Finite Group Databasebeta

← Group #13021028

Character table — Group #13021028

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122224444444444445555555588888888888888881010101016161616161616162020202020202020202020202020202020202020404040404040404040404040
order12222222444444445101010101010104444444444442020202020202020202020204444202020202020202044448888888888888888444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-111111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1iiii−i−i−i−i
χ6111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-111111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1−i−i−i−iiiii
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1111−i−i−i−iiiii
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1111iiii−i−i−i−i
χ9111111111111-1-1-1-1111111111111111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-1
χ10111111111111-1-1-1-1111111111111111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-111
χ11111111111111-1-1-1-11111111111111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111
χ12111111111111-1-1-1-11111111111111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-111-1-1
χ13111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-111ii−i−i−i−iii
χ14111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-111−i−iiiii−i−i
χ15111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiii11-1-1−i−iiiii−i−i
χ16111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i11-1-1ii−i−i−i−iii
χ1722222222-2-2-2-222-2-222222222222222220000-2-2-2-22222-2-2-2-2-2-2-2-20000000022-2-20000000000000000000000000000
χ1822222222-2-2-2-222-2-222222222-2-2-2-2-2-2-2-20000-2-2-2-22222-2-2-2-2222200000000-2-2220000000000000000000000000000
χ1922222222-2-2-2-2-2-22222222222222222220000-2-2-2-2-2-2-2-22222-2-2-2-200000000-2-2220000000000000000000000000000
χ2022222222-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-20000-2-2-2-2-2-2-2-2222222220000000022-2-20000000000000000000000000000
χ21222-2-2-2-2222-2-200002-2-2-2222-22i2i−2i−2i2i2i−2i−2i002i−2i22-2-2000000002i−2i2i−2i00002i2i−2i−2i00000000000000000000002-200000000
χ22222-2-2-2-2222-2-200002-2-2-2222-22i2i−2i−2i2i2i−2i−2i00−2i2i22-2-2000000002i−2i2i−2i0000−2i−2i2i2i0000000000000000000000-2200000000
χ23222-2-2-2-2222-2-200002-2-2-2222-2−2i−2i2i2i−2i−2i2i2i002i−2i22-2-200000000−2i2i−2i2i00002i2i−2i−2i0000000000000000000000-2200000000
χ24222-2-2-2-2222-2-200002-2-2-2222-2−2i−2i2i2i−2i−2i2i2i00−2i2i22-2-200000000−2i2i−2i2i0000−2i−2i2i2i00000000000000000000002-200000000
χ25222-2-2-2-22-2-22200002-2-2-2222-22i2i−2i−2i2i2i−2i−2i2i−2i00-2-22200000000−2i2i−2i2i2i2i−2i−2i0000000000000000000000002-20000000000
χ26222-2-2-2-22-2-22200002-2-2-2222-22i2i−2i−2i2i2i−2i−2i−2i2i00-2-22200000000−2i2i−2i2i−2i−2i2i2i000000000000000000000000-220000000000
χ27222-2-2-2-22-2-22200002-2-2-2222-2−2i−2i2i2i−2i−2i2i2i2i−2i00-2-222000000002i−2i2i−2i2i2i−2i−2i000000000000000000000000-220000000000
χ28222-2-2-2-22-2-22200002-2-2-2222-2−2i−2i2i2i−2i−2i2i2i−2i2i00-2-222000000002i−2i2i−2i−2i−2i2i2i0000000000000000000000002-20000000000
χ2922-222-2-2-20000002-2222-22-2-2-22222-2-2-2-200000000000022-2-2000000000000002-222−2−222−2−222−2−222−2−2000000000000
χ3022-222-2-2-20000002-2222-22-2-2-22222-2-2-2-200000000000022-2-2000000000000002-2−2−222−2−222−2−222−2−222000000000000
χ3122-222-2-2-20000002-2222-22-2-2-2-2-2-2-2222200000000000022-2-200000000000000-22i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2000000000000
χ3222-222-2-2-20000002-2222-22-2-2-2-2-2-2-2222200000000000022-2-200000000000000-22−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2000000000000
χ3322-222-2-2-2000000-22222-22-2-2-22222-2-2-2-2000000000000-2-22200000000000000-2222−2−2−2−22222−2−2−2−222000000000000
χ3422-222-2-2-2000000-22222-22-2-2-22222-2-2-2-2000000000000-2-22200000000000000-22−2−22222−2−2−2−22222−2−2000000000000
χ3522-222-2-2-2000000-22222-22-2-2-2-2-2-2-22222000000000000-2-222000000000000002-2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2000000000000
χ3622-222-2-2-2000000-22222-22-2-2-2-2-2-2-22222000000000000-2-222000000000000002-2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2000000000000
χ372-222-2-22-200002-20022-2-2-22-222i−2i2i−2i2i−2i2i−2i0000000022-2-200000000000000002i−2i001+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i000000000000
χ382-222-2-22-200002-20022-2-2-22-222i−2i2i−2i2i−2i2i−2i0000000022-2-200000000000000002i−2i00−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i000000000000
χ392-222-2-22-200002-20022-2-2-22-22−2i2i−2i2i−2i2i−2i2i0000000022-2-20000000000000000−2i2i001−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i000000000000
χ402-222-2-22-200002-20022-2-2-22-22−2i2i−2i2i−2i2i−2i2i0000000022-2-20000000000000000−2i2i00−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i000000000000
χ412-222-2-22-20000-220022-2-2-22-222i−2i2i−2i2i−2i2i−2i00000000-2-2220000000000000000−2i2i001+i−1−i1+i−1−i−1−i1+i−1−i1+i1−i−1+i1−i−1+i−1+i1−i−1+i1−i000000000000
χ422-222-2-22-20000-220022-2-2-22-222i−2i2i−2i2i−2i2i−2i00000000-2-2220000000000000000−2i2i00−1−i1+i−1−i1+i1+i−1−i1+i−1−i−1+i1−i−1+i1−i1−i−1+i1−i−1+i000000000000
χ432-222-2-22-20000-220022-2-2-22-22−2i2i−2i2i−2i2i−2i2i00000000-2-22200000000000000002i−2i001−i−1+i1−i−1+i−1+i1−i−1+i1−i1+i−1−i1+i−1−i−1−i1+i−1−i1+i000000000000
χ442-222-2-22-20000-220022-2-2-22-22−2i2i−2i2i−2i2i−2i2i00000000-2-22200000000000000002i−2i00−1+i1−i−1+i1−i1−i−1+i1−i−1+i−1−i1+i−1−i1+i1+i−1−i1+i−1−i000000000000
χ452-2-22-22-222-22-2000022-22-2-22-22i−2i2i−2i−2i2i−2i2i00002-22-2000000002i−2i−2i2i0000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000000000
χ462-2-22-22-222-22-2000022-22-2-22-22i−2i2i−2i−2i2i−2i2i00002-22-2000000002i−2i−2i2i00000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000000000
χ472-2-22-22-222-22-2000022-22-2-22-2−2i2i−2i2i2i−2i2i−2i00002-22-200000000−2i2i2i−2i0000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000000000
χ482-2-22-22-222-22-2000022-22-2-22-2−2i2i−2i2i2i−2i2i−2i00002-22-200000000−2i2i2i−2i00000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000000000
χ492-2-22-22-22-22-22000022-22-2-22-22i−2i2i−2i−2i2i−2i2i0000-22-2200000000−2i2i2i−2i000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000000000000000
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χ512-2-22-22-22-22-22000022-22-2-22-2−2i2i−2i2i2i−2i2i−2i0000-22-22000000002i−2i−2i2i000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370000000000000000
χ522-2-22-22-22-22-22000022-22-2-22-2−2i2i−2i2i2i−2i2i−2i0000-22-22000000002i−2i−2i2i0000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000000000000000
χ532-2-2-22-2222-2-2200002-22-2-2-2222-2-22-222-200002-2-220000000022-2-2000000000000000000000000000000002i−2i002i−2i00
χ542-2-2-22-2222-2-2200002-22-2-2-2222-2-22-222-200002-2-220000000022-2-200000000000000000000000000000000−2i2i00−2i2i00
χ552-2-2-22-2222-2-2200002-22-2-2-222-222-22-2-2200002-2-2200000000-2-222000000000000000000000000000000002-200-2200
χ562-2-2-22-2222-2-2200002-22-2-2-222-222-22-2-2200002-2-2200000000-2-22200000000000000000000000000000000-22002-200
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χ614444444444444444-1-1-1-1-1-1-1-1000000004444-1-1-1-1-1-1-1-1-1-1-1-10000-1-1-1-1-1-1-1-100000000000000000000000000000000
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χ928-8-8-88-888-888-80000-22-2222-2-20000000000002-2-220000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 40 (ζ40 = 1); i = ζ10.