Finite Group Databasebeta

← Group #13020852

Character table — Group #13020852

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11112222444444444444455558888888888888888101010101616161616161616202020202040404040404040404040404080808080
order12224444458888101010202020202222888820202020404040404040404044444040404040404040488884444888888884444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-11111-1-1-1-1
χ41111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111-1-1-1-11111111111111111-1-1-1-111111111-1-1-1-1-1i−ii−i-1-1-1-1ii−i−ii−ii−i
χ6111111111111111111111-1-1-1-11111111111111111-1-1-1-111111111-1-1-1-1-1−ii−ii-1-1-1-1−i−iii−ii−ii
χ7111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1i−ii−i1111ii−i−i−ii−ii
χ8111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−ii−ii1111−i−iiii−ii−i
χ91111111111-1-1-1-11111111111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1-1-1111111-1-1-1-1-1-111-1-1
χ101111111111-1-1-1-11111111111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-11111-1-111
χ111111111111-1-1-1-111111111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1-1-11111-1-111-1-1-1-1-1-111
χ121111111111-1-1-1-111111111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1-1-1-1-1-1-1-1-111111111-1-1
χ131111111111-1-1-1-11111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111i−ii−i-1-111−i−iiii−i−ii
χ141111111111-1-1-1-11111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111−ii−ii-1-111ii−i−i−iii−i
χ151111111111-1-1-1-11111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11111i−ii−i11-1-1−i−iii−iii−i
χ161111111111-1-1-1-11111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11111−ii−ii11-1-1ii−i−ii−i−ii
χ1722222-2-22-220000222222222220000-2-2-2-20000000022-2-200000000-2000022-2-2000000000000
χ1822222-2-22-220000222222222220000-2-2-2-20000000022-2-200000000-20000-2-222000000000000
χ1922222-2-22-2200002222222-2-2-2-20000-2-2-2-200000000-2-22200000000200002i−2i−2i2i000000000000
χ2022222-2-22-2200002222222-2-2-2-20000-2-2-2-200000000-2-2220000000020000−2i2i2i−2i000000000000
χ212222-222-2-2222-2-2222-2-2-2-222220000-2-2222222-2-2-2-2-2-22200000000-222-2-20000000000000000
χ222222-222-2-2222-2-2222-2-2-2-2-2-2-2-20000-2-2222222-2-2-2-222-2-2000000002-2-2220000000000000000
χ232222-222-2-22-2-222222-2-2-2-222220000-2-222-2-2-2-22222-2-22200000000-2-2-2220000000000000000
χ242222-222-2-22-2-222222-2-2-2-2-2-2-2-20000-2-222-2-2-2-2222222-2-200000000222-2-20000000000000000
χ252222-2-2-2-2220000222-2-2-2-22222000022-2-200000000-2-2-2-20000000020000000000002i−2i2i−2i0000
χ262222-2-2-2-2220000222-2-2-2-22222000022-2-200000000-2-2-2-2000000002000000000000−2i2i−2i2i0000
χ272222-2-2-2-2220000222-2-2-2-2-2-2-2-2000022-2-200000000222200000000-20000000000002-2-220000
χ282222-2-2-2-2220000222-2-2-2-2-2-2-2-2000022-2-200000000222200000000-2000000000000-222-20000
χ2922-2-202-2002002i−2i2-2-200002-22-2i2−i22−2002-200002i2i−2i−2i00-22i2i2−i2−i222−2−20002i−2i0000i2−i22−200000000
χ3022-2-202-2002002i−2i2-2-200002-22-2−i2i2−22002-200002i2i−2i−2i00-22−i2−i2i2i2−2−2220002i−2i0000−i2i2−2200000000
χ3122-2-202-2002002i−2i2-2-20000-22-22i2−i22−2002-200002i2i−2i−2i002-2i2i2−i2−i222−2−2000−2i2i0000−i2i2−2200000000
χ3222-2-202-2002002i−2i2-2-20000-22-22−i2i2−22002-200002i2i−2i−2i002-2−i2−i2i2i2−2−222000−2i2i0000i2−i22−200000000
χ3322-2-202-200200−2i2i2-2-200002-22-2i2−i2−22002-20000−2i−2i2i2i00-22i2i2−i2−i2−2−222000−2i2i0000i2−i2−2200000000
χ3422-2-202-200200−2i2i2-2-200002-22-2−i2i22−2002-20000−2i−2i2i2i00-22−i2−i2i2i222−2−2000−2i2i0000−i2i22−200000000
χ3522-2-202-200200−2i2i2-2-20000-22-22i2−i2−22002-20000−2i−2i2i2i002-2i2i2−i2−i2−2−2220002i−2i0000−i2i22−200000000
χ3622-2-202-200200−2i2i2-2-20000-22-22−i2i22−2002-20000−2i−2i2i2i002-2−i2−i2i2i222−2−20002i−2i0000i2−i2−2200000000
χ37444444444-14444-1-1-1-1-1-1-100004444-1-1-1-1-1-1-1-1-1-1-1-10000-1-1-1-1-1-1-1-1000000000000000000000
χ38444444444-14444-1-1-1-1-1-1-10000-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-1000011111111000000000000000000000
χ39444444444-1-4-4-4-4-1-1-1-1-1-1-1000044-4-4-1-1-1-1111111110000-1-1-1-11111000000000000000000000
χ40444444444-1-4-4-4-4-1-1-1-1-1-1-10000-4-444-1-1-1-11111111100001111-1-1-1-1000000000000000000000
χ414444-444-4-4-144-4-4-1-1-111110000000011-1-1-1-1-1-111110000i5−i5i5−i5i5−i5i5−i5000000000000000000000
χ424444-444-4-4-144-4-4-1-1-111110000000011-1-1-1-1-1-111110000−i5i5−i5i5−i5i5−i5i5000000000000000000000
χ434444-444-4-4-1-4-444-1-1-111110000000011-1-11111-1-1-1-10000i5−i5i5−i5−i5i5−i5i5000000000000000000000
χ444444-444-4-4-1-4-444-1-1-111110000000011-1-11111-1-1-1-10000−i5i5−i5i5i5−i5i5−i5000000000000000000000
χ4544-4-404-400-1004i−4i-111i5−i5i5−i500002i2−2i222−22i5−i5-1155−5−5−i−iii0000ζ7+ζ21+ζ23+ζ29ζ13+ζ31+ζ37+ζ39−ζ7−ζ21−ζ23−ζ29−ζ13−ζ31−ζ37−ζ39−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39000000000000000000000
χ4644-4-404-400-1004i−4i-111i5−i5i5−i50000−2i22i2−2222i5−i5-1155−5−5−i−iii0000−ζ7−ζ21−ζ23−ζ29−ζ13−ζ31−ζ37−ζ39ζ7+ζ21+ζ23+ζ29ζ13+ζ31+ζ37+ζ39ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39000000000000000000000
χ4744-4-404-400-1004i−4i-111−i5i5−i5i500002i2−2i222−22−i5i5-11−5−555−i−iii0000ζ13+ζ31+ζ37+ζ39ζ7+ζ21+ζ23+ζ29−ζ13−ζ31−ζ37−ζ39−ζ7−ζ21−ζ23−ζ29ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ29−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ29000000000000000000000
χ4844-4-404-400-1004i−4i-111−i5i5−i5i50000−2i22i2−2222−i5i5-11−5−555−i−iii0000−ζ13−ζ31−ζ37−ζ39−ζ7−ζ21−ζ23−ζ29ζ13+ζ31+ζ37+ζ39ζ7+ζ21+ζ23+ζ29−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ29ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ29000000000000000000000
χ4944-4-404-400-100−4i4i-111i5−i5i5−i500002i2−2i2−2222i5−i5-11−5−555ii−i−i0000ζ7+ζ21+ζ23+ζ29ζ13+ζ31+ζ37+ζ39−ζ7−ζ21−ζ23−ζ29−ζ13−ζ31−ζ37−ζ39ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39000000000000000000000
χ5044-4-404-400-100−4i4i-111i5−i5i5−i50000−2i22i222−22i5−i5-11−5−555ii−i−i0000−ζ7−ζ21−ζ23−ζ29−ζ13−ζ31−ζ37−ζ39ζ7+ζ21+ζ23+ζ29ζ13+ζ31+ζ37+ζ39−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39000000000000000000000
χ5144-4-404-400-100−4i4i-111−i5i5−i5i500002i2−2i2−2222−i5i5-1155−5−5ii−i−i0000ζ13+ζ31+ζ37+ζ39ζ7+ζ21+ζ23+ζ29−ζ13−ζ31−ζ37−ζ39−ζ7−ζ21−ζ23−ζ29−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ29ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ29000000000000000000000
χ5244-4-404-400-100−4i4i-111−i5i5−i5i50000−2i22i222−22−i5i5-1155−5−5ii−i−i0000−ζ13−ζ31−ζ37−ζ39−ζ7−ζ21−ζ23−ζ29ζ13+ζ31+ζ37+ζ39ζ7+ζ21+ζ23+ζ29ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ29−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ29000000000000000000000
χ5344-4-40-4400400004-4-400004-44-4000000-4400000000004-400000000000000000000000000000
χ5444-4-40-4400400004-4-40000-44-44000000-440000000000-4400000000000000000000000000000
χ554-44-400000422−2200-44-4000044-4-40000000022−2222−220000000000000000022−22000000000000000000
χ564-44-400000422−2200-44-40000-4-4440000000022−2222−2200000000000000000−2222000000000000000000
χ574-44-4000004−222200-44-4000044-4-400000000−2222−222200000000000000000−2222000000000000000000
χ584-44-4000004−222200-44-40000-4-44400000000−2222−22220000000000000000022−22000000000000000000
χ594-4-44400-4040000-4-4444-4-44-4-4400000000000000004-40000000000000000000000000000000
χ604-4-44400-4040000-4-4444-4-4-444-40000000000000000-440000000000000000000000000000000
χ614-4-44-4004040000-4-44-4-4444-4-440000000000000000-440000000000000000000000000000000
χ624-4-44-4004040000-4-44-4-444-444-400000000000000004-40000000000000000000000000000000
χ6388888-8-88-8-20000-2-2-2-2-2-2-200000000222200000000000000000000000000000000000000000
χ648888-8-8-8-88-20000-2-2-2222200000000-2-22200000000000000000000000000000000000000000
χ6588-8-80-8800-20000-2222i5−2i52i5−2i500000000−2i52i52-200000000000000000000000000000000000000000
χ6688-8-80-8800-20000-222−2i52i5−2i52i5000000002i5−2i52-200000000000000000000000000000000000000000
χ678-88-800000-242−42002-222i5−2i5−2i52i5000000000000−22−22i10−i10i10−i10000000000000000000000000000000000
χ688-88-800000-242−42002-22−2i52i52i5−2i5000000000000−22−22−i10i10−i10i10000000000000000000000000000000000
χ698-88-800000-2−4242002-222i5−2i5−2i52i50000000000002−22−2−i10i10−i10i10000000000000000000000000000000000
χ708-88-800000-2−4242002-22−2i52i52i5−2i50000000000002−22−2i10−i10i10−i10000000000000000000000000000000000
χ718-8-88800-80-2000022-2-2-22200000000000010−10−101010−10−1010000000000000000000000000000000000
χ728-8-88800-80-2000022-2-2-222000000000000−101010−10−101010−10000000000000000000000000000000000
χ738-8-88-80080-2000022-222-2-200000000000010−10−1010−101010−10000000000000000000000000000000000
χ748-8-88-80080-2000022-222-2-2000000000000−101010−1010−10−1010000000000000000000000000000000000

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