−52−3−521−51−51+51+5−3+52−3+520000000000000000000000000000000000
χ5988-48-4-2-23−5−2−25−2+253+5-2-23−5−2−25−2+253+5-40011−3+521+51−5−3−52-2-23−5−2−25−2+253+511−3+521+51−5−3−521111−3+52−3+521+51+51−51−5−3−52−3−520000000000000000000000000000000000
χ6088-48-4-2-2−2+253−53+5−2−25-2-2−2+253−53+5−2−25-400111−5−3+52−3−521+5-2-2−2+253−53+5−2−25111−5−3+52−3−521+511111−51−5−3+52−3+52−3−52−3−521+51+50000000000000000000000000000000000
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χ6488-4-8-4-2-23+5−2+25−2−253−5-2-23+5−2+25−2−253−540011−3−521−51+5−3+5222−3−52−252+25−3+511−3−521−51+5−3+52-1-1-1-13+523+52−1+5−1+5−1−5−1−53−523−520000000000000000000000000000000000
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χ808-8-404-2-23+5−2+25−2−253−522−3−52−252+25−3+500011−3−521−51+5−3+52000000-1-13+52−1+5−1−53−5215−1515−15−3ζ7+2ζ11−2ζ19+3ζ23−2ζ31−3ζ43+3ζ47+2ζ593ζ7−2ζ11+2ζ19−3ζ23+2ζ31+3ζ43−3ζ47−2ζ5900002ζ7−3ζ11+3ζ19−2ζ23+3ζ31+2ζ43−2ζ47−3ζ59−2ζ7+3ζ11−3ζ19+2ζ23−3ζ31−2ζ43+2ζ47+3ζ590000000000000000000000000000000000
χ818-8-404-2-23−5−2−25−2+253+522−3+52+252−25−3−500011−3+521+51−5−3−52000000-1-13−52−1−5−1+53+52−1515−1515−2ζ7+3ζ11−3ζ19+2ζ23−3ζ31−2ζ43+2ζ47+3ζ592ζ7−3ζ11+3ζ19−2ζ23+3ζ31+2ζ43−2ζ47−3ζ5900003ζ7−2ζ11+2ζ19−3ζ23+2ζ31+3ζ43−3ζ47−2ζ59−3ζ7+2ζ11−2ζ19+3ζ23−2ζ31−3ζ43+3ζ47+2ζ590000000000000000000000000000000000
χ828-8-404-2-23−5−2−25−2+253+522−3+52+252−25−3−500011−3+521+51−5−3−52000000-1-13−52−1−5−1+53+5215−1515−152ζ7−3ζ11+3ζ19−2ζ23+3ζ31+2ζ43−2ζ47−3ζ59−2ζ7+3ζ11−3ζ19+2ζ23−3ζ31−2ζ43+2ζ47+3ζ590000−3ζ7+2ζ11−2ζ19+3ζ23−2ζ31−3ζ43+3ζ47+2ζ593ζ7−2ζ11+2ζ19−3ζ23+2ζ31+3ζ43−3ζ47−2ζ590000000000000000000000000000000000
χ838-8-404-2-2−2+253−53+5−2−25222−25−3+5−3−52+25000111−5−3+52−3−521+5000000-1-1−1+53−523+52−1−5−151515−15002ζ7−3ζ11+3ζ19−2ζ23+3ζ31+2ζ43−2ζ47−3ζ59−2ζ7+3ζ11−3ζ19+2ζ23−3ζ31−2ζ43+2ζ47+3ζ59−3ζ7+2ζ11−2ζ19+3ζ23−2ζ31−3ζ43+3ζ47+2ζ593ζ7−2ζ11+2ζ19−3ζ23+2ζ31+3ζ43−3ζ47−2ζ59000000000000000000000000000000000000
χ848-8-404-2-2−2+253−53+5−2−25222−25−3+5−3−52+25000111−5−3+52−3−521+5000000-1-1−1+53−523+52−1−515−15−151500−2ζ7+3ζ11−3ζ19+2ζ23−3ζ31−2ζ43+2ζ47+3ζ592ζ7−3ζ11+3ζ19−2ζ23+3ζ31+2ζ43−2ζ47−3ζ593ζ7−2ζ11+2ζ19−3ζ23+2ζ31+3ζ43−3ζ47−2ζ59−3ζ7+2ζ11−2ζ19+3ζ23−2ζ31−3ζ43+3ζ47+2ζ59000000000000000000000000000000000000

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