Finite Group Databasebeta

← Group #13031791

Character table — Group #13031791

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116
size111122222244445555888888881010101010101010101010101010101010101010101016161616404040404040111122222244445555888888881010101010101010101010101010101010101010101016161616404040404040
order12224488885101010444444202040404040448888888888888888888820202020248888222244888810101010444444202040404040448888888888888888888820202020248888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ3111111111111111111-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111111111111-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111-1-1-1-111111111-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1ii−i−i11111111111111-1-1-1-111111111-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1ii−i−i
χ611111111111111-1-1-1-111111111-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1−i−iii11111111111111-1-1-1-111111111-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1−i−iii
χ711111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-111−i−iii11111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-111−i−iii
χ811111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-111ii−i−i11111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-111ii−i−i
χ9111111-1-1-1-1111111111-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11-11-11-1111111-1-1-1-1111111111-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11-11-11-1
χ10111111-1-1-1-1111111111-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11-1-11-11111111-1-1-1-1111111111-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11-1-11-11
χ11111111-1-1-1-111111111-1111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-11-11-11111111-1-1-1-111111111-1111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-11-11-11
χ12111111-1-1-1-111111111-1111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-111-11-1111111-1-1-1-111111111-1111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-111-11-1
χ13111111-1-1-1-11111-1-1-1-11-111-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii11-1-1-11i−i−ii111111-1-1-1-11111-1-1-1-11-111-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii11-1-1-11i−i−ii
χ14111111-1-1-1-11111-1-1-1-11-111-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i11-1-1-11−iii−i111111-1-1-1-11111-1-1-1-11-111-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i11-1-1-11−iii−i
χ15111111-1-1-1-11111-1-1-1-1-1111-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-1111-1−iii−i111111-1-1-1-11111-1-1-1-1-1111-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-1111-1−iii−i
χ16111111-1-1-1-11111-1-1-1-1-1111-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-1111-1i−i−ii111111-1-1-1-11111-1-1-1-1-1111-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-1111-1i−i−ii
χ172222-2-200002222222200-2-20000-2-2000022-2-222-2-20000000000000000002222-2-200002222222200-2-20000-2-2000022-2-222-2-2000000000000000000
χ182222-2-200002222222200-2-20000-2-20000-2-222-2-2220000000000000000002222-2-200002222222200-2-20000-2-20000-2-222-2-222000000000000000000
χ192222-2-200002222-2-2-2-200-2-200002200002i2i−2i−2i−2i−2i2i2i0000000000000000002222-2-200002222-2-2-2-200-2-200002200002i2i−2i−2i−2i−2i2i2i000000000000000000
χ202222-2-200002222-2-2-2-200-2-20000220000−2i−2i2i2i2i2i−2i−2i0000000000000000002222-2-200002222-2-2-2-200-2-20000220000−2i−2i2i2i2i2i−2i−2i000000000000000000
χ2122-2-200i2i2−i2−i22-22-222-2-20000i2i2−i2−i200i2i2−i2−i2002i−2i002i−2i22−2−222−2−2000000000022-2-200i2i2−i2−i22-22-222-2-20000i2i2−i2−i200i2i2−i2−i2002i−2i002i−2i22−2−222−2−20000000000
χ2222-2-200i2i2−i2−i22-22-222-2-20000i2i2−i2−i200i2i2−i2−i200−2i2i00−2i2i−2−222−2−222000000000022-2-200i2i2−i2−i22-22-222-2-20000i2i2−i2−i200i2i2−i2−i200−2i2i00−2i2i−2−222−2−2220000000000
χ2322-2-200i2i2−i2−i22-22-2-2-2220000i2i2−i2−i200−i2−i2i2i2002-200-22−i2−i2i2i2i2i2−i2−i2000000000022-2-200i2i2−i2−i22-22-2-2-2220000i2i2−i2−i200−i2−i2i2i2002-200-22−i2−i2i2i2i2i2−i2−i20000000000
χ2422-2-200i2i2−i2−i22-22-2-2-2220000i2i2−i2−i200−i2−i2i2i200-22002-2i2i2−i2−i2−i2−i2i2i2000000000022-2-200i2i2−i2−i22-22-2-2-2220000i2i2−i2−i200−i2−i2i2i200-22002-2i2i2−i2−i2−i2−i2i2i20000000000
χ2522-2-200−i2−i2i2i22-22-222-2-20000−i2−i2i2i200−i2−i2i2i2002i−2i002i−2i−2−222−2−222000000000022-2-200−i2−i2i2i22-22-222-2-20000−i2−i2i2i200−i2−i2i2i2002i−2i002i−2i−2−222−2−2220000000000
χ2622-2-200−i2−i2i2i22-22-222-2-20000−i2−i2i2i200−i2−i2i2i200−2i2i00−2i2i22−2−222−2−2000000000022-2-200−i2−i2i2i22-22-222-2-20000−i2−i2i2i200−i2−i2i2i200−2i2i00−2i2i22−2−222−2−20000000000
χ2722-2-200−i2−i2i2i22-22-2-2-2220000−i2−i2i2i200i2i2−i2−i2002-200-22i2i2−i2−i2−i2−i2i2i2000000000022-2-200−i2−i2i2i22-22-2-2-2220000−i2−i2i2i200i2i2−i2−i2002-200-22i2i2−i2−i2−i2−i2i2i20000000000
χ2822-2-200−i2−i2i2i22-22-2-2-2220000−i2−i2i2i200i2i2−i2−i200-22002-2−i2−i2i2i2i2i2−i2−i2000000000022-2-200−i2−i2i2i22-22-2-2-2220000−i2−i2i2i200i2i2−i2−i200-22002-2−i2−i2i2i2i2i2−i2−i20000000000
χ292-22-200i2−i2i2−i22-2-222i−2i2i−2i0000i2−i2i2−i2002−22−2−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000002-22-200i2−i2i2−i22-2-222i−2i2i−2i0000i2−i2i2−i2002−22−2−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000
χ302-22-200i2−i2i2−i22-2-222i−2i2i−2i0000i2−i2i2−i2002−22−22ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000002-22-200i2−i2i2−i22-2-222i−2i2i−2i0000i2−i2i2−i2002−22−22ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000
χ312-22-200i2−i2i2−i22-2-22−2i2i−2i2i0000i2−i2i2−i200−22−22−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000002-22-200i2−i2i2−i22-2-22−2i2i−2i2i0000i2−i2i2−i200−22−22−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000
χ322-22-200i2−i2i2−i22-2-22−2i2i−2i2i0000i2−i2i2−i200−22−222ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000002-22-200i2−i2i2−i22-2-22−2i2i−2i2i0000i2−i2i2−i200−22−222ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000
χ332-22-200−i2i2−i2i22-2-222i−2i2i−2i0000−i2i2−i2i200−22−22−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000002-22-200−i2i2−i2i22-2-222i−2i2i−2i0000−i2i2−i2i200−22−22−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000
χ342-22-200−i2i2−i2i22-2-222i−2i2i−2i0000−i2i2−i2i200−22−222ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000002-22-200−i2i2−i2i22-2-222i−2i2i−2i0000−i2i2−i2i200−22−222ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000
χ352-22-200−i2i2−i2i22-2-22−2i2i−2i2i0000−i2i2−i2i2002−22−2−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000002-22-200−i2i2−i2i22-2-22−2i2i−2i2i0000−i2i2−i2i2002−22−2−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000
χ362-22-200−i2i2−i2i22-2-22−2i2i−2i2i0000−i2i2−i2i2002−22−22ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000002-22-200−i2i2−i2i22-2-22−2i2i−2i2i0000−i2i2−i2i2002−22−22ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000
χ372-2-222-22-2-2222-2-22i−2i−2i2i00-222-2-222i−2i−2i2i2i−2i000000000000000000000000002-2-222-22-2-2222-2-22i−2i−2i2i00-222-2-222i−2i−2i2i2i−2i00000000000000000000000000
χ382-2-222-22-2-2222-2-2−2i2i2i−2i00-222-2-22−2i2i2i−2i−2i2i000000000000000000000000002-2-222-22-2-2222-2-2−2i2i2i−2i00-222-2-22−2i2i2i−2i−2i2i00000000000000000000000000
χ392-2-222-2-222-222-2-22i−2i−2i2i00-22-222-22i−2i2i−2i−2i2i000000000000000000000000002-2-222-2-222-222-2-22i−2i−2i2i00-22-222-22i−2i2i−2i−2i2i00000000000000000000000000
χ402-2-222-2-222-222-2-2−2i2i2i−2i00-22-222-2−2i2i−2i2i2i−2i000000000000000000000000002-2-222-2-222-222-2-2−2i2i2i−2i00-22-222-2−2i2i−2i2i2i−2i00000000000000000000000000
χ412-2-22-22000022-2-22i−2i−2i2i002-20000−2i2i000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700000000002-2-22-22000022-2-22i−2i−2i2i002-20000−2i2i000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370000000000
χ422-2-22-22000022-2-22i−2i−2i2i002-20000−2i2i0000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700000000002-2-22-22000022-2-22i−2i−2i2i002-20000−2i2i0000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000000000
χ432-2-22-22000022-2-2−2i2i2i−2i002-200002i−2i000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900000000002-2-22-22000022-2-2−2i2i2i−2i002-200002i−2i000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000000000
χ442-2-22-22000022-2-2−2i2i2i−2i002-200002i−2i0000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900000000002-2-22-22000022-2-2−2i2i2i−2i002-200002i−2i0000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000000000
χ454444444444-1-1-1-1000044-1-1-1-1-1-10000000000000000000000-1-1-1-10000004444444444-1-1-1-1000044-1-1-1-1-1-10000000000000000000000-1-1-1-1000000
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χ47444444-4-4-4-4-1-1-1-100004-4-1-111110000000000000000000000-1-111000000444444-4-4-4-4-1-1-1-100004-4-1-111110000000000000000000000-1-111000000
χ48444444-4-4-4-4-1-1-1-10000-44-1-11111000000000000000000000011-1-1000000444444-4-4-4-4-1-1-1-10000-44-1-11111000000000000000000000011-1-1000000
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χ1074-4-444-44-4-44-1-1110000001-1-111-10000000000000000000000i5−i5i5−i5000000-444-4-44-444-411-1-1000000-111-1-110000000000000000000000−i5i5−i5i5000000
χ1084-4-444-44-4-44-1-1110000001-1-111-10000000000000000000000−i5i5−i5i5000000-444-4-44-444-411-1-1000000-111-1-110000000000000000000000i5−i5i5−i5000000
χ1094-4-444-4-444-4-1-1110000001-11-1-110000000000000000000000i5−i5−i5i5000000-444-4-444-4-4411-1-1000000-11-111-10000000000000000000000−i5i5i5−i5000000
χ1104-4-444-4-444-4-1-1110000001-11-1-110000000000000000000000−i5i5i5−i5000000-444-4-444-4-4411-1-1000000-11-111-10000000000000000000000i5−i5−i5i5000000
χ1118888-8-80000-2-2-2-200000022000000000000000000000000000000000000-8-8-8-88800002222000000-2-2000000000000000000000000000000000000
χ11288-8-8004i24i2−4i2−4i2-22-2200000000−i2−i2i2i200000000000000000000000000000000-8-88800−4i2−4i24i24i22-22-200000000i2i2−i2−i200000000000000000000000000000000
χ11388-8-800−4i2−4i24i24i2-22-2200000000i2i2−i2−i200000000000000000000000000000000-8-888004i24i2−4i2−4i22-22-200000000−i2−i2i2i200000000000000000000000000000000
χ1148-88-8004i2−4i24i2−4i2-222-200000000−i2i2−i2i200000000000000000000000000000000-88-8800−4i24i2−4i24i22-2-2200000000i2−i2i2−i200000000000000000000000000000000
χ1158-88-800−4i24i2−4i24i2-222-200000000i2−i2i2−i200000000000000000000000000000000-88-88004i2−4i24i2−4i22-2-2200000000−i2i2−i2i200000000000000000000000000000000
χ1168-8-88-880000-2-222000000-22000000000000000000000000000000000000-888-88-8000022-2-20000002-2000000000000000000000000000000000000

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