Finite Group Databasebeta

← Group #14298570

Character table — Group #14298570

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11112222224444444455556688888888888810101010101012121212121212161616161616202020202020202020202020202020202424242424243030404040404040404060606060606060120120
order122234466644510101012124444441212152020202020203030302212121212244202020206060606060604444446612121212121212121010202020202288121224242424444444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1111-1-1-1-1-1-1
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
χ41111111111111111111111-1-1111111111111111111-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1111111
χ5111111111111111111-1-1-1-111111111111111-1-1-1-1-1-11111111111111-1-1ii−i−i-1-1iiii−i−i−i−i111111-1-1i−i-1-1ii−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−ii-1-1−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-1-1-1-1-1-111i−i-1-1ii−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−ii-1-1−i−iii111ii−i−ii−i
χ91111111111-1-1111111111111-1-11-1-1-1-1111111111111-1-1111111-1-1-1-1-1-11111111111111111-1-1-1-111-1-1-1-1-1-1-1-11-1-11111-1-1
χ101111111111-1-1111111111111-1-11-1-1-1-1111111111111-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-111111-1-1-1-1-1-111
χ111111111111-1-11111111111-1-1-1-11-1-1-1-111111111111-111-1-1-1-111-1-1-1-1-1-111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111
χ121111111111-1-11111111111-1-1-1-11-1-1-1-111111111111-111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-111-1-11111-1111111-1-1
χ131111111111-1-1111111-1-1-1-111-1-11-1-1-1-111111-1-1-1-1-1-11-1-1111111-1-1-1-111ii−i−i-1-1iiii−i−i−i−i11-1-1-1-1-1-1−ii11−i−iii-111ii−i−i−ii
χ141111111111-1-1111111-1-1-1-111-1-11-1-1-1-111111-1-1-1-1-1-11-1-1111111-1-1-1-111−i−iii-1-1−i−i−i−iiiii11-1-1-1-1-1-1i−i11ii−i−i-111−i−iiii−i
χ151111111111-1-1111111-1-1-1-1-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111ii−i−i-1-1iiii−i−i−i−i-1-1111111−ii11−i−iii1-1-1−i−iiii−i
χ161111111111-1-1111111-1-1-1-1-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111−i−iii-1-1−i−i−i−iiiii-1-1111111i−i11ii−i−i1-1-1ii−i−i−ii
χ1722222-2-2222002222-2-22222220020000-2-2222-2-22222-2002222-2-20000000000-2-200000000-2-200002200000000-200000000
χ1822222-2-2222002222-2-22222-2-20020000-2-2222-2-22222200-2-2-2-2-2-20000000000-2-200000000220000-2-200000000200000000
χ1922222-2-2222002222-2-2-2-2-2-2220020000-2-222222-2-2-2-2-2002222-2-200000000002200000000-2-20000-2-200000000200000000
χ2022222-2-2222002222-2-2-2-2-2-2-2-20020000-2-222222-2-2-2-2200-2-2-2-2-2-2000000000022000000002200002200000000-200000000
χ212222-122-1-1-1222222-1-1222200-1-1-1222222-1-1-122-1-1-1-10000000-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-10000000022-1-1-1-1-1-1000000000
χ222222-122-1-1-1222222-1-1222200-1-1-1222222-1-1-122-1-1-1-10000000-1-1-1-1-1-122-2-2-2-2-1-11111111100000000-2-2-1-11111000000000
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−iiiii000000002i−2i11−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−i00000000−2i2i11ii−i−i000000000
χ252222-122-1-1-1-2-22222-1-122220011-1-2-2-2-222-1-1-122-1-1-1-10000000-1-11111-2-22222-1-1-1-1-1-1-1-1-1-100000000-2-2111111000000000
χ262222-122-1-1-1-2-22222-1-122220011-1-2-2-2-222-1-1-122-1-1-1-10000000-1-11111-2-2-2-2-2-2-1-111111111000000002211-1-1-1-1000000000
χ272222-122-1-1-1-2-22222-1-1-2-2-2-20011-1-2-2-2-222-1-1-1-2-211110000000-1-11111222i2i−2i−2i11−i−i−i−iiiii00000000−2i2i-1-1ii−i−i000000000
χ282222-122-1-1-1-2-22222-1-1-2-2-2-20011-1-2-2-2-222-1-1-1-2-211110000000-1-1111122−2i−2i2i2i11iiii−i−i−i−i000000002i−2i-1-1−i−iii000000000
χ292-22-222-2-22-2002-22-22-222-2-20000200002-2-22-22-2-2-22202i−2i00002-20000000000-2200000000002i2i−2i−2i000000000002i−2i000000
χ302-22-222-2-22-2002-22-22-222-2-20000200002-2-22-22-2-2-2220−2i2i00002-20000000000-220000000000−2i−2i2i2i00000000000−2i2i000000
χ312-22-222-2-22-2002-22-22-2-2-2220000200002-2-22-2-2222-2-202i−2i00002-200000000002-200000000002i2i−2i−2i00000000000−2i2i000000
χ322-22-222-2-22-2002-22-22-2-2-2220000200002-2-22-2-2222-2-20−2i2i00002-200000000002-20000000000−2i−2i2i2i000000000002i−2i000000
χ332-22-22-22-22-22i−2i2-22-2-2222-2-2002i−2i22i2i−2i−2i-22-22-2-22-2-2220000000-222i2i−2i−2i2i−2i00002-20000000000000000002i−2i0000000000000
χ342-22-22-22-22-22i−2i2-22-2-22-2-222002i−2i22i2i−2i−2i-22-22-22-222-2-20000000-222i2i−2i−2i−2i2i0000-22000000000000000000−2i2i0000000000000
χ352-22-22-22-22-2−2i2i2-22-2-2222-2-200−2i2i2−2i−2i2i2i-22-22-2-22-2-2220000000-22−2i−2i2i2i−2i2i00002-2000000000000000000−2i2i0000000000000
χ362-22-22-22-22-2−2i2i2-22-2-22-2-22200−2i2i2−2i−2i2i2i-22-22-22-222-2-20000000-22−2i−2i2i2i2i−2i0000-220000000000000000002i−2i0000000000000
χ372-22-2-1-221-112i−2i2-22-21-122-2-200−ii-12i2i−2i−2i-221-11-2211-1-100000001-1−i−iii2i−2i0000-1133−3−333−3−30000000000−ii−i3i3−i3i3000000000
χ382-22-2-1-221-112i−2i2-22-21-122-2-200−ii-12i2i−2i−2i-221-11-2211-1-100000001-1−i−iii2i−2i0000-11−3−333−3−3330000000000−iii3−i3i3−i3000000000
χ392-22-2-1-221-112i−2i2-22-21-1-2-22200−ii-12i2i−2i−2i-221-112-2-1-11100000001-1−i−iii−2i2i00001-1−i3−i3i3i3i3i3−i3−i30000000000i−i−333−3000000000
χ402-22-2-1-221-112i−2i2-22-21-1-2-22200−ii-12i2i−2i−2i-221-112-2-1-11100000001-1−i−iii−2i2i00001-1i3i3−i3−i3−i3−i3i3i30000000000i−i3−3−33000000000
χ412-22-2-1-221-11−2i2i2-22-21-122-2-200i−i-1−2i−2i2i2i-221-11-2211-1-100000001-1ii−i−i−2i2i0000-1133−3−333−3−30000000000i−ii3−i3i3−i3000000000
χ422-22-2-1-221-11−2i2i2-22-21-122-2-200i−i-1−2i−2i2i2i-221-11-2211-1-100000001-1ii−i−i−2i2i0000-11−3−333−3−3330000000000i−i−i3i3−i3i3000000000
χ432-22-2-1-221-11−2i2i2-22-21-1-2-22200i−i-1−2i−2i2i2i-221-112-2-1-11100000001-1ii−i−i2i−2i00001-1−i3−i3i3i3i3i3−i3−i30000000000−ii3−3−33000000000
χ442-22-2-1-221-11−2i2i2-22-21-1-2-22200i−i-1−2i−2i2i2i-221-112-2-1-11100000001-1ii−i−i2i−2i00001-1i3i3−i3−i3−i3−i3i3i30000000000−ii−333−3000000000
χ452-2-222002-2-20022-2-2002i−2i2i−2i2i−2i002000000-2-22002i−2i2i−2i0002i2i−2i−2i000000001+i−1−i1−i−1+i001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000002-2000000000001−i−1+i1+i−1−i00
χ462-2-222002-2-20022-2-2002i−2i2i−2i2i−2i002000000-2-22002i−2i2i−2i0002i2i−2i−2i00000000−1−i1+i−1+i1−i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000002-200000000000−1+i1−i−1−i1+i00
χ472-2-222002-2-20022-2-2002i−2i2i−2i−2i2i002000000-2-22002i−2i2i−2i000−2i−2i2i2i000000001+i−1−i1−i−1+i001+i−1−i1+i−1−i1−i−1+i1−i−1+i000000-2200000000000−1+i1−i−1−i1+i00
χ482-2-222002-2-20022-2-2002i−2i2i−2i−2i2i002000000-2-22002i−2i2i−2i000−2i−2i2i2i00000000−1−i1+i−1+i1−i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000-22000000000001−i−1+i1+i−1−i00
χ492-2-222002-2-20022-2-200−2i2i−2i2i2i−2i002000000-2-2200−2i2i−2i2i0002i2i−2i−2i000000001−i−1+i1+i−1−i001−i−1+i1−i−1+i1+i−1−i1+i−1−i000000-2200000000000−1−i1+i−1+i1−i00
χ502-2-222002-2-20022-2-200−2i2i−2i2i2i−2i002000000-2-2200−2i2i−2i2i0002i2i−2i−2i00000000−1+i1−i−1−i1+i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000-22000000000001+i−1−i1−i−1+i00
χ512-2-222002-2-20022-2-200−2i2i−2i2i−2i2i002000000-2-2200−2i2i−2i2i000−2i−2i2i2i000000001−i−1+i1+i−1−i001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000002-2000000000001+i−1−i1−i−1+i00
χ522-2-222002-2-20022-2-200−2i2i−2i2i−2i2i002000000-2-2200−2i2i−2i2i000−2i−2i2i2i00000000−1+i1−i−1−i1+i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000002-200000000000−1−i1+i−1+i1−i00
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
χ554444444444-4-4-1-1-1-144000044-4-4-11111-1-1-1-1-10000004-4-4-1-1-1-1-1-111110000000000000000-1-111110000000000000000000
χ564444444444-4-4-1-1-1-1440000-4-4-4-4-11111-1-1-1-1-1000000-4441111-1-11111000000000000000011-1-1-1-10000000000000000000
χ5744444-4-444400-1-1-1-1-4-400004400-1−55−5511-1-1-1000000-400-1-1-1-111−55−55000000000000000011−55−550000000000000000000
χ5844444-4-444400-1-1-1-1-4-400004400-15−55−511-1-1-1000000-400-1-1-1-1115−55−50000000000000000115−55−50000000000000000000
χ5944444-4-444400-1-1-1-1-4-40000-4-400-1−55−5511-1-1-1000000400111111−55−550000000000000000-1-15−55−50000000000000000000
χ6044444-4-444400-1-1-1-1-4-40000-4-400-15−55−511-1-1-10000004001111115−55−50000000000000000-1-1−55−550000000000000000000
χ614444-2-4-4-2-2-20044442244440000-20000-4-4-2-2-2-4-4-2-2-2-2000000022000000000022000000000000000000000000000000000
χ624444-2-4-4-2-2-200444422-4-4-4-40000-20000-4-4-2-2-24422220000000220000000000-2-2000000000000000000000000000000000
χ6344-4-4400-4-44004-4-44004i−4i−4i4i000040000004-4-400−4i4i4i−4i000000000000000000000000000000000000000000000000000000
χ6444-4-4400-4-44004-4-4400−4i4i4i−4i000040000004-4-4004i−4i−4i4i000000000000000000000000000000000000000000000000000000
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χ6844-4-4-20022-2004-4-4400−4i4i4i−4i0000-2000000-22200−2i2i2i−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−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
χ694-44-444-4-44-400-11-114-400000000-1−i5i5i5−i5-111-1100000004i−4i−55−55-11−i5i5i5−i50000000000000000−55−i−iii0000000000000000000
χ704-44-444-4-44-400-11-114-400000000-1−i5i5i5−i5-111-110000000−4i4i5−55−5-11−i5i5i5−i500000000000000005−5ii−i−i0000000000000000000
χ714-44-444-4-44-400-11-114-400000000-1i5−i5−i5i5-111-1100000004i−4i5−55−5-11i5−i5−i5i500000000000000005−5−i−iii0000000000000000000
χ724-44-444-4-44-400-11-114-400000000-1i5−i5−i5i5-111-110000000−4i4i−55−55-11i5−i5−i5i50000000000000000−55ii−i−i0000000000000000000
χ734-44-44-44-44-44i−4i-11-11-440000004i−4i-1−i−iii1-11-11000000000−55−551-1−i−iii00000000000000005−5−i5i5i5−i50000000000000000000
χ744-44-44-44-44-44i−4i-11-11-440000004i−4i-1−i−iii1-11-110000000005−55−51-1−i−iii0000000000000000−55i5−i5−i5i50000000000000000000
χ754-44-44-44-44-4−4i4i-11-11-44000000−4i4i-1ii−i−i1-11-11000000000−55−551-1ii−i−i00000000000000005−5i5−i5−i5i50000000000000000000
χ764-44-44-44-44-4−4i4i-11-11-44000000−4i4i-1ii−i−i1-11-110000000005−55−51-1ii−i−i0000000000000000−55−i5i5i5−i50000000000000000000
χ774-44-4-24-42-22004-44-4-2244-4-40000-200004-42-224-422-2-20000000-2200000000002-2000000000000000000000000000000000
χ784-44-4-24-42-22004-44-4-22-4-4440000-200004-42-22-44-2-2220000000-220000000000-22000000000000000000000000000000000
χ794-4-44-200-2220044-4-4004i−4i4i−4i0000-200000022-200−2i2i−2i2i0000000000000002+2i−2−2i2−2i−2+2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000000000000
χ804-4-44-200-2220044-4-4004i−4i4i−4i0000-200000022-200−2i2i−2i2i000000000000000−2−2i2+2i−2+2i2−2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000000000000
χ814-4-44-200-2220044-4-400−4i4i−4i4i0000-200000022-2002i−2i2i−2i0000000000000002−2i−2+2i2+2i−2−2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000000000000
χ824-4-44-200-2220044-4-400−4i4i−4i4i0000-200000022-2002i−2i2i−2i000000000000000−2+2i2−2i−2−2i2+2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000000000000
χ838888-488-4-4-488-2-2-2-2-4-4000000-4-41-2-2-2-2-2-2111000000000000011111100000000000000000000000000000000000000000
χ848888-488-4-4-4-8-8-2-2-2-2-4-40000004412222-2-2111000000000000011-1-1-1-100000000000000000000000000000000000000000
χ858888-4-8-8-4-4-400-2-2-2-244000000001−2525−2525221110000000000000-1-15−55−500000000000000000000000000000000000000000
χ868888-4-8-8-4-4-400-2-2-2-24400000000125−2525−25221110000000000000-1-1−55−5500000000000000000000000000000000000000000
χ8788-8-8800-8-8800-222-20000000000-2000000-222000000000−2i52i52i5−2i500000000000000000000000000000000000000000000000
χ8888-8-8800-8-8800-222-20000000000-2000000-2220000000002i5−2i5−2i52i500000000000000000000000000000000000000000000000
χ898-88-8-48-84-4400-22-22-44000000001−2i52i52i5−2i5-22-11-100000000000001-1i5−i5−i5i500000000000000000000000000000000000000000
χ908-88-8-48-84-4400-22-22-440000000012i5−2i5−2i52i5-22-11-100000000000001-1−i5i5i5−i500000000000000000000000000000000000000000
χ918-88-8-4-884-448i−8i-22-224-4000000−4i4i1−2i−2i2i2i2-2-11-10000000000000-11ii−i−i00000000000000000000000000000000000000000
χ928-88-8-4-884-44−8i8i-22-224-40000004i−4i12i2i−2i−2i2-2-11-10000000000000-11−i−iii00000000000000000000000000000000000000000
χ938-8-888008-8-800-2-2220000008i−8i00-200000022-2000000000−2i−2i2i2i00000000000000000000000000000000000000000000000
χ948-8-888008-8-800-2-222000000−8i8i00-200000022-20000000002i2i−2i−2i00000000000000000000000000000000000000000000000
χ951616-16-16-80088-800-444-4000000000020000002-2-2000000000000000000000000000000000000000000000000000000000000
χ9616-16-1616-800-88800-4-44400000000002000000-2-22000000000000000000000000000000000000000000000000000000000000

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