Finite Group Databasebeta

← Group #14300574

Character table — Group #14300574

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size111122222244444455556688888888810101010101012161616161616161620202020202020202020202020202020202024242424243030404040404040404848606060606060606060120
order1222344666510101012124444222661520203030302212121212410103030303060604444668888121212121212121241010202044412122424242420202444488884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111-1-1-1-1-1-1-1-11
χ31111111111111111111111-1-1-11111111111111-1-1-1-1-1-111111111-1-1-1-111111111-1111111-1-1-1-1-1-1-1-1-111111-1-1-1-1-1
χ41111111111111111111111-1-1-11111111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1111111-1-1-11111-1-11-1-1-1-11111-1
χ511111111111111111111-1-1111111111111111-111111111111111111111111111-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1
χ611111111111111111111-1-1111111111111111-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-111111111-1
χ711111111111111111111-1-1-1-1-1111111111111-1-1-1-1-1-1-111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111111
χ811111111111111111111-1-1-1-1-1111111111111-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1111111-11111-1-1-1-11
χ91111111111111111-1-1-1-111111111111-1-1-1-1-1-1111111111ii−i−i-1-1ii−i−iiiii−i−i−i−i11111-1-1-1-1-1ii−i−i11-1ii−i−iii−i−i-1
χ101111111111111111-1-1-1-111111111111-1-1-1-1-1-1111111111−i−iii-1-1−i−iii−i−i−i−iiiii11111-1-1-1-1-1−i−iii11-1−i−iii−i−iii-1
χ111111111111111111-1-1-1-111-1-1-1111111-1-1-1-1-1-11-1-1-1-1-1-111ii−i−i-1-1−i−iiiiiii−i−i−i−i-11111-1-1111−i−iii-1-1-1ii−i−i−i−iii1
χ121111111111111111-1-1-1-111-1-1-1111111-1-1-1-1-1-11-1-1-1-1-1-111−i−iii-1-1ii−i−i−i−i−i−iiiii-11111-1-1111ii−i−i-1-1-1−i−iiiii−i−i1
χ131111111111111111-1-1-1-1-1-1111111111-1-1-1-1-1-1-111111111ii−i−i-1-1ii−i−iiiii−i−i−i−i-1-1-1-1-111-1-1-1ii−i−i-1-11−i−iii−i−iii1
χ141111111111111111-1-1-1-1-1-1111111111-1-1-1-1-1-1-111111111−i−iii-1-1−i−iii−i−i−i−iiiii-1-1-1-1-111-1-1-1−i−iii-1-11ii−i−iii−i−i1
χ151111111111111111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-111ii−i−i-1-1−i−iiiiiii−i−i−i−i1-1-1-1-111111−i−iii111−i−iiiii−i−i-1
χ161111111111111111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-111−i−iii-1-1ii−i−i−i−i−i−iiiii1-1-1-1-111111ii−i−i111ii−i−i−i−iii-1
χ1722222-2-22222222-2-22222220002-2-2222-2-22222-2000000-2-20000-2-2000000000000022-2-222000000000-2000000000
χ1822222-2-22222222-2-22222-2-20002-2-2222-2-222222000000-2-20000-2-20000000000000-2-222-2-20000000002000000000
χ1922222-2-22222222-2-2-2-2-2-2220002-2-222222-2-2-2-2-2000000-2-2000022000000000000022-2-2-2-20000000002000000000
χ2022222-2-22222222-2-2-2-2-2-2-2-20002-2-222222-2-2-2-22000000-2-20000220000000000000-2-22222000000000-2000000000
χ212222-122-1-1-12222-1-12222002-1-1-122-1-1-122-1-1-1-1022-1-1-1-1-1-12222-1-12222-1-1-1-1-1-1-1-100000002-1-1-1-1-1-1000000000000
χ222222-122-1-1-12222-1-12222002-1-1-122-1-1-122-1-1-1-1022-1-1-1-1-1-1-2-2-2-2-1-1-2-2-2-21111111100000002-1-11111000000000000
χ232222-122-1-1-12222-1-1222200-211-122-1-1-122-1-1-1-10-2-21111-1-12222-1-1-2-2-2-2-1-1-1-1-1-1-1-10000000-2111111000000000000
χ242222-122-1-1-12222-1-1222200-211-122-1-1-122-1-1-1-10-2-21111-1-1-2-2-2-2-1-12222111111110000000-211-1-1-1-1000000000000
χ252222-122-1-1-12222-1-1-2-2-2-2002-1-1-122-1-1-1-2-21111022-1-1-1-1-1-12i2i−2i−2i112i2i−2i−2i−i−i−i−iiiii0000000-211−i−iii000000000000
χ262222-122-1-1-12222-1-1-2-2-2-2002-1-1-122-1-1-1-2-21111022-1-1-1-1-1-1−2i−2i2i2i11−2i−2i2i2iiiii−i−i−i−i0000000-211ii−i−i000000000000
χ272222-122-1-1-12222-1-1-2-2-2-200-211-122-1-1-1-2-211110-2-21111-1-12i2i−2i−2i11−2i−2i2i2i−i−i−i−iiiii00000002-1-1ii−i−i000000000000
χ282222-122-1-1-12222-1-1-2-2-2-200-211-122-1-1-1-2-211110-2-21111-1-1−2i−2i2i2i112i2i−2i−2iiiii−i−i−i−i00000002-1-1−i−iii000000000000
χ2922-2-22002-2-22-2-22002i−2i2i−2i2-20002002-2-2002i−2i2i−2i0000000001+i−1−i1−i−1+i0000001+i1+i−1−i−1−i1−i1−i−1+i−1+i02-2002i−2i00000000001+i−1−i1−i−1+i00000
χ3022-2-22002-2-22-2-22002i−2i2i−2i2-20002002-2-2002i−2i2i−2i000000000−1−i1+i−1+i1−i000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i02-2002i−2i0000000000−1−i1+i−1+i1−i00000
χ3122-2-22002-2-22-2-22002i−2i2i−2i-220002002-2-2002i−2i2i−2i0000000001+i−1−i1−i−1+i0000001+i1+i−1−i−1−i1−i1−i−1+i−1+i0-2200−2i2i0000000000−1−i1+i−1+i1−i00000
χ3222-2-22002-2-22-2-22002i−2i2i−2i-220002002-2-2002i−2i2i−2i000000000−1−i1+i−1+i1−i000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i0-2200−2i2i00000000001+i−1−i1−i−1+i00000
χ3322-2-22002-2-22-2-2200−2i2i−2i2i2-20002002-2-200−2i2i−2i2i0000000001−i−1+i1+i−1−i0000001−i1−i−1+i−1+i1+i1+i−1−i−1−i02-200−2i2i00000000001−i−1+i1+i−1−i00000
χ3422-2-22002-2-22-2-2200−2i2i−2i2i2-20002002-2-200−2i2i−2i2i000000000−1+i1−i−1−i1+i000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i02-200−2i2i0000000000−1+i1−i−1−i1+i00000
χ3522-2-22002-2-22-2-2200−2i2i−2i2i-220002002-2-200−2i2i−2i2i0000000001−i−1+i1+i−1−i0000001−i1−i−1+i−1+i1+i1+i−1−i−1−i0-22002i−2i0000000000−1+i1−i−1−i1+i00000
χ3622-2-22002-2-22-2-2200−2i2i−2i2i-220002002-2-200−2i2i−2i2i000000000−1+i1−i−1−i1+i000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i0-22002i−2i00000000001−i−1+i1+i−1−i00000
χ372-2-2222-2-2-222-22-22-222-2-20000022-2-2-222-222-2-200000002-20000-220000000000000000000000000000000002i−2i2i−2i0
χ382-2-2222-2-2-222-22-22-222-2-20000022-2-2-222-222-2-200000002-20000-22000000000000000000000000000000000−2i2i−2i2i0
χ392-2-2222-2-2-222-22-22-2-2-2220000022-2-2-22-22-2-22200000002-200002-20000000000000000000000000000000002-2-220
χ402-2-2222-2-2-222-22-22-2-2-2220000022-2-2-22-22-2-22200000002-200002-2000000000000000000000000000000000-222-20
χ412-2-222-22-2-222-22-2-2222-2-2000002-22-2-22-2222-2-20000000-2200002-22i−2i2i−2i0000000000000000002i−2i2i−2i000000000000
χ422-2-222-22-2-222-22-2-2222-2-2000002-22-2-22-2222-2-20000000-2200002-2−2i2i−2i2i000000000000000000−2i2i−2i2i000000000000
χ432-2-222-22-2-222-22-2-22-2-222000002-22-2-222-2-2-2220000000-220000-222-2-220000000000000000002-2-22000000000000
χ442-2-222-22-2-222-22-2-22-2-222000002-22-2-222-2-2-2220000000-220000-22-222-2000000000000000000-222-2000000000000
χ452-2-22-1-2211-12-22-21-122-2-2000−i3i3-1-2211-1-22-1-111000−i3−i3i3i31-10000-112i−2i2i−2i3−33−33−33−300000000−i3i3−ii−ii000000000000
χ462-2-22-1-2211-12-22-21-122-2-2000−i3i3-1-2211-1-22-1-111000−i3−i3i3i31-10000-11−2i2i−2i2i−33−33−33−3300000000−i3i3i−ii−i000000000000
χ472-2-22-1-2211-12-22-21-122-2-2000i3−i3-1-2211-1-22-1-111000i3i3−i3−i31-10000-112i−2i2i−2i−33−33−33−3300000000i3−i3−ii−ii000000000000
χ482-2-22-1-2211-12-22-21-122-2-2000i3−i3-1-2211-1-22-1-111000i3i3−i3−i31-10000-11−2i2i−2i2i3−33−33−33−300000000i3−i3i−ii−i000000000000
χ492-2-22-1-2211-12-22-21-1-2-222000−i3i3-1-2211-12-211-1-1000−i3−i3i3i31-100001-12-2-22−i3i3−i3i3i3−i3i3−i300000000i3−i3-111-1000000000000
χ502-2-22-1-2211-12-22-21-1-2-222000−i3i3-1-2211-12-211-1-1000−i3−i3i3i31-100001-1-222-2i3−i3i3−i3−i3i3−i3i300000000i3−i31-1-11000000000000
χ512-2-22-1-2211-12-22-21-1-2-222000i3−i3-1-2211-12-211-1-1000i3i3−i3−i31-100001-12-2-22i3−i3i3−i3−i3i3−i3i300000000−i3i3-111-1000000000000
χ522-2-22-1-2211-12-22-21-1-2-222000i3−i3-1-2211-12-211-1-1000i3i3−i3−i31-100001-1-222-2−i3i3−i3i3i3−i3i3−i300000000−i3i31-1-11000000000000
χ534444444444-1-1-1-144000044444-1-1-1-1-1-10000004-1-1-1-1-1-1-1-10000000000000000004-1-1-1-1000000000-1-10000000000
χ544444444444-1-1-1-144000044-4-4-4-1-1-1-1-1-10000004111111-1-1000000000000000000-4-1-1-1-1000000000110000000000
χ554444444444-1-1-1-1440000-4-4444-1-1-1-1-1-1000000-4-1-1-1-1-1-1-1-1000000000000000000-41111000000000110000000000
χ564444444444-1-1-1-1440000-4-4-4-4-4-1-1-1-1-1-1000000-4111111-1-100000000000000000041111000000000-1-10000000000
χ5744444-4-4444-1-1-1-1-4-4000044000-111-1-1-1000000-4−55−55−55110000000000000000000-1-111000000000−550000000000
χ5844444-4-4444-1-1-1-1-4-4000044000-111-1-1-1000000-45−55−55−5110000000000000000000-1-1110000000005−50000000000
χ5944444-4-4444-1-1-1-1-4-40000-4-4000-111-1-1-10000004−55−55−5511000000000000000000011-1-10000000005−50000000000
χ6044444-4-4444-1-1-1-1-4-40000-4-4000-111-1-1-100000045−55−55−511000000000000000000011-1-1000000000−550000000000
χ614444-2-4-4-2-2-2444422444400000-2-4-4-2-2-2-4-4-2-2-2-200000002200002200000000000000000000000000000000000000
χ624444-2-4-4-2-2-2444422-4-4-4-400000-2-4-4-2-2-24422220000000220000-2-200000000000000000000000000000000000000
χ6344-4-4-200-2224-4-44004i−4i4i−4i00000-200-22200−2i2i−2i2i0000000002+2i−2−2i2−2i−2+2i000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000000000000000000000
χ6444-4-4-200-2224-4-44004i−4i4i−4i00000-200-22200−2i2i−2i2i000000000−2−2i2+2i−2+2i2−2i0000001+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000000000000000000000
χ6544-4-4-200-2224-4-4400−4i4i−4i4i00000-200-222002i−2i2i−2i0000000002−2i−2+2i2+2i−2−2i000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000000000000000000000
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χ674-44-4400-44-444-4-4004i−4i−4i4i00000400-44-4004i−4i−4i4i00000000000000000000000000000000000000000000000000000
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χ891616-16-16-800-888-444-4000000000002002-2-200000000000000000000000000000000000000000000000000000000000
χ9016-1616-16-8008-88-4-44400000000000200-22-200000000000000000000000000000000000000000000000000000000000

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