Finite Group Databasebeta

← Group #13013821

Character table — Group #13013821

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111224444444488888881010101016161616161616161616161616162020202020202020202020204040404040808080808080
order12222244445101010410102020202044448820202020404040404040404022448888888828888888888
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-1
χ31111111111111111111111111-1-11111-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1
χ41111111111111111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-1-1-1-11111
χ5111111111111111111111-1-1-1-111111111111111-1-1-1-1iiii−i−i−i−i-1ii−i−i-1-1ii−i−i
χ6111111111111111111111-1-1-1-111111111111111-1-1-1-1−i−i−i−iiiii-1−i−iii-1-1−i−iii
χ7111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i-1ii−i−i11−i−iii
χ8111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii-1−i−iii11ii−i−i
χ911111111-1-11111-111-1-1-1-11111i−i-1-111iiii−i−i−i−i11-1-111111111-1-1-1-1-1i−ii−ii−i
χ1011111111-1-11111-111-1-1-1-11111i−i-1-111iiii−i−i−i−i11-1-1-1-1-1-1-1-1-1-1-11111i−i−ii−ii
χ1111111111-1-11111-111-1-1-1-11111−ii-1-111−i−i−i−iiiii11-1-111111111-1-1-1-1-1−ii−ii−ii
χ1211111111-1-11111-111-1-1-1-11111−ii-1-111−i−i−i−iiiii11-1-1-1-1-1-1-1-1-1-1-11111−iii−ii−i
χ1311111111-1-11111-111-1-1-1-1-1-1-1-1i−i-1-111iiii−i−i−i−i-1-111iiii−i−i−i−i1−i−iii−ii-111-1
χ1411111111-1-11111-111-1-1-1-1-1-1-1-1i−i-1-111iiii−i−i−i−i-1-111−i−i−i−iiiii1ii−i−i−ii1-1-11
χ1511111111-1-11111-111-1-1-1-1-1-1-1-1−ii-1-111−i−i−i−iiiii-1-111iiii−i−i−i−i1−i−iiii−i1-1-11
χ1611111111-1-11111-111-1-1-1-1-1-1-1-1−ii-1-111−i−i−i−iiiii-1-111−i−i−i−iiiii1ii−i−ii−i-111-1
χ17222222-2-2222222-2222222222200-2-2-2-200000000-2-2-2-20000000020000000000
χ18222222-2-2222222-2222222-2-2-2-200-2-2-2-200000000222200000000-20000000000
χ19222222-2-2-2-22222222-2-2-2-222220022-2-200000000-2-22200000000-20000000000
χ20222222-2-2-2-22222222-2-2-2-2-2-2-2-20022-2-20000000022-2-20000000020000000000
χ2122-2-22-2002i−2i2-22-202-22i2i−2i−2i0000000000000000002-22i−2ii2i2−i2−i2i2i2−i2−i202−22−2000000
χ2222-2-22-2002i−2i2-22-202-22i2i−2i−2i0000000000000000002-22i−2i−i2−i2i2i2−i2−i2i2i20−22−22000000
χ2322-2-22-2002i−2i2-22-202-22i2i−2i−2i000000000000000000-22−2i2i22−2−2−2−2220−i2i2i2−i2000000
χ2422-2-22-2002i−2i2-22-202-22i2i−2i−2i000000000000000000-22−2i2i−2−22222−2−20i2−i2−i2i2000000
χ2522-2-22-200−2i2i2-22-202-2−2i−2i2i2i0000000000000000002-2−2i2ii2i2−i2−i2i2i2−i2−i20−22−22000000
χ2622-2-22-200−2i2i2-22-202-2−2i−2i2i2i0000000000000000002-2−2i2i−i2−i2i2i2−i2−i2i2i202−22−2000000
χ2722-2-22-200−2i2i2-22-202-2−2i−2i2i2i000000000000000000-222i−2i22−2−2−2−2220i2−i2−i2i2000000
χ2822-2-22-200−2i2i2-22-202-2−2i−2i2i2i000000000000000000-222i−2i−2−22222−2−20−i2i2i2−i2000000
χ294444444444-1-1-1-14-1-1-1-1-1-1000044-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000
χ304444444444-1-1-1-14-1-1-1-1-1-10000-4-4-1-1-1-11111111100000000000000000000000
χ3144444444-4-4-1-1-1-1-4-1-1111100004i−4i11-1-1−i−i−i−iiiii00000000000000000000000
χ3244444444-4-4-1-1-1-1-4-1-111110000−4i4i11-1-1iiii−i−i−i−i00000000000000000000000
χ33444444-4-444-1-1-1-1-4-1-1-1-1-1-1000000111155−5−555−5−500000000000000000000000
χ34444444-4-444-1-1-1-1-4-1-1-1-1-1-10000001111−5−555−5−55500000000000000000000000
χ35444444-4-4-4-4-1-1-1-14-1-11111000000-1-111i5i5−i5−i5−i5−i5i5i500000000000000000000000
χ36444444-4-4-4-4-1-1-1-14-1-11111000000-1-111−i5−i5i5i5i5i5−i5−i500000000000000000000000
χ374444-4-4000044440-4-400004-4-440000000000000000000000000000000000000
χ384444-4-4000044440-4-40000-444-40000000000000000000000000000000000000
χ3944-4-4-444i−4i004-44-40-440000000000004i−4i0000000000000000000000000000000
χ4044-4-4-444i−4i00-11-1101-1i5−i5i5−i50000005−5−iiζ7−ζ21−ζ23+ζ29−ζ7+ζ21+ζ23−ζ29−ζ13+ζ31+ζ37−ζ39ζ13−ζ31−ζ37+ζ39−ζ13−ζ31+ζ37+ζ39ζ13+ζ31−ζ37−ζ39−ζ7−ζ21+ζ23+ζ29ζ7+ζ21−ζ23−ζ2900000000000000000000000
χ4144-4-4-444i−4i00-11-1101-1i5−i5i5−i50000005−5−ii−ζ7+ζ21+ζ23−ζ29ζ7−ζ21−ζ23+ζ29ζ13−ζ31−ζ37+ζ39−ζ13+ζ31+ζ37−ζ39ζ13+ζ31−ζ37−ζ39−ζ13−ζ31+ζ37+ζ39ζ7+ζ21−ζ23−ζ29−ζ7−ζ21+ζ23+ζ2900000000000000000000000
χ4244-4-4-444i−4i00-11-1101-1−i5i5−i5i5000000−55−ii−ζ13+ζ31+ζ37−ζ39ζ13−ζ31−ζ37+ζ39−ζ7+ζ21+ζ23−ζ29ζ7−ζ21−ζ23+ζ29ζ7+ζ21−ζ23−ζ29−ζ7−ζ21+ζ23+ζ29−ζ13−ζ31+ζ37+ζ39ζ13+ζ31−ζ37−ζ3900000000000000000000000
χ4344-4-4-444i−4i00-11-1101-1−i5i5−i5i5000000−55−iiζ13−ζ31−ζ37+ζ39−ζ13+ζ31+ζ37−ζ39ζ7−ζ21−ζ23+ζ29−ζ7+ζ21+ζ23−ζ29−ζ7−ζ21+ζ23+ζ29ζ7+ζ21−ζ23−ζ29ζ13+ζ31−ζ37−ζ39−ζ13−ζ31+ζ37+ζ3900000000000000000000000
χ4444-4-4-44−4i4i004-44-40-44000000000000−4i4i0000000000000000000000000000000
χ4544-4-4-44−4i4i00-11-1101-1i5−i5i5−i5000000−55i−i−ζ7−ζ21+ζ23+ζ29ζ7+ζ21−ζ23−ζ29−ζ13−ζ31+ζ37+ζ39ζ13+ζ31−ζ37−ζ39ζ13−ζ31−ζ37+ζ39−ζ13+ζ31+ζ37−ζ39−ζ7+ζ21+ζ23−ζ29ζ7−ζ21−ζ23+ζ2900000000000000000000000
χ4644-4-4-44−4i4i00-11-1101-1i5−i5i5−i5000000−55i−iζ7+ζ21−ζ23−ζ29−ζ7−ζ21+ζ23+ζ29ζ13+ζ31−ζ37−ζ39−ζ13−ζ31+ζ37+ζ39−ζ13+ζ31+ζ37−ζ39ζ13−ζ31−ζ37+ζ39ζ7−ζ21−ζ23+ζ29−ζ7+ζ21+ζ23−ζ2900000000000000000000000
χ4744-4-4-44−4i4i00-11-1101-1−i5i5−i5i50000005−5i−i−ζ13−ζ31+ζ37+ζ39ζ13+ζ31−ζ37−ζ39ζ7+ζ21−ζ23−ζ29−ζ7−ζ21+ζ23+ζ29ζ7−ζ21−ζ23+ζ29−ζ7+ζ21+ζ23−ζ29ζ13−ζ31−ζ37+ζ39−ζ13+ζ31+ζ37−ζ3900000000000000000000000
χ4844-4-4-44−4i4i00-11-1101-1−i5i5−i5i50000005−5i−iζ13+ζ31−ζ37−ζ39−ζ13−ζ31+ζ37+ζ39−ζ7−ζ21+ζ23+ζ29ζ7+ζ21−ζ23−ζ29−ζ7+ζ21+ζ23−ζ29ζ7−ζ21−ζ23+ζ29−ζ13+ζ31+ζ37−ζ39ζ13−ζ31−ζ37+ζ3900000000000000000000000
χ494-44-400000044-4-4000000004i−4i0000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900000000000
χ504-44-400000044-4-4000000004i−4i00000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900000000000
χ514-44-400000044-4-400000000−4i4i0000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700000000000
χ524-44-400000044-4-400000000−4i4i00000000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700000000000
χ534-4-440000004-4-440000000400-40000000000000000002i−2i−2i2i−2i2i2i−2i00000000000
χ544-4-440000004-4-440000000400-4000000000000000000−2i2i2i−2i2i−2i−2i2i00000000000
χ554-4-440000004-4-440000000-40040000000000000000002-2-222-2-2200000000000
χ564-4-440000004-4-440000000-4004000000000000000000-222-2-222-200000000000
χ578888-8-80000-2-2-2-202225−25−252500000000000000000000000000000000000000000
χ588888-8-80000-2-2-2-2022−252525−2500000000000000000000000000000000000000000
χ5988-8-88-8008i−8i-22-220-22−2i−2i2i2i00000000000000000000000000000000000000000
χ6088-8-88-800−8i8i-22-220-222i2i−2i−2i00000000000000000000000000000000000000000
χ6116-1616-16000000-4-444000000000000000000000000000000000000000000000000
χ6216-16-1616000000-444-4000000000000000000000000000000000000000000000000

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