Finite Group Databasebeta

← Group #13025127

Character table — Group #13025127

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111222222444444444444444444444444444455558888888888888888888888881010101010102020202020202020202020208080808080808080
order122244888824588101010161616161616161620202020404040404040404044441010202040404040808080808080808080808080808080804488884488161616161616161688888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1i−iiii−i−i−i
χ411111111111111111111111111111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−ii−i−i−iiii
χ5111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111-1-11-1-1
χ6111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-111-111
χ7111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111i−ii−i−i−iii
χ8111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−ii−iiii−i−i
χ91111111111-1-11-1-11111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111-11-1-11-1
χ101111111111-1-11-1-11111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-11-111-11
χ111111111111-1-11-1-11111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111i−i−ii−ii−ii
χ121111111111-1-11-1-11111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111−iii−ii−ii−i
χ131111111111-1-11-1-1111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1111111-1-11-1-11
χ141111111111-1-11-1-1111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11111-1-111-111-1
χ151111111111-1-11-1-1111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1i−i−i−iiii−i
χ161111111111-1-11-1-1111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1−iiii−i−i−ii
χ17222222-2-2-2-2222-2-2222000000002222-2-2-2-2-2-2-2-222222222-2-2-2-2000000000000000022-2-2-2-222-2-20000000000000000
χ18222222-2-2-2-2222-2-2222000000002222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-20000000000000000-2-22222-2-2220000000000000000
χ19222222-2-2-2-2-2-2222222000000002222-2-2-2-2-2-2-2-22222-2-2-2-22222000000000000000022-2-2-2-2-2-2220000000000000000
χ20222222-2-2-2-2-2-2222222000000002222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000-2-2222222-2-20000000000000000
χ212222-2-200002-220022222−2−222−2−2-2-2-2-200000000222222-2-200002222−2−2−2−22222−2−2−2−2-2-200002-20022−2−222−2−200000000
χ222222-2-200002-220022222−2−222−2−2-2-2-2-200000000-2-2-2-222-2-200002222−2−2−2−22222−2−2−2−2220000-2200−2−222−2−22200000000
χ232222-2-200002-2200222−2−222−2−222-2-2-2-200000000222222-2-20000−2−2−2−22222−2−2−2−22222-2-200002-200−2−222−2−22200000000
χ242222-2-200002-2200222−2−222−2−222-2-2-2-200000000-2-2-2-222-2-20000−2−2−2−22222−2−2−2−22222220000-220022−2−222−2−200000000
χ252222-2-20000-2220022222−2−2−2−222-2-2-2-2000000002222-2-22200002222−2−2−2−2−2−2−2−22222-2-20000-220022−2−2−2−22200000000
χ262222-2-20000-2220022222−2−2−2−222-2-2-2-200000000-2-2-2-2-2-22200002222−2−2−2−2−2−2−2−222222200002-200−2−22222−2−200000000
χ272222-2-20000-22200222−2−22222−2−2-2-2-2-2000000002222-2-2220000−2−2−2−222222222−2−2−2−2-2-20000-2200−2−22222−2−200000000
χ282222-2-20000-22200222−2−22222−2−2-2-2-2-200000000-2-2-2-2-2-2220000−2−2−2−222222222−2−2−2−22200002-20022−2−2−2−22200000000
χ2922-2-22-222-2-200200-2-2200002-22-2-2-222-2-2-2-222222i−2i2i−2i000000000000000022-2-222-2-22i−2i2i2i−2i−2i000000002i−2i2i−2i00000000
χ3022-2-22-222-2-200200-2-2200002-22-2-2-222-2-2-2-22222−2i2i−2i2i000000000000000022-2-222-2-2−2i2i−2i−2i2i2i00000000−2i2i−2i2i00000000
χ3122-2-22-222-2-200200-2-220000-22-22-2-222-2-2-2-222222i−2i2i−2i0000000000000000-2-222-2-2222i−2i2i2i−2i−2i00000000−2i2i−2i2i00000000
χ3222-2-22-222-2-200200-2-220000-22-22-2-222-2-2-2-22222−2i2i−2i2i0000000000000000-2-222-2-222−2i2i−2i−2i2i2i000000002i−2i2i−2i00000000
χ3322-2-22-2-2-22200200-2-222i−2i2i−2i0000-2-2222222-2-2-2-22i−2i2i−2i000000002i2i−2i−2i2i2i−2i−2i000000002i−2i−2i−2i2i2i00002-22-2000000000000
χ3422-2-22-2-2-22200200-2-222i−2i2i−2i0000-2-2222222-2-2-2-2−2i2i−2i2i000000002i2i−2i−2i2i2i−2i−2i00000000−2i2i2i2i−2i−2i0000-22-22000000000000
χ3522-2-22-2-2-22200200-2-22−2i2i−2i2i0000-2-2222222-2-2-2-22i−2i2i−2i00000000−2i−2i2i2i−2i−2i2i2i000000002i−2i−2i−2i2i2i0000-22-22000000000000
χ3622-2-22-2-2-22200200-2-22−2i2i−2i2i0000-2-2222222-2-2-2-2−2i2i−2i2i00000000−2i−2i2i2i−2i−2i2i2i00000000−2i2i2i2i−2i−2i00002-22-2000000000000
χ3722-2-2-2200000022i−2i-2-22i2−i2−i2i22−2−2222-2-2000000002i−2i2i−2i00002i2i−2i−2ii2i2−i2−i2−i2−i2i2i222−2−2−2−222−2i2i0000002-22−2−22i2−i2−i2i200000000
χ3822-2-2-2200000022i−2i-2-22i2−i2−i2i22−2−2222-2-200000000−2i2i−2i2i00002i2i−2i−2ii2i2−i2−i2−i2−i2i2i222−2−2−2−2222i−2i000000-22−222−2−i2i2i2−i200000000
χ3922-2-2-2200000022i−2i-2-22−i2i2i2−i2−222−222-2-2000000002i−2i2i−2i00002i2i−2i−2i−i2−i2i2i2i2i2−i2−i2−2−22222−2−2−2i2i0000002-2−222−2−i2i2i2−i200000000
χ4022-2-2-2200000022i−2i-2-22−i2i2i2−i2−222−222-2-200000000−2i2i−2i2i00002i2i−2i−2i−i2−i2i2i2i2i2−i2−i2−2−22222−2−22i−2i000000-222−2−22i2−i2−i2i200000000
χ4122-2-2-220000002−2i2i-2-22i2−i2−i2i2−222−222-2-2000000002i−2i2i−2i0000−2i−2i2i2ii2i2−i2−i2−i2−i2i2i2−2−22222−2−2−2i2i000000-222−2−22−i2i2i2−i200000000
χ4222-2-2-220000002−2i2i-2-22i2−i2−i2i2−222−222-2-200000000−2i2i−2i2i0000−2i−2i2i2ii2i2−i2−i2−i2−i2i2i2−2−22222−2−22i−2i0000002-2−222−2i2−i2−i2i200000000
χ4322-2-2-220000002−2i2i-2-22−i2i2i2−i22−2−2222-2-2000000002i−2i2i−2i0000−2i−2i2i2i−i2−i2i2i2i2i2−i2−i222−2−2−2−222−2i2i000000-22−222−2i2−i2−i2i200000000
χ4422-2-2-220000002−2i2i-2-22−i2i2i2−i22−2−2222-2-200000000−2i2i−2i2i0000−2i−2i2i2i−i2−i2i2i2i2i2−i2−i222−2−2−2−2222i−2i0000002-22−2−22−i2i2i2−i200000000
χ45444444444444-144-1-1-144444444-1-1-1-1-1-1-1-1-1-1-1-10000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000000
χ46444444444444-144-1-1-1-4-4-4-4-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-10000-1-1-1-1-1-1-1-1111111111111111100000000000000000000000000
χ474444444444-4-4-1-4-4-1-1-14444-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-1000011111111-1-1-1-1-1-1-1-11111111100000000000000000000000000
χ484444444444-4-4-1-4-4-1-1-1-4-4-4-44444-1-1-1-1-1-1-1-1-1-1-1-100001111111111111111-1-1-1-1-1-1-1-100000000000000000000000000
χ49444444-4-4-4-444-1-4-4-1-1-100000000-1-1-1-1111111110000-1-1-1-11111i5−i5i5−i5i5−i5i5−i5i5−i5i5−i5i5−i5i5−i500000000000000000000000000
χ50444444-4-4-4-444-1-4-4-1-1-100000000-1-1-1-1111111110000-1-1-1-11111−i5i5−i5i5−i5i5−i5i5−i5i5−i5i5−i5i5−i5i500000000000000000000000000
χ51444444-4-4-4-4-4-4-144-1-1-100000000-1-1-1-11111111100001111-1-1-1-1i5−i5i5−i5i5−i5i5−i5−i5i5−i5i5−i5i5−i5i500000000000000000000000000
χ52444444-4-4-4-4-4-4-144-1-1-100000000-1-1-1-11111111100001111-1-1-1-1−i5i5−i5i5−i5i5−i5i5i5−i5i5−i5i5−i5i5−i500000000000000000000000000
χ534444-4-400004-4-100-1-1-12222−22−222222−22−221111i5i5−i5−i5i5i5−i5−i50000-1-111i5−i5i5−i5−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ3900000000000000000000000000
χ544444-4-400004-4-100-1-1-12222−22−222222−22−221111−i5−i5i5i5−i5−i5i5i50000-1-111−i5i5−i5i5ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ29−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ29ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ29−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ2900000000000000000000000000
χ554444-4-400004-4-100-1-1-1−22−222222−22−2222221111i5i5−i5−i5i5i5−i5−i50000-1-111i5−i5i5−i5ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ3900000000000000000000000000
χ564444-4-400004-4-100-1-1-1−22−222222−22−2222221111−i5−i5i5i5−i5−i5i5i50000-1-111−i5i5−i5i5−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ29ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ29−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ29ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ2900000000000000000000000000
χ574444-4-40000-44-100-1-1-12222−22−22−22−2222221111i5i5−i5−i5i5i5−i5−i5000011-1-1−i5i5−i5i5−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ3900000000000000000000000000
χ584444-4-40000-44-100-1-1-12222−22−22−22−2222221111−i5−i5i5i5−i5−i5i5i5000011-1-1i5−i5i5−i5ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ29−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ29ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ2900000000000000000000000000
χ594444-4-40000-44-100-1-1-1−22−2222222222−22−221111i5i5−i5−i5i5i5−i5−i5000011-1-1−i5i5−i5i5ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ3900000000000000000000000000
χ604444-4-40000-44-100-1-1-1−22−2222222222−22−221111−i5−i5i5i5−i5−i5i5i5000011-1-1i5−i5i5−i5−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ29ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ29−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ2900000000000000000000000000
χ6144-4-44-444-4-400-10011-100004-44-411-1-11111-1-1-1-100005−55−55−5−55−555−5−555−5-1-111-1-11100000000000000000000000000
χ6244-4-44-444-4-400-10011-100004-44-411-1-11111-1-1-1-10000−55−55−555−55−5−555−5−55-1-111-1-11100000000000000000000000000
χ6344-4-44-444-4-400-10011-10000-44-4411-1-11111-1-1-1-100005−55−55−5−555−5−555−5−5511-1-111-1-100000000000000000000000000
χ6444-4-44-444-4-400-10011-10000-44-4411-1-11111-1-1-1-10000−55−55−555−5−555−5−555−511-1-111-1-100000000000000000000000000
χ6544-4-44-4-4-44400-10011-14i−4i4i−4i000011-1-1-1-1-1-1111100005−55−5−555−5−i−iii−i−iii−i5i5i5−i5−i5i5i5−i500000000000000000000000000
χ6644-4-44-4-4-44400-10011-14i−4i4i−4i000011-1-1-1-1-1-111110000−55−555−5−55−i−iii−i−iiii5−i5−i5i5i5−i5−i5i500000000000000000000000000
χ6744-4-44-4-4-44400-10011-1−4i4i−4i4i000011-1-1-1-1-1-1111100005−55−5−555−5ii−i−iii−i−ii5−i5−i5i5i5−i5−i5i500000000000000000000000000
χ6844-4-44-4-4-44400-10011-1−4i4i−4i4i000011-1-1-1-1-1-111110000−55−555−5−55ii−i−iii−i−i−i5i5i5−i5−i5i5i5−i500000000000000000000000000
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Here ζ is a primitive root of unity of order 40 (ζ40 = 1); i = ζ10.