Finite Group Databasebeta

← Group #13019859

Character table — Group #13019859

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size1111222244444444455558888881010101010101010101010101616161616161616161620202020202020202020202020202020203232404040404040808080
order12224444444445101010444488202020202244888888882202020202040404040224448888888888881010444488488
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111-1-1
χ3111111111111111111111-1-11111111111111111-111111-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111
χ511111111111111111-1-1-1-1111111-1-1-1-1iiii−i−i−i−i1111111111-1-1-1-1-1iiiiii−i−i−i−i−i−i11ii−i−i-1-1-1i−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−i−iii-1-1-1−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-1-1−i−iii111−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-1-1ii−i−i111i−i
χ9111111111-1-1-1-111111111111111111111111111-11-1-1-1-11111-1-11-1-111-1-1-1-111-1-1-1-1-1-1111111-1-1-1
χ10111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-11-1-1-1-11111-1-11111-1-1-1-1-1-111-111
χ11111111111-1-1-1-111111111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-11-1-111-1-1-1-111-1-1-1-111-1-1-1-1-1-1111
χ12111111111-1-1-1-111111111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-11111111111-1-11-1-1
χ13111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1iiii−i−i−i−i-11-1-1-1-1111111-111ii−i−i−i−i−i−iiiii-1-1ii−i−i-1-11−ii
χ14111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1−i−i−i−iiiii-11-1-1-1-1111111-111−i−iiiiiii−i−i−i−i-1-1−i−iii-1-11i−i
χ15111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−i11-1-1-1-1-1-1-1-111-111ii−i−i−i−i−i−iiiii11−i−iii11-1i−i
χ16111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii11-1-1-1-1-1-1-1-111-111−i−iiiiiii−i−i−i−i11ii−i−i11-1−ii
χ17222222-2-2-20000222222220022-2-2-2-222222222220-20000000000-200-2-20000-2-2000000000000000
χ18222222-2-2-20000222222220022-2-2-2-222-2-2-2-2-2-2-2-20-20000000000-20022000022000000000000000
χ19222222-2-2-200002222-2-2-2-20022-2-222-2-22i2i2i2i−2i−2i−2i−2i0-20000000000200−2i−2i00002i2i000000000000000
χ20222222-2-2-200002222-2-2-2-20022-2-222-2-2−2i−2i−2i−2i2i2i2i2i0-200000000002002i2i0000−2i−2i000000000000000
χ212222-2-222-222-2-22222222200-2-22222-2-2000000000-222-2-20000-2-2-22200000000000000000000000
χ222222-2-222-222-2-22222-2-2-2-200-2-222-2-222000000000-222-2-20000222-2-200000000000000000000000
χ232222-2-222-2-2-2222222222200-2-22222-2-2000000000-2-2-222000022-2-2-200000000000000000000000
χ242222-2-222-2-2-2222222-2-2-2-200-2-222-2-222000000000-2-2-2220000-2-222200000000000000000000000
χ252222-2-2-2-2200002222222200-2-2-2-2-2-2-2-200000000020000000000200002i2i−2i−2i002i2i−2i−2i00000000000
χ262222-2-2-2-2200002222222200-2-2-2-2-2-2-2-20000000002000000000020000−2i−2i2i2i00−2i−2i2i2i00000000000
χ272222-2-2-2-2200002222-2-2-2-200-2-2-2-2222200000000020000000000-2000022-2-200-2-22200000000000
χ282222-2-2-2-2200002222-2-2-2-200-2-2-2-2222200000000020000000000-20000-2-2220022-2-200000000000
χ292-22-22-2000000022-2-22i−2i2i−2ii2−i22-200002i−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−i200000000000000000001−i−1+i1+i−1−i2−2000
χ302-22-22-2000000022-2-22i−2i2i−2ii2−i22-200002i−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−i20000000000000000000−1+i1−i−1−i1+i2−2000
χ312-22-22-2000000022-2-22i−2i2i−2i−i2i22-200002i−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−i2i2i20000000000000000000−1+i1−i−1−i1+i−22000
χ322-22-22-2000000022-2-22i−2i2i−2i−i2i22-200002i−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−i2i2i200000000000000000001−i−1+i1+i−1−i−22000
χ332-22-22-2000000022-2-2−2i2i−2i2ii2−i22-20000−2i2i−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−i200000000000000000001+i−1−i1−i−1+i−22000
χ342-22-22-2000000022-2-2−2i2i−2i2ii2−i22-20000−2i2i2ζ7+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−i20000000000000000000−1−i1+i−1+i1−i−22000
χ352-22-22-2000000022-2-2−2i2i−2i2i−i2i22-20000−2i2i−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−i2i2i20000000000000000000−1−i1+i−1+i1−i2−2000
χ362-22-22-2000000022-2-2−2i2i−2i2i−i2i22-20000−2i2i2ζ7+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−i2i2i200000000000000000001+i−1−i1−i−1+i2−2000
χ372-2-22002-202i−2i002-22-222-2-200002-2-2200i2−i2i2−i2i2−i2i2−i2002i−2i0000000002i−2ii2−i22−22−2i2−i22−22−200000000000
χ382-2-22002-202i−2i002-22-222-2-200002-2-2200−i2i2−i2i2−i2i2−i2i2002i−2i0000000002i−2i−i2i2−22−22−i2i2−22−2200000000000
χ392-2-22002-202i−2i002-22-2-2-22200002-22-2002−22−2−22−22002i−2i000000000−2i2i2−2−i2i2−i2i2−22i2−i2i2−i200000000000
χ402-2-22002-202i−2i002-22-2-2-22200002-22-200−22−222−22−2002i−2i000000000−2i2i−22i2−i2i2−i22−2−i2i2−i2i200000000000
χ412-2-22002-20−2i2i002-22-222-2-200002-2-2200i2−i2i2−i2i2−i2i2−i200−2i2i000000000−2i2ii2−i2−22−22i2−i2−22−2200000000000
χ422-2-22002-20−2i2i002-22-222-2-200002-2-2200−i2i2−i2i2−i2i2−i2i200−2i2i000000000−2i2i−i2i22−22−2−i2i22−22−200000000000
χ432-2-22002-20−2i2i002-22-2-2-22200002-22-2002−22−2−22−2200−2i2i0000000002i−2i2−2i2−i2i2−i2−22−i2i2−i2i200000000000
χ442-2-22002-20−2i2i002-22-2-2-22200002-22-200−22−222−22−200−2i2i0000000002i−2i−22−i2i2−i2i22−2i2−i2i2−i200000000000
χ452-2-2200-220002-22-22-222-2-20000-222-200i2−i2i2−i2i2−i2i2−i200002-200002-2000−i2i2i2−i2−i2i2−i2i2i2−i2−i2i200000000000
χ462-2-2200-220002-22-22-222-2-20000-222-200−i2i2−i2i2−i2i2−i2i200002-200002-2000i2−i2−i2i2i2−i2i2−i2−i2i2i2−i200000000000
χ472-2-2200-220002-22-22-2-2-2220000-22-22002−22−2−22−2200002-20000-22000−222−2−222−2−222−200000000000
χ482-2-2200-220002-22-22-2-2-2220000-22-2200−22−222−22−200002-20000-220002−2−222−2−222−2−2200000000000
χ492-2-2200-22000-222-22-222-2-20000-222-200i2−i2i2−i2i2−i2i2−i20000-220000-22000−i2i2−i2i2i2−i2−i2i2−i2i2i2−i200000000000
χ502-2-2200-22000-222-22-222-2-20000-222-200−i2i2−i2i2−i2i2−i2i20000-220000-22000i2−i2i2−i2−i2i2i2−i2i2−i2−i2i200000000000
χ512-2-2200-22000-222-22-2-2-2220000-22-22002−22−2−22−220000-2200002-2000−22−222−22−22−2−2200000000000
χ522-2-2200-22000-222-22-2-2-2220000-22-2200−22−222−22−20000-2200002-20002−22−2−22−22−222−200000000000
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
χ574444-4-444-444-4-4-1-1-1-100000011-1-100000000000001-1-1115−55−5000000000000000005−5000000000
χ584444-4-444-444-4-4-1-1-1-100000011-1-100000000000001-1-111−55−5500000000000000000−55000000000
χ594444-4-444-4-4-444-1-1-1-100000011-1-10000000000000111-1-15−55−500000000000000000−55000000000
χ604444-4-444-4-4-444-1-1-1-100000011-1-10000000000000111-1-1−55−55000000000000000005−5000000000
χ6144-4-40000000004-4-444i−4i−4i4i00000000002−2i−2+2i−2+2i2−2i2+2i−2−2i−2−2i2+2i00000000000000000000000000000000000000
χ6244-4-40000000004-4-444i−4i−4i4i0000000000−2+2i2−2i2−2i−2+2i−2−2i2+2i2+2i−2−2i00000000000000000000000000000000000000
χ6344-4-40000000004-4-44−4i4i4i−4i00000000002+2i−2−2i−2−2i2+2i2−2i−2+2i−2+2i2−2i00000000000000000000000000000000000000
χ6444-4-40000000004-4-44−4i4i4i−4i0000000000−2−2i2+2i2+2i−2−2i−2+2i2−2i2−2i−2+2i00000000000000000000000000000000000000
χ654-44-4-44000000044-4-44i−4i4i−4i00-440000−4i4i0000000000000000000000000000000000000000000000
χ664-44-4-44000000044-4-4−4i4i−4i4i00-4400004i−4i0000000000000000000000000000000000000000000000
χ67888888-8-8-80000-2-2-2-2000000-2-22200000000000002000000000000000000000000000000000000
χ688888-8-8-8-880000-2-2-2-200000022220000000000000-2000000000000000000000000000000000000
χ698-88-88-80000000-2-22200004i2−4i2-2200000000000000000000−i2−i2i2i20000000000000000000000000000
χ708-88-88-80000000-2-2220000−4i24i2-2200000000000000000000i2i2−i2−i20000000000000000000000000000
χ718-88-8-880000000-2-2220000002-200000000000000000000i10−i10−i10i100000000000000000000000000000
χ728-88-8-880000000-2-2220000002-200000000000000000000−i10i10i10−i100000000000000000000000000000
χ738-8-88008-808i−8i00-22-2200000000-2200000000000000−2i2i0000000000000000000000000000000000
χ748-8-88008-80−8i8i00-22-2200000000-22000000000000002i−2i0000000000000000000000000000000000
χ758-8-8800-880008-8-22-22000000002-20000000000000000-2200000000000000000000000000000000
χ768-8-8800-88000-88-22-22000000002-200000000000000002-200000000000000000000000000000000
χ771616-16-16000000000-444-4000000000000000000000000000000000000000000000000000000000000

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