Finite Group Databasebeta

← Group #13019875

Character table — Group #13019875

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size1111222244444444455558888881010101010101010101010101616161616161616161620202020202020202020202020202020203232404040404040808080
order12224444444445101010444488202020204444888888884202020202040404040222448888888888882020888888488
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-1-1
χ3111111111111111111111-1-11111111111111111-111111-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111
χ511111111111111111-1-1-1-1111111-1-1-1-1iiii−i−i−i−i1111111111-1-1-1-1-1iiiiii−i−i−i−i−i−i11-1-1ii−i−i-1i−i
χ611111111111111111-1-1-1-1111111-1-1-1-1−i−i−i−iiiii1111111111-1-1-1-1-1−i−i−i−i−i−iiiiiii11-1-1−i−iii-1−ii
χ711111111111111111-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−i-111111-1-1-1-1-1-1-1-1-1iiiiii−i−i−i−i−i−i-1-111−i−iii1−ii
χ811111111111111111-1-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii-111111-1-1-1-1-1-1-1-1-1−i−i−i−i−i−iiiiiii-1-111ii−i−i1i−i
χ9111111111-1-1-1-111111111111111111111111111-11-1-1-1-111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1111111-1-1-1
χ10111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-11-1-1-1-111111-1-1-1-1-1-11111-1-11111-1-111-1-1-1-1-111
χ11111111111-1-1-1-111111111-1-1111111111111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-1-1-1111
χ12111111111-1-1-1-111111111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-1-1-11111-1-1111111-1-111111-1-1
χ13111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1iiii−i−i−i−i-11-1-1-1-11111-11111ii−i−i−i−i−i−iiiii-1-1-1-1ii−i−i1−ii
χ14111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1−i−i−i−iiiii-11-1-1-1-11111-11111−i−iiiiiii−i−i−i−i-1-1-1-1−i−iii1i−i
χ15111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−i11-1-1-1-1-1-1-1-1-11111ii−i−i−i−i−i−iiiii1111−i−iii-1i−i
χ16111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii11-1-1-1-1-1-1-1-1-11111−i−iiiiiii−i−i−i−i1111ii−i−i-1−ii
χ17222222-2-2-200002222222200-222-2-2-222222222220-200000000-20000-2-20000-2-2000000000000000
χ18222222-2-2-200002222222200-222-2-2-222-2-2-2-2-2-2-2-20-200000000-2000022000022000000000000000
χ19222222-2-2-200002222-2-2-2-200-222-222-2-22i2i2i2i−2i−2i−2i−2i0-20000000020000−2i−2i00002i2i000000000000000
χ20222222-2-2-200002222-2-2-2-200-222-222-2-2−2i−2i−2i−2i2i2i2i2i0-200000000200002i2i0000−2i−2i000000000000000
χ212222-2-222-222-2-222222222002-2-2222-2-2000000000-222-2-20000-222-2-200000000000000000000000
χ222222-2-222-222-2-22222-2-2-2-2002-2-22-2-222000000000-222-2-200002-2-22200000000000000000000000
χ232222-2-222-2-2-22222222222002-2-2222-2-2000000000-2-2-2220000-2-2-22200000000000000000000000
χ242222-2-222-2-2-2222222-2-2-2-2002-2-22-2-222000000000-2-2-2220000222-2-200000000000000000000000
χ252222-2-2-2-2200002222222200-2-2-2-2-2-2-2-200000000020000000020000002i2i−2i−2i002i2i−2i−2i00000000000
χ262222-2-2-2-2200002222222200-2-2-2-2-2-2-2-20000000002000000002000000−2i−2i2i2i00−2i−2i2i2i00000000000
χ272222-2-2-2-2200002222-2-2-2-200-2-2-2-22222000000000200000000-200000022-2-200-2-22200000000000
χ282222-2-2-2-2200002222-2-2-2-200-2-2-2-22222000000000200000000-2000000-2-2220022-2-200000000000
χ292-22-22-200000002-2-222i−2i2i−2ii2−i202-20002i−2i−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39000000i2i2−i2−i200000000000000000002−21−i−1+i1+i−1−i000
χ302-22-22-200000002-2-222i−2i2i−2ii2−i202-20002i−2i2ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000i2i2−i2−i200000000000000000002−2−1+i1−i−1−i1+i000
χ312-22-22-200000002-2-222i−2i2i−2i−i2i202-20002i−2i−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39000000−i2−i2i2i20000000000000000000−22−1+i1−i−1−i1+i000
χ322-22-22-200000002-2-222i−2i2i−2i−i2i202-20002i−2i2ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000−i2−i2i2i20000000000000000000−221−i−1+i1+i−1−i000
χ332-22-22-200000002-2-22−2i2i−2i2ii2−i202-2000−2i2i−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37000000i2i2−i2−i20000000000000000000−221+i−1−i1−i−1+i000
χ342-22-22-200000002-2-22−2i2i−2i2ii2−i202-2000−2i2i2ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000i2i2−i2−i20000000000000000000−22−1−i1+i−1+i1−i000
χ352-22-22-200000002-2-22−2i2i−2i2i−i2i202-2000−2i2i−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37000000−i2−i2i2i200000000000000000002−2−1−i1+i−1+i1−i000
χ362-22-22-200000002-2-22−2i2i−2i2i−i2i202-2000−2i2i2ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000−i2−i2i2i200000000000000000002−21+i−1−i1−i−1+i000
χ372-2-22002-202i−2i0022-2-22i−2i−2i2i00-20022i−2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i002i−2i00000002-2001+i−1−i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000
χ382-2-22002-202i−2i0022-2-22i−2i−2i2i00-20022i−2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i002i−2i00000002-200−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000
χ392-2-22002-202i−2i0022-2-2−2i2i2i−2i00-2002−2i2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i002i−2i0000000-22001−i−1+i−1−i1+i−1−i1+i1+i−1−i−1+i1−i−1+i1−i00000000000
χ402-2-22002-202i−2i0022-2-2−2i2i2i−2i00-2002−2i2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i002i−2i0000000-2200−1+i1−i1+i−1−i1+i−1−i−1−i1+i1−i−1+i1−i−1+i00000000000
χ412-2-22002-20−2i2i0022-2-22i−2i−2i2i00-20022i−2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i00−2i2i0000000-22001+i−1−i−1+i1−i−1+i1−i1−i−1+i−1−i1+i−1−i1+i00000000000
χ422-2-22002-20−2i2i0022-2-22i−2i−2i2i00-20022i−2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i00−2i2i0000000-2200−1−i1+i1−i−1+i1−i−1+i−1+i1−i1+i−1−i1+i−1−i00000000000
χ432-2-22002-20−2i2i0022-2-2−2i2i2i−2i00-2002−2i2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i00−2i2i00000002-2001−i−1+i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000
χ442-2-22002-20−2i2i0022-2-2−2i2i2i−2i00-2002−2i2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i00−2i2i00000002-200−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000
χ452-2-2200-220002-222-2-22i−2i−2i2i00200-2−2i2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i00002-200000002i−2i−1−i1+i1+i−1−i−1−i1+i−1+i1−i−1+i1−i1−i−1+i00000000000
χ462-2-2200-220002-222-2-22i−2i−2i2i00200-2−2i2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i00002-200000002i−2i1+i−1−i−1−i1+i1+i−1−i1−i−1+i1−i−1+i−1+i1−i00000000000
χ472-2-2200-220002-222-2-2−2i2i2i−2i00200-22i−2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i00002-20000000−2i2i−1+i1−i1−i−1+i−1+i1−i−1−i1+i−1−i1+i1+i−1−i00000000000
χ482-2-2200-220002-222-2-2−2i2i2i−2i00200-22i−2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i00002-20000000−2i2i1−i−1+i−1+i1−i1−i−1+i1+i−1−i1+i−1−i−1−i1+i00000000000
χ492-2-2200-22000-2222-2-22i−2i−2i2i00200-2−2i2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000-220000000−2i2i−1−i1+i−1−i1+i1+i−1−i−1+i1−i1−i−1+i−1+i1−i00000000000
χ502-2-2200-22000-2222-2-22i−2i−2i2i00200-2−2i2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000-220000000−2i2i1+i−1−i1+i−1−i−1−i1+i1−i−1+i−1+i1−i1−i−1+i00000000000
χ512-2-2200-22000-2222-2-2−2i2i2i−2i00200-22i−2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000-2200000002i−2i−1+i1−i−1+i1−i1−i−1+i−1−i1+i1+i−1−i−1−i1+i00000000000
χ522-2-2200-22000-2222-2-2−2i2i2i−2i00200-22i−2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000-2200000002i−2i1−i−1+i1−i−1+i−1+i1−i1+i−1−i−1−i1+i1+i−1−i00000000000
χ534444444444444-1-1-1-1000044-1-1-1-10000000000004-1-1-1-1-1-1-1-1-100000000000000000-1-1000000000
χ544444444444444-1-1-1-10000-4-4-1-1-1-1000000000000-4-1-1-1-1-111110000000000000000011000000000
χ55444444444-4-4-4-4-1-1-1-1000044-1-1-1-1000000000000-4-11111-1-1-1-10000000000000000011000000000
χ56444444444-4-4-4-4-1-1-1-10000-4-4-1-1-1-10000000000004-11111111100000000000000000-1-1000000000
χ574444-4-444-444-4-4-1-1-1-1000000-111-100000000000001-1-1115−55−5000000000000000005−5000000000
χ584444-4-444-444-4-4-1-1-1-1000000-111-100000000000001-1-111−55−5500000000000000000−55000000000
χ594444-4-444-4-4-444-1-1-1-1000000-111-10000000000000111-1-15−55−500000000000000000−55000000000
χ604444-4-444-4-4-444-1-1-1-1000000-111-10000000000000111-1-1−55−55000000000000000005−5000000000
χ6144-4-40000000004-44-444-4-4000000000022−22−2222−222222−2200000000000000000000000000000000000000
χ6244-4-40000000004-44-444-4-40000000000−222222−2222−22−222200000000000000000000000000000000000000
χ6344-4-40000000004-44-4-4-44400000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000000
χ6444-4-40000000004-44-4-4-4440000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000000
χ654-44-4-4400000004-4-444i−4i4i−4i000-44000−4i4i0000000000000000000000000000000000000000000000
χ664-44-4-4400000004-4-44−4i4i−4i4i000-440004i−4i0000000000000000000000000000000000000000000000
χ67888888-8-8-80000-2-2-2-20000002-2-2200000000000002000000000000000000000000000000000000
χ688888-8-8-8-880000-2-2-2-200000022220000000000000-2000000000000000000000000000000000000
χ698-88-88-80000000-222-200004i2−4i20-220000000000000000000−i2−i2i2i20000000000000000000000000000
χ708-88-88-80000000-222-20000−4i24i20-220000000000000000000i2i2−i2−i20000000000000000000000000000
χ718-88-8-880000000-222-200000002-20000000000000000000i10−i10−i10i100000000000000000000000000000
χ728-88-8-880000000-222-200000002-20000000000000000000−i10i10i10−i100000000000000000000000000000
χ738-8-88008-808i−8i00-2-222000000200-200000000000000−2i2i0000000000000000000000000000000000
χ748-8-88008-80−8i8i00-2-222000000200-2000000000000002i−2i0000000000000000000000000000000000
χ758-8-8800-880008-8-2-222000000-20020000000000000000-2200000000000000000000000000000000
χ768-8-8800-88000-88-2-222000000-200200000000000000002-200000000000000000000000000000000
χ771616-16-16000000000-44-44000000000000000000000000000000000000000000000000000000000000

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