Finite Group Databasebeta

← Group #13019019

Character table — Group #13019019

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111222244444444444444455558888888888888881010101016161616161616162020202020202020202020404040404040404040404040408080
order12224444444588881010102020202044442882020202040404040404040402244101020204040404044488888888444448888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-11-1-1-1-111-1-1-1-1-1-1-1-1
χ311111111111111111111111-1-1-1-1111111111111111-1-1-1-111111111-1-1-1-1-1-1-1ii−i−i-1ii−i−i-1-1ii−i−ii−ii−i
χ411111111111111111111111-1-1-1-1111111111111111-1-1-1-111111111-1-1-1-1-1-1-1−i−iii-1−i−iii-1-1−i−iii−ii−ii
χ5111111111111-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1111-1-1-1-111111-1-1-1-1-1-1111111-1-1
χ6111111111111-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111
χ7111111111111-1-1-1-11111111-1-1-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-11111ii−i−i-1−i−iii11ii−i−ii−i−ii
χ8111111111111-1-1-1-11111111-1-1-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-11111−i−iii-1ii−i−i11−i−iii−iii−i
χ911111111-1-111111111111111111-1-1-11111111111111111-1-1-1-1-1-1-1-11-1-111111111-11111-1-1-1-1-1-111-1-1
χ1011111111-1-111111111111111111-1-1-11111111111111111-1-1-1-1-1-1-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ1111111111-1-11111111111111-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1ii−i−i1ii−i−i11−i−iiii−i−ii
χ1211111111-1-11111111111111-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1−i−iii1−i−iii11ii−i−i−iii−i
χ1311111111-1-111-1-1-1-111111111111-1111111-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1-1-1-1-11111-1-1-1-1-111-1-1-1-11111
χ1411111111-1-111-1-1-1-111111111111-1111111-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ1511111111-1-111-1-1-1-11111111-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1111111ii−i−i1−i−iii-1-1−i−iiii−ii−i
χ1611111111-1-111-1-1-1-11111111-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1111111−i−iii1ii−i−i-1-1ii−i−i−ii−ii
χ17222222-2-222-220000222-2-2-2-22222-20022-2-20000000022-2-2-2-2220000-22200000000-200000000000000
χ18222222-2-222-220000222-2-2-2-2-2-2-2-2-20022-2-200000000-2-222-2-22200002-2-200000000200000000000000
χ19222222-2-2-2-2-220000222-2-2-2-2222220022-2-20000000022-2-222-2-20000-2-2-200000000200000000000000
χ20222222-2-2-2-2-220000222-2-2-2-2-2-2-2-220022-2-200000000-2-22222-2-2000022200000000-200000000000000
χ212222-2-22200-22000022222222222000-2-2-2-200000000-2-22200000000-2000000222200000000000-2-200
χ222222-2-22200-22000022222222222000-2-2-2-200000000-2-22200000000-2000000-2-2-2-2000000000002200
χ232222-2-22200-2200002222222-2-2-2-2000-2-2-2-20000000022-2-20000000020000002i2i−2i−2i00000000000−2i2i00
χ242222-2-22200-2200002222222-2-2-2-2000-2-2-2-20000000022-2-2000000002000000−2i−2i2i2i000000000002i−2i00
χ252222-2-2-2-200220000222-2-2-2-22222000-2-22200000000-2-2-2-2000000002000000000000000002-22-20000
χ262222-2-2-2-200220000222-2-2-2-22222000-2-22200000000-2-2-2-200000000200000000000000000-22-220000
χ272222-2-2-2-200220000222-2-2-2-2-2-2-2-2000-2-22200000000222200000000-2000000000000000002i−2i−2i2i0000
χ282222-2-2-2-200220000222-2-2-2-2-2-2-2-2000-2-22200000000222200000000-200000000000000000−2i2i2i−2i0000
χ2922-2-2002-2000222−2−2-2-22-2-2222i−2i2i−2i00000002222−2−2−2−2002i−2i00000000000i2i2−i2−i2−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3901+i−1−i1−i−1+i0000000000
χ3022-2-2002-2000222−2−2-2-22-2-2222i−2i2i−2i00000002222−2−2−2−2002i−2i00000000000i2i2−i2−i22ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ390−1−i1+i−1+i1−i0000000000
χ3122-2-2002-2000222−2−2-2-22-2-222−2i2i−2i2i00000002222−2−2−2−200−2i2i00000000000−i2−i2i2i2−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370−1+i1−i−1−i1+i0000000000
χ3222-2-2002-2000222−2−2-2-22-2-222−2i2i−2i2i00000002222−2−2−2−200−2i2i00000000000−i2−i2i2i22ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ3701−i−1+i1+i−1−i0000000000
χ3322-2-2002-20002−2−222-2-22-2-2222i−2i2i−2i0000000−2−2−2−22222002i−2i00000000000−i2−i2i2i2−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390−1−i1+i−1+i1−i0000000000
χ3422-2-2002-20002−2−222-2-22-2-2222i−2i2i−2i0000000−2−2−2−22222002i−2i00000000000−i2−i2i2i22ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ3901+i−1−i1−i−1+i0000000000
χ3522-2-2002-20002−2−222-2-22-2-222−2i2i−2i2i0000000−2−2−2−2222200−2i2i00000000000i2i2−i2−i2−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3701−i−1+i1+i−1−i0000000000
χ3622-2-2002-20002−2−222-2-22-2-222−2i2i−2i2i0000000−2−2−2−2222200−2i2i00000000000i2i2−i2−i22ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ370−1+i1−i−1−i1+i0000000000
χ372-22-22-2002i−2i02i2−i2i2−i22-2-2000022-2-202−22-200i2i2−i2−i2i2i2−i2−i2-2200002i−2i22−2−202i−2ii2−i2i2−i20000000002−200000000
χ382-22-22-2002i−2i02i2−i2i2−i22-2-20000-2-22202−22-200i2i2−i2−i2i2i2−i2−i22-200002i−2i22−2−20−2i2i−i2i2−i2i2000000000−2200000000
χ392-22-22-2002i−2i02−i2i2−i2i22-2-2000022-2-20−222-200−i2−i2i2i2−i2−i2i2i2-2200002i−2i−2−22202i−2i−i2i2−i2i2000000000−2200000000
χ402-22-22-2002i−2i02−i2i2−i2i22-2-20000-2-2220−222-200−i2−i2i2i2−i2−i2i2i22-200002i−2i−2−2220−2i2ii2−i2i2−i20000000002−200000000
χ412-22-22-200−2i2i02i2−i2i2−i22-2-2000022-2-20−222-200i2i2−i2−i2i2i2−i2−i2-220000−2i2i−2−2220−2i2ii2−i2i2−i2000000000−2200000000
χ422-22-22-200−2i2i02i2−i2i2−i22-2-20000-2-2220−222-200i2i2−i2−i2i2i2−i2−i22-20000−2i2i−2−22202i−2i−i2i2−i2i20000000002−200000000
χ432-22-22-200−2i2i02−i2i2−i2i22-2-2000022-2-202−22-200−i2−i2i2i2−i2−i2i2i2-220000−2i2i22−2−20−2i2i−i2i2−i2i20000000002−200000000
χ442-22-22-200−2i2i02−i2i2−i2i22-2-20000-2-22202−22-200−i2−i2i2i2−i2−i2i2i22-20000−2i2i22−2−202i−2ii2−i2i2−i2000000000−2200000000
χ4544444444444-14444-1-1-1-1-1-1-10000444-1-1-1-1-1-1-1-1-1-1-1-10000-1-1-1-1-1-1-1-100000000000000000000000000
χ4644444444444-1-4-4-4-4-1-1-1-1-1-1-100004-4-4-1-1-1-1111111110000-1-1-1-1111100000000000000000000000000
χ4744444444-4-44-14444-1-1-1-1-1-1-10000-4-4-4-1-1-1-1-1-1-1-1-1-1-1-100001111111100000000000000000000000000
χ4844444444-4-44-1-4-4-4-4-1-1-1-1-1-1-10000-444-1-1-1-11111111100001111-1-1-1-100000000000000000000000000
χ49444444-4-444-4-10000-1-1-111110000-400-1-111i5−i5i5−i5i5−i5i5−i5000011-1-1i5−i5i5−i500000000000000000000000000
χ50444444-4-444-4-10000-1-1-111110000-400-1-111−i5i5−i5i5−i5i5−i5i5000011-1-1−i5i5−i5i500000000000000000000000000
χ51444444-4-4-4-4-4-10000-1-1-111110000400-1-111i5−i5i5−i5i5−i5i5−i50000-1-111−i5i5−i5i500000000000000000000000000
χ52444444-4-4-4-4-4-10000-1-1-111110000400-1-111−i5i5−i5i5−i5i5−i5i50000-1-111i5−i5i5−i500000000000000000000000000
χ5344-4-400-4400040000-4-4444-4-44i−4i4i−4i00000000000000000−4i4i0000000000000000000000000000000000
χ5444-4-400-4400040000-4-4444-4-4−4i4i−4i4i000000000000000004i−4i0000000000000000000000000000000000
χ554-44-44-4004i−4i0-12i2−2i22i2−2i2-111i5−i5i5−i50000022−22-11i5−i5ζ7+ζ21+ζ23+ζ29ζ13+ζ31+ζ37+ζ39−ζ7−ζ21−ζ23−ζ29−ζ13−ζ31−ζ37−ζ39ζ7+ζ21+ζ23+ζ29ζ13+ζ31+ζ37+ζ39−ζ7−ζ21−ζ23−ζ29−ζ13−ζ31−ζ37−ζ3900005−5−iiζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ29−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ2900000000000000000000000000
χ564-44-44-4004i−4i0-12i2−2i22i2−2i2-111−i5i5−i5i50000022−22-11−i5i5ζ13+ζ31+ζ37+ζ39ζ7+ζ21+ζ23+ζ29−ζ13−ζ31−ζ37−ζ39−ζ7−ζ21−ζ23−ζ29ζ13+ζ31+ζ37+ζ39ζ7+ζ21+ζ23+ζ29−ζ13−ζ31−ζ37−ζ39−ζ7−ζ21−ζ23−ζ290000−55−ii−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ3900000000000000000000000000
χ574-44-44-4004i−4i0-1−2i22i2−2i22i2-111i5−i5i5−i500000−2222-11i5−i5−ζ7−ζ21−ζ23−ζ29−ζ13−ζ31−ζ37−ζ39ζ7+ζ21+ζ23+ζ29ζ13+ζ31+ζ37+ζ39−ζ7−ζ21−ζ23−ζ29−ζ13−ζ31−ζ37−ζ39ζ7+ζ21+ζ23+ζ29ζ13+ζ31+ζ37+ζ3900005−5−ii−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ29ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ2900000000000000000000000000
χ584-44-44-4004i−4i0-1−2i22i2−2i22i2-111−i5i5−i5i500000−2222-11−i5i5−ζ13−ζ31−ζ37−ζ39−ζ7−ζ21−ζ23−ζ29ζ13+ζ31+ζ37+ζ39ζ7+ζ21+ζ23+ζ29−ζ13−ζ31−ζ37−ζ39−ζ7−ζ21−ζ23−ζ29ζ13+ζ31+ζ37+ζ39ζ7+ζ21+ζ23+ζ290000−55−iiζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ3900000000000000000000000000
χ594-44-44-400−4i4i0-12i2−2i22i2−2i2-111i5−i5i5−i500000−2222-11i5−i5ζ7+ζ21+ζ23+ζ29ζ13+ζ31+ζ37+ζ39−ζ7−ζ21−ζ23−ζ29−ζ13−ζ31−ζ37−ζ39ζ7+ζ21+ζ23+ζ29ζ13+ζ31+ζ37+ζ39−ζ7−ζ21−ζ23−ζ29−ζ13−ζ31−ζ37−ζ390000−55i−i−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ29ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ2900000000000000000000000000
χ604-44-44-400−4i4i0-12i2−2i22i2−2i2-111−i5i5−i5i500000−2222-11−i5i5ζ13+ζ31+ζ37+ζ39ζ7+ζ21+ζ23+ζ29−ζ13−ζ31−ζ37−ζ39−ζ7−ζ21−ζ23−ζ29ζ13+ζ31+ζ37+ζ39ζ7+ζ21+ζ23+ζ29−ζ13−ζ31−ζ37−ζ39−ζ7−ζ21−ζ23−ζ2900005−5i−iζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ3900000000000000000000000000
χ614-44-44-400−4i4i0-1−2i22i2−2i22i2-111i5−i5i5−i50000022−22-11i5−i5−ζ7−ζ21−ζ23−ζ29−ζ13−ζ31−ζ37−ζ39ζ7+ζ21+ζ23+ζ29ζ13+ζ31+ζ37+ζ39−ζ7−ζ21−ζ23−ζ29−ζ13−ζ31−ζ37−ζ39ζ7+ζ21+ζ23+ζ29ζ13+ζ31+ζ37+ζ390000−55i−iζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ29−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ2900000000000000000000000000
χ624-44-44-400−4i4i0-1−2i22i2−2i22i2-111−i5i5−i5i50000022−22-11−i5i5−ζ13−ζ31−ζ37−ζ39−ζ7−ζ21−ζ23−ζ29ζ13+ζ31+ζ37+ζ39ζ7+ζ21+ζ23+ζ29−ζ13−ζ31−ζ37−ζ39−ζ7−ζ21−ζ23−ζ29ζ13+ζ31+ζ37+ζ39ζ7+ζ21+ζ23+ζ2900005−5i−i−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ3900000000000000000000000000
χ634-44-4-4400000400004-4-4000044-4-4000-4400000000004-4000000000000000000000000000000000000
χ644-44-4-4400000400004-4-40000-4-444000-440000000000-44000000000000000000000000000000000000
χ654-4-44000000042i−2i−2i2i-44-400004i−4i−4i4i00000002i2i−2i−2i−2i−2i2i2i000000000000000-222-20000000000000000000
χ664-4-44000000042i−2i−2i2i-44-40000−4i4i4i−4i00000002i2i−2i−2i−2i−2i2i2i0000000000000002-2-220000000000000000000
χ674-4-4400000004−2i2i2i−2i-44-400004i−4i−4i4i0000000−2i−2i2i2i2i2i−2i−2i0000000000000002-2-220000000000000000000
χ684-4-4400000004−2i2i2i−2i-44-40000−4i4i4i−4i0000000−2i−2i2i2i2i2i−2i−2i000000000000000-222-20000000000000000000
χ698888-8-88800-8-20000-2-2-2-2-2-2-2000000022220000000000000000000000000000000000000000000000
χ708888-8-8-8-8008-20000-2-2-22222000000022-2-20000000000000000000000000000000000000000000000
χ7188-8-8008-8000-24242−42−4222-222-2-200000000000−2−2−2−2222200000000000000000000000000000000000000
χ7288-8-8008-8000-2−42−42424222-222-2-2000000000002222−2−2−2−200000000000000000000000000000000000000
χ7388-8-800-88000-2000022-2-2-22200000000000i10−i10i10−i10−i10i10−i10i1000000000000000000000000000000000000000
χ7488-8-800-88000-2000022-2-2-22200000000000−i10i10−i10i10i10−i10i10−i1000000000000000000000000000000000000000
χ758-88-8-8800000-20000-2222i5−2i52i5−2i500000002-2−2i52i50000000000000000000000000000000000000000000000
χ768-88-8-8800000-20000-222−2i52i5−2i52i500000002-22i5−2i50000000000000000000000000000000000000000000000
χ778-8-880000000-24i−4i−4i4i2-222i5−2i5−2i52i500000000000ζ4−ζ6−ζ12−ζ14−ζ22−ζ28+ζ36−ζ38−ζ4−ζ6+ζ12−ζ14−ζ22+ζ28−ζ36−ζ38−ζ4+ζ6+ζ12+ζ14+ζ22+ζ28−ζ36+ζ38ζ4+ζ6−ζ12+ζ14+ζ22−ζ28+ζ36+ζ38−ζ4+ζ6+ζ12+ζ14+ζ22+ζ28−ζ36+ζ38ζ4+ζ6−ζ12+ζ14+ζ22−ζ28+ζ36+ζ38ζ4−ζ6−ζ12−ζ14−ζ22−ζ28+ζ36−ζ38−ζ4−ζ6+ζ12−ζ14−ζ22+ζ28−ζ36−ζ3800000000000000000000000000000000000000
χ788-8-880000000-24i−4i−4i4i2-22−2i52i52i5−2i500000000000−ζ4−ζ6+ζ12−ζ14−ζ22+ζ28−ζ36−ζ38ζ4−ζ6−ζ12−ζ14−ζ22−ζ28+ζ36−ζ38ζ4+ζ6−ζ12+ζ14+ζ22−ζ28+ζ36+ζ38−ζ4+ζ6+ζ12+ζ14+ζ22+ζ28−ζ36+ζ38ζ4+ζ6−ζ12+ζ14+ζ22−ζ28+ζ36+ζ38−ζ4+ζ6+ζ12+ζ14+ζ22+ζ28−ζ36+ζ38−ζ4−ζ6+ζ12−ζ14−ζ22+ζ28−ζ36−ζ38ζ4−ζ6−ζ12−ζ14−ζ22−ζ28+ζ36−ζ3800000000000000000000000000000000000000
χ798-8-880000000-2−4i4i4i−4i2-222i5−2i5−2i52i500000000000−ζ4+ζ6+ζ12+ζ14+ζ22+ζ28−ζ36+ζ38ζ4+ζ6−ζ12+ζ14+ζ22−ζ28+ζ36+ζ38ζ4−ζ6−ζ12−ζ14−ζ22−ζ28+ζ36−ζ38−ζ4−ζ6+ζ12−ζ14−ζ22+ζ28−ζ36−ζ38ζ4−ζ6−ζ12−ζ14−ζ22−ζ28+ζ36−ζ38−ζ4−ζ6+ζ12−ζ14−ζ22+ζ28−ζ36−ζ38−ζ4+ζ6+ζ12+ζ14+ζ22+ζ28−ζ36+ζ38ζ4+ζ6−ζ12+ζ14+ζ22−ζ28+ζ36+ζ3800000000000000000000000000000000000000
χ808-8-880000000-2−4i4i4i−4i2-22−2i52i52i5−2i500000000000ζ4+ζ6−ζ12+ζ14+ζ22−ζ28+ζ36+ζ38−ζ4+ζ6+ζ12+ζ14+ζ22+ζ28−ζ36+ζ38−ζ4−ζ6+ζ12−ζ14−ζ22+ζ28−ζ36−ζ38ζ4−ζ6−ζ12−ζ14−ζ22−ζ28+ζ36−ζ38−ζ4−ζ6+ζ12−ζ14−ζ22+ζ28−ζ36−ζ38ζ4−ζ6−ζ12−ζ14−ζ22−ζ28+ζ36−ζ38ζ4+ζ6−ζ12+ζ14+ζ22−ζ28+ζ36+ζ38−ζ4+ζ6+ζ12+ζ14+ζ22+ζ28−ζ36+ζ3800000000000000000000000000000000000000

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