Finite Group Databasebeta

← Group #13022590

Character table — Group #13022590

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111222222444444444444555588888888888888881010101010101616161616161616202020204040404040404040404040404040404040404040
order12222244445888810101020202020444424881010202040404040404040402222441010202040404040888824444444448888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1iiii−i−i−i−i-1-1iiii−i−i−i−i
χ61111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1−i−i−i−iiiii-1-1−i−i−i−iiiii
χ71111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111iiii−i−i−i−i11−i−i−i−iiiii
χ81111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111−i−i−i−iiiii11iiii−i−i−i−i
χ911111111111-1-1-1-11111111111111-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-111-1-1
χ1011111111111-1-1-1-11111111111111-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-111-1-111
χ1111111111111-1-1-1-111111111111-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-1-111-1-111
χ1211111111111-1-1-1-111111111111-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1111111-1-111-1-1
χ1311111111111-1-1-1-11111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1ii−i−i−i−iii11ii−i−i−i−iii
χ1411111111111-1-1-1-11111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1−i−iiiii−i−i11−i−iiiii−i−i
χ1511111111111-1-1-1-11111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111ii−i−i−i−iii-1-1−i−iiiii−i−i
χ1611111111111-1-1-1-11111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111−i−iiiii−i−i-1-1ii−i−i−i−iii
χ17222222-2-2-2-220000222-2-2-2-22222002i−2i22-2-200000000-2-2-2-22200002i2i−2i−2i000000000000002i−2i00000000
χ18222222-2-2-2-220000222-2-2-2-2222200−2i2i22-2-200000000-2-2-2-2220000−2i−2i2i2i00000000000000−2i2i00000000
χ19222222-2-2-2-220000222-2-2-2-2-2-2-2-2002i−2i22-2-2000000002222-2-200002i2i−2i−2i00000000000000−2i2i00000000
χ20222222-2-2-2-220000222-2-2-2-2-2-2-2-200−2i2i22-2-2000000002222-2-20000−2i−2i2i2i000000000000002i−2i00000000
χ212222-2-222-2-220000222-2-2-2-222222-200-2-222000000002-2-22-2-222-2-200000000-22000000000000000000
χ222222-2-222-2-220000222-2-2-2-22222-2200-2-222000000002-2-22-2-2-2-222000000002-2000000000000000000
χ232222-2-222-2-220000222-2-2-2-2-2-2-2-22-200-2-22200000000-222-22222-2-2000000002-2000000000000000000
χ242222-2-222-2-220000222-2-2-2-2-2-2-2-2-2200-2-22200000000-222-222-2-22200000000-22000000000000000000
χ252222-2-2-2-222222-2-2222222222220000-2-2-2-22222-2-2-2-2-222-2-2-20000000022-2-200000000000000000000
χ262222-2-2-2-222222-2-22222222-2-2-2-20000-2-2-2-22222-2-2-2-22-2-222200000000-2-22200000000000000000000
χ272222-2-2-2-2222-2-222222222222220000-2-2-2-2-2-2-2-22222-222-2-2-200000000-2-22200000000000000000000
χ282222-2-2-2-2222-2-2222222222-2-2-2-20000-2-2-2-2-2-2-2-222222-2-22220000000022-2-200000000000000000000
χ292-2-222-22-22-220000-2-2222-2-222-2-200002-22-20000000022-2-22-200000000000000002i−2i002i−2i0000000000
χ302-2-222-22-22-220000-2-2222-2-222-2-200002-22-20000000022-2-22-20000000000000000−2i2i00−2i2i0000000000
χ312-2-222-22-22-220000-2-2222-2-2-2-22200002-22-200000000-2-222-2200000000000000002-200-220000000000
χ322-2-222-22-22-220000-2-2222-2-2-2-22200002-22-200000000-2-222-220000000000000000-22002-20000000000
χ332-2-222-2-22-2220000-2-22-2-22222-2-200002-2-2200000000-2-2222-20000000000000000000000002-2002-200
χ342-2-222-2-22-2220000-2-22-2-22222-2-200002-2-2200000000-2-2222-2000000000000000000000000-2200-2200
χ352-2-222-2-22-2220000-2-22-2-222-2-22200002-2-220000000022-2-2-220000000000000000000000002i−2i00−2i2i00
χ362-2-222-2-22-2220000-2-22-2-222-2-22200002-2-220000000022-2-2-22000000000000000000000000−2i2i002i−2i00
χ372-2-22-222-2-2220000-2-22-2-22222-2-20000-222-2000000002-22-2-22000000000000000000000000002i−2i002i−2i
χ382-2-22-222-2-2220000-2-22-2-22222-2-20000-222-2000000002-22-2-2200000000000000000000000000−2i2i00−2i2i
χ392-2-22-222-2-2220000-2-22-2-222-2-2220000-222-200000000-22-222-2000000000000000000000000002-200-22
χ402-2-22-222-2-2220000-2-22-2-222-2-2220000-222-200000000-22-222-200000000000000000000000000-22002-2
χ412-2-22-22-222-220000-2-2222-2-222-2-20000-22-2200000000-22-22-22000000000000002-2002-2000000000000
χ422-2-22-22-222-220000-2-2222-2-222-2-20000-22-2200000000-22-22-2200000000000000-2200-22000000000000
χ432-2-22-22-222-220000-2-2222-2-2-2-2220000-22-22000000002-22-22-2000000000000002i−2i00−2i2i000000000000
χ442-2-22-22-222-220000-2-2222-2-2-2-2220000-22-22000000002-22-22-200000000000000−2i2i002i−2i000000000000
χ454444444444-14444-1-1-1-1-1-1-100004444-1-1-1-1-1-1-1-1-1-1-1-1000000-1-1-1-1-1-1-1-1000000000000000000000000
χ464444444444-14444-1-1-1-1-1-1-10000-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-100000011111111000000000000000000000000
χ474444444444-1-4-4-4-4-1-1-1-1-1-1-1000044-4-4-1-1-1-111111111000000-1-1-1-11111000000000000000000000000
χ484444444444-1-4-4-4-4-1-1-1-1-1-1-10000-4-444-1-1-1-1111111110000001111-1-1-1-1000000000000000000000000
χ49444444-4-4-4-4-10000-1-1-111110000004i−4i-1-111i5i5−i5−i5i5i5−i5−i50000005−55−5−i−iii000000000000000000000000
χ50444444-4-4-4-4-10000-1-1-111110000004i−4i-1-111−i5−i5i5i5−i5−i5i5i5000000−55−55−i−iii000000000000000000000000
χ51444444-4-4-4-4-10000-1-1-11111000000−4i4i-1-111i5i5−i5−i5i5i5−i5−i5000000−55−55ii−i−i000000000000000000000000
χ52444444-4-4-4-4-10000-1-1-11111000000−4i4i-1-111−i5−i5i5i5−i5−i5i5i50000005−55−5ii−i−i000000000000000000000000
χ534444-4-444-4-4-10000-1-1-1111100004-40011-1-1i5i5−i5−i5−i5−i5i5i5000000-1-111i5−i5i5−i5000000000000000000000000
χ544444-4-444-4-4-10000-1-1-1111100004-40011-1-1−i5−i5i5i5i5i5−i5−i5000000-1-111−i5i5−i5i5000000000000000000000000
χ554444-4-444-4-4-10000-1-1-111110000-440011-1-1i5i5−i5−i5−i5−i5i5i500000011-1-1−i5i5−i5i5000000000000000000000000
χ564444-4-444-4-4-10000-1-1-111110000-440011-1-1−i5−i5i5i5i5i5−i5−i500000011-1-1i5−i5i5−i5000000000000000000000000
χ574444-4-4-4-444-144-4-4-1-1-1-1-1-1-1000000001111-1-1-1-111110000005−5−555−5−55000000000000000000000000
χ584444-4-4-4-444-144-4-4-1-1-1-1-1-1-1000000001111-1-1-1-11111000000−555−5−555−5000000000000000000000000
χ594444-4-4-4-444-1-4-444-1-1-1-1-1-1-10000000011111111-1-1-1-10000005−5−55−555−5000000000000000000000000
χ604444-4-4-4-444-1-4-444-1-1-1-1-1-1-10000000011111111-1-1-1-1000000−555−55−5−55000000000000000000000000
χ6144-4-40000004002i2−2i24-4-400004i−4i4i−4i0000000000002i2−2i22i2−2i2000000000000000022−2200000000000000000000
χ6244-4-40000004002i2−2i24-4-40000−4i4i−4i4i0000000000002i2−2i22i2−2i20000000000000000−222200000000000000000000
χ6344-4-4000000400−2i22i24-4-400004i−4i4i−4i000000000000−2i22i2−2i22i20000000000000000−222200000000000000000000
χ6444-4-4000000400−2i22i24-4-40000−4i4i−4i4i000000000000−2i22i2−2i22i2000000000000000022−2200000000000000000000
χ654-44-4000000422−2200-44-400004i−4i−4i4i0000000022−2222−220000000000000000002i2−2i20000000000000000000000
χ664-44-4000000422−2200-44-40000−4i4i4i−4i0000000022−2222−22000000000000000000−2i22i20000000000000000000000
χ674-44-40000004−222200-44-400004i−4i−4i4i00000000−2222−2222000000000000000000−2i22i20000000000000000000000
χ684-44-40000004−222200-44-40000−4i4i4i−4i00000000−2222−22220000000000000000002i2−2i20000000000000000000000
χ6988-8-8000000-2004i2−4i2-2222i5−2i52i5−2i500000000000000002ζ7+2ζ21+2ζ23+2ζ29−2ζ7−2ζ21−2ζ23−2ζ292ζ13+2ζ31+2ζ37+2ζ39−2ζ13−2ζ31−2ζ37−2ζ3900000000000000000000000000000000000000
χ7088-8-8000000-2004i2−4i2-222−2i52i5−2i52i500000000000000002ζ13+2ζ31+2ζ37+2ζ39−2ζ13−2ζ31−2ζ37−2ζ392ζ7+2ζ21+2ζ23+2ζ29−2ζ7−2ζ21−2ζ23−2ζ2900000000000000000000000000000000000000
χ7188-8-8000000-200−4i24i2-2222i5−2i52i5−2i50000000000000000−2ζ7−2ζ21−2ζ23−2ζ292ζ7+2ζ21+2ζ23+2ζ29−2ζ13−2ζ31−2ζ37−2ζ392ζ13+2ζ31+2ζ37+2ζ3900000000000000000000000000000000000000
χ7288-8-8000000-200−4i24i2-222−2i52i5−2i52i50000000000000000−2ζ13−2ζ31−2ζ37−2ζ392ζ13+2ζ31+2ζ37+2ζ39−2ζ7−2ζ21−2ζ23−2ζ292ζ7+2ζ21+2ζ23+2ζ2900000000000000000000000000000000000000
χ738-88-8000000-242−42002-222i5−2i5−2i52i5000000000000−2ζ7+2ζ21−2ζ23+2ζ292ζ7−2ζ21+2ζ23−2ζ292ζ13−2ζ31+2ζ37−2ζ39−2ζ13+2ζ31−2ζ37+2ζ39000000000000000000000000000000000000000000
χ748-88-8000000-242−42002-22−2i52i52i5−2i50000000000002ζ13−2ζ31+2ζ37−2ζ39−2ζ13+2ζ31−2ζ37+2ζ39−2ζ7+2ζ21−2ζ23+2ζ292ζ7−2ζ21+2ζ23−2ζ29000000000000000000000000000000000000000000
χ758-88-8000000-2−4242002-222i5−2i5−2i52i50000000000002ζ7−2ζ21+2ζ23−2ζ29−2ζ7+2ζ21−2ζ23+2ζ29−2ζ13+2ζ31−2ζ37+2ζ392ζ13−2ζ31+2ζ37−2ζ39000000000000000000000000000000000000000000
χ768-88-8000000-2−4242002-22−2i52i52i5−2i5000000000000−2ζ13+2ζ31−2ζ37+2ζ392ζ13−2ζ31+2ζ37−2ζ392ζ7−2ζ21+2ζ23−2ζ29−2ζ7+2ζ21−2ζ23+2ζ29000000000000000000000000000000000000000000
χ778-8-888-88-88-8-2000022-2-2-22200000000-22-220000000000000000000000000000000000000000000000
χ788-8-888-8-88-88-2000022-222-2-200000000-222-20000000000000000000000000000000000000000000000
χ798-8-88-888-8-88-2000022-222-2-2000000002-2-220000000000000000000000000000000000000000000000
χ808-8-88-88-888-8-2000022-2-2-222000000002-22-20000000000000000000000000000000000000000000000

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