Finite Group Databasebeta

← Group #13018293

Character table — Group #13018293

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size11112222224444444444444444444444444444888888888888888888888888101010101010101010101010202020202020202020208080808080808080
order12222244444444588888888101010101010102020202020202020202020202020202040404040404040404040404040404040444488888888222244888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii
χ5111111111111111-1-1-1-1-1-1-1-111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-1
χ6111111111111111-1-1-1-1-1-1-1-111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-111
χ7111111111111111-1-1-1-1-1-1-1-111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111ii−i−i−i−iii
χ8111111111111111-1-1-1-1-1-1-1-111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111−i−iiiii−i−i
χ91111111111-1-1-1-111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11-11-11-11-1
χ101111111111-1-1-1-111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-11-11-11-11
χ111111111111-1-1-1-111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111i−ii−i−ii−ii
χ121111111111-1-1-1-111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−ii−iii−ii−i
χ131111111111-1-1-1-11-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-111111-1-111-1-11
χ141111111111-1-1-1-11-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-111-1-111-1
χ151111111111-1-1-1-11-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-11111-1-1-1-1i−i−ii−iii−i
χ161111111111-1-1-1-11-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-11111-1-1-1-1−iii−ii−i−ii
χ17222222-2-2-2-222-2-22000000002222222-2-2-2-2-2-2-2-22222-2-2-2-20000000000000000222200000000-2-222-2-2000000000000
χ18222222-2-2-2-222-2-22000000002222222-2-2-2-2-2-2-2-22222-2-2-2-20000000000000000-2-2-2-20000000022-2-222000000000000
χ19222222-2-2-2-2-2-2222000000002222222-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000222200000000-2-2-2-222000000000000
χ20222222-2-2-2-2-2-2222000000002222222-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000-2-2-2-2000000002222-2-2000000000000
χ212222-2-222-2-20000200002i2i−2i−2i-2-2-2-22222222-2-2-2-200000000000000002i2i2i2i−2i−2i−2i−2i22-2-2000000002-200002i2i−2i−2i00000000
χ222222-2-222-2-20000200002i2i−2i−2i-2-2-2-22222222-2-2-2-200000000000000002i2i2i2i−2i−2i−2i−2i-2-22200000000-220000−2i−2i2i2i00000000
χ232222-2-222-2-2000020000−2i−2i2i2i-2-2-2-22222222-2-2-2-20000000000000000−2i−2i−2i−2i2i2i2i2i22-2-2000000002-20000−2i−2i2i2i00000000
χ242222-2-222-2-2000020000−2i−2i2i2i-2-2-2-22222222-2-2-2-20000000000000000−2i−2i−2i−2i2i2i2i2i-2-22200000000-2200002i2i−2i−2i00000000
χ252222-2-2-2-2220000222-2-20000-2-2-2-2222-2-2-2-22222000000002222-2-2-2-20000000022-2-22222-2-2-2-2-220000000000000000
χ262222-2-2-2-2220000222-2-20000-2-2-2-2222-2-2-2-22222000000002222-2-2-2-200000000-2-222-2-2-2-222222-20000000000000000
χ272222-2-2-2-22200002-2-2220000-2-2-2-2222-2-2-2-2222200000000-2-2-2-222220000000022-2-2-2-2-2-22222-220000000000000000
χ282222-2-2-2-22200002-2-2220000-2-2-2-2222-2-2-2-2222200000000-2-2-2-2222200000000-2-2222222-2-2-2-22-20000000000000000
χ2922-2-22-20000002-222−22−22−22−222-2-22-2-200000000000022-2-222−2−222−2−222−2−222−2−22i−2i2i−2ii2i2−i2−i2i2i2−i2−i200002i−2ii2−i2i2−i200000000
χ3022-2-22-20000002-222−22−22−22−222-2-22-2-200000000000022-2-222−2−222−2−222−2−222−2−2−2i2i−2i2i−i2−i2i2i2−i2−i2i2i20000−2i2i−i2i2−i2i200000000
χ3122-2-22-20000002-22−22−22−22−2222-2-22-2-200000000000022-2-2−2−222−2−222−2−222−2−2222i−2i2i−2i−i2−i2i2i2−i2−i2i2i200002i−2i−i2i2−i2i200000000
χ3222-2-22-20000002-22−22−22−22−2222-2-22-2-200000000000022-2-2−2−222−2−222−2−222−2−222−2i2i−2i2ii2i2−i2−i2i2i2−i2−i20000−2i2ii2−i2i2−i200000000
χ3322-2-22-2000000-2222−22−2−22−2222-2-22-2-2000000000000-2-22222−2−222−2−2−2−222−2−2222i−2i2i−2ii2i2−i2−i2i2i2−i2−i20000−2i2i−i2i2−i2i200000000
χ3422-2-22-2000000-2222−22−2−22−2222-2-22-2-2000000000000-2-22222−2−222−2−2−2−222−2−222−2i2i−2i2i−i2−i2i2i2−i2−i2i2i200002i−2ii2−i2i2−i200000000
χ3522-2-22-2000000-222−22−222−22−222-2-22-2-2000000000000-2-222−2−222−2−22222−2−222−2−22i−2i2i−2i−i2−i2i2i2−i2−i2i2i20000−2i2ii2−i2i2−i200000000
χ3622-2-22-2000000-222−22−222−22−222-2-22-2-2000000000000-2-222−2−222−2−22222−2−222−2−2−2i2i−2i2ii2i2−i2−i2i2i2−i2−i200002i−2i−i2i2−i2i200000000
χ3722-2-2-2200002i−2i0022−2−22i2−i2−i2i2-2-2222-2-2000000002i2i−2i−2i000022−2−2−2−222i2i2−i2−i2−i2−i2i2i22i−2i−2i2ii2i2−i2−i2−i2−i2i2i2002-200−222−200000000
χ3822-2-2-2200002i−2i0022−2−22i2−i2−i2i2-2-2222-2-2000000002i2i−2i−2i000022−2−2−2−222i2i2−i2−i2−i2−i2i2i2−2i2i2i−2i−i2−i2i2i2i2i2−i2−i200-22002−2−2200000000
χ3922-2-2-2200002i−2i002−222−2−i2i2i2−i2-2-2222-2-2000000002i2i−2i−2i0000−2−22222−2−2−i2−i2i2i2i2i2−i2−i22i−2i−2i2i−i2−i2i2i2i2i2−i2−i2002-2002−2−2200000000
χ4022-2-2-2200002i−2i002−222−2−i2i2i2−i2-2-2222-2-2000000002i2i−2i−2i0000−2−22222−2−2−i2−i2i2i2i2i2−i2−i2−2i2i2i−2ii2i2−i2−i2−i2−i2i2i200-2200−222−200000000
χ4122-2-2-220000−2i2i0022−2−22−i2i2i2−i2-2-2222-2-200000000−2i−2i2i2i000022−2−2−2−222−i2−i2i2i2i2i2−i2−i22i−2i−2i2ii2i2−i2−i2−i2−i2i2i200-22002−2−2200000000
χ4222-2-2-220000−2i2i0022−2−22−i2i2i2−i2-2-2222-2-200000000−2i−2i2i2i000022−2−2−2−222−i2−i2i2i2i2i2−i2−i2−2i2i2i−2i−i2−i2i2i2i2i2−i2−i2002-200−222−200000000
χ4322-2-2-220000−2i2i002−222−2i2−i2−i2i2-2-2222-2-200000000−2i−2i2i2i0000−2−22222−2−2i2i2−i2−i2−i2−i2i2i22i−2i−2i2i−i2−i2i2i2i2i2−i2−i200-2200−222−200000000
χ4422-2-2-220000−2i2i002−222−2i2−i2−i2i2-2-2222-2-200000000−2i−2i2i2i0000−2−22222−2−2i2i2−i2−i2−i2−i2i2i2−2i2i2i−2ii2i2−i2−i2−i2−i2i2i2002-2002−2−2200000000
χ4544444444444444-144444444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000000000
χ4644444444444444-1-4-4-4-4-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111000000000000000000000000000000
χ474444444444-4-4-4-4-14444-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111000000000000000000000000000000
χ484444444444-4-4-4-4-1-4-4-4-44444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1000000000000000000000000000000
χ49444444-4-4-4-444-4-4-100000000-1-1-1-1-1-1-111111111-1-1-1-11111i5−i5i5−i5i5−i5i5−i5i5−i5i5−i5i5−i5i5−i5000000000000000000000000000000
χ50444444-4-4-4-444-4-4-100000000-1-1-1-1-1-1-111111111-1-1-1-11111−i5i5−i5i5−i5i5−i5i5−i5i5−i5i5−i5i5−i5i5000000000000000000000000000000
χ51444444-4-4-4-4-4-444-100000000-1-1-1-1-1-1-1111111111111-1-1-1-1i5−i5i5−i5i5−i5i5−i5−i5i5−i5i5−i5i5−i5i5000000000000000000000000000000
χ52444444-4-4-4-4-4-444-100000000-1-1-1-1-1-1-1111111111111-1-1-1-1−i5i5−i5i5−i5i5−i5i5i5−i5i5−i5i5−i5i5−i5000000000000000000000000000000
χ534444-4-444-4-40000-100004i4i−4i−4i1111-1-1-1-1-1-1-111115−55−55−55−5i5−i5i5−i5−i5i5−i5i5−i−i−i−iiiii000000000000000000000000000000
χ544444-4-444-4-40000-100004i4i−4i−4i1111-1-1-1-1-1-1-11111−55−55−55−55−i5i5−i5i5i5−i5i5−i5−i−i−i−iiiii000000000000000000000000000000
χ554444-4-444-4-40000-10000−4i−4i4i4i1111-1-1-1-1-1-1-111115−55−55−55−5−i5i5−i5i5i5−i5i5−i5iiii−i−i−i−i000000000000000000000000000000
χ564444-4-444-4-40000-10000−4i−4i4i4i1111-1-1-1-1-1-1-11111−55−55−55−55i5−i5i5−i5−i5i5−i5i5iiii−i−i−i−i000000000000000000000000000000
χ574444-4-4-4-4440000-144-4-400001111-1-1-11111-1-1-1-15−55−5−55−55-1-1-1-111115−55−5−55−55000000000000000000000000000000
χ584444-4-4-4-4440000-144-4-400001111-1-1-11111-1-1-1-1−55−555−55−5-1-1-1-11111−55−555−55−5000000000000000000000000000000
χ594444-4-4-4-4440000-1-4-44400001111-1-1-11111-1-1-1-15−55−5−55−551111-1-1-1-1−55−555−55−5000000000000000000000000000000
χ604444-4-4-4-4440000-1-4-44400001111-1-1-11111-1-1-1-1−55−555−55−51111-1-1-1-15−55−5−55−55000000000000000000000000000000
χ6144-4-44-40000004-4-122−2222−2222−2222−22-1-111-111i5i5−i5−i5i5−i5i5−i5i5−i5−i5i5-1-111−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ29−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ29ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ29−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ29000000000000000000000000000000
χ6244-4-44-40000004-4-122−2222−2222−2222−22-1-111-111−i5−i5i5i5−i5i5−i5i5−i5i5i5−i5-1-111ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ29−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ29ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ29−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ29−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39000000000000000000000000000000
χ6344-4-44-40000004-4-1−2222−2222−2222−2222-1-111-111i5i5−i5−i5i5−i5i5−i5i5−i5−i5i5-1-111ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ29ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ29−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ29ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ29000000000000000000000000000000
χ6444-4-44-40000004-4-1−2222−2222−2222−2222-1-111-111−i5−i5i5i5−i5i5−i5i5−i5i5i5−i5-1-111−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ29ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ29−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ29ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ29ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39000000000000000000000000000000
χ6544-4-44-4000000-44-122−2222−22−2222−2222-1-111-111i5i5−i5−i5i5−i5i5−i5−i5i5i5−i511-1-1−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ29ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ29−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ29ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ29000000000000000000000000000000
χ6644-4-44-4000000-44-122−2222−22−2222−2222-1-111-111−i5−i5i5i5−i5i5−i5i5i5−i5−i5i511-1-1ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ29−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ29ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ29−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ29ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39000000000000000000000000000000
χ6744-4-44-4000000-44-1−2222−222222−2222−22-1-111-111i5i5−i5−i5i5−i5i5−i5−i5i5i5−i511-1-1ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ29−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ29ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ29−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ29000000000000000000000000000000
χ6844-4-44-4000000-44-1−2222−222222−2222−22-1-111-111−i5−i5i5i5−i5i5−i5i5i5−i5−i5i511-1-1−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ29ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ29−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ29ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ29−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39000000000000000000000000000000
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Here ζ is a primitive root of unity of order 40 (ζ40 = 1); i = ζ10.