Finite Group Databasebeta

← Group #13018961

Character table — Group #13018961

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11112244444455558888888888101016161616161616161620202020202032324040404040404040404040404040404040404040
order12222244510101044442444881010202044202020202040404040448888102044448888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-1
χ4111111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111-1-111-1-111111111111-1-1-1-1111111-1-1-1-111-1-111-1-1-1-11111-1-1-1-1
χ61111111111111111-1-111-1-111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111
χ71111111111111111-1-1-1-1111111111-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ81111111111111111-1-1-1-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1
χ9111111111111-1-1-1-11111111111-1-1111111111-1-1ii−i−i11-1-1-1-1-1-1i−iii−i−iii−i−iii−i−i
χ10111111111111-1-1-1-11111111111-1-1111111111-1-1−i−iii11-1-1-1-1-1-1−ii−i−iii−i−iii−i−iii
χ11111111111111-1-1-1-111-1-1-1-11111-1-11-1-1-1-1-1-1-1-1-1-1ii−i−i11-1-11111i−iii−i−i−i−iii−i−iii
χ12111111111111-1-1-1-111-1-1-1-11111-1-11-1-1-1-1-1-1-1-1-1-1−i−iii11-1-11111−ii−i−iiiii−i−iii−i−i
χ13111111111111-1-1-1-1-1-111-1-11111-1-111111-1-1-1-1-1-1ii−i−i-1-111-1-111i−i−i−iiiii−i−i−i−iii
χ14111111111111-1-1-1-1-1-111-1-11111-1-111111-1-1-1-1-1-1−i−iii-1-111-1-111−iiii−i−i−i−iiiii−i−i
χ15111111111111-1-1-1-1-1-1-1-1111111-1-11-1-1-1-11111-1-1ii−i−i-1-11111-1-1i−i−i−iii−i−iiiii−i−i
χ16111111111111-1-1-1-1-1-1-1-1111111-1-11-1-1-1-11111-1-1−i−iii-1-11111-1-1−iiii−i−iii−i−i−i−iii
χ17222222-2-22222222200000022-2-222-200000000-2-2222200000000-2-2000000000000
χ18222222-2-22222222200000022-2-222-200000000-2-2-2-2-2-20000000022000000000000
χ19222222-2-22222-2-2-2-200000022-2-2-2-2-200000000222i2i−2i−2i00000000−2i2i000000000000
χ20222222-2-22222-2-2-2-200000022-2-2-2-2-20000000022−2i−2i2i2i000000002i−2i000000000000
χ212222-2-22-2222222222-20000-2-2-2-2-2-2200000000-2200002-2-22000000000000000000
χ222222-2-22-222222222-220000-2-2-2-2-2-2200000000-220000-222-2000000000000000000
χ232222-2-22-22222-2-2-2-22-20000-2-2-2-2222000000002-200002-22-2000000000000000000
χ242222-2-22-22222-2-2-2-2-220000-2-2-2-2222000000002-20000-22-22000000000000000000
χ252222-2-2-2222222222000000-2-222-2-2-2000000002-2000000000000002-22-200000000
χ262222-2-2-2222222222000000-2-222-2-2-2000000002-200000000000000-22-2200000000
χ272222-2-2-222222-2-2-2-2000000-2-22222-200000000-22000000000000002i−2i−2i2i00000000
χ282222-2-2-222222-2-2-2-2000000-2-22222-200000000-2200000000000000−2i2i2i−2i00000000
χ2922-2-22-2002-22-22i2i−2i−2i00002−2-22002i−2i0000022−2−200−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000i2−i200000000001+i−1−i1−i−1+i
χ3022-2-22-2002-22-22i2i−2i−2i00002−2-22002i−2i0000022−2−2002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000i2−i20000000000−1−i1+i−1+i1−i
χ3122-2-22-2002-22-22i2i−2i−2i0000−22-22002i−2i00000−2−22200−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000−i2i20000000000−1−i1+i−1+i1−i
χ3222-2-22-2002-22-22i2i−2i−2i0000−22-22002i−2i00000−2−222002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000−i2i200000000001+i−1−i1−i−1+i
χ3322-2-22-2002-22-2−2i−2i2i2i00002−2-2200−2i2i0000022−2−200−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000−i2i20000000000−1+i1−i−1−i1+i
χ3422-2-22-2002-22-2−2i−2i2i2i00002−2-2200−2i2i0000022−2−2002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000−i2i200000000001−i−1+i1+i−1−i
χ3522-2-22-2002-22-2−2i−2i2i2i0000−22-2200−2i2i00000−2−22200−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000i2−i200000000001−i−1+i1+i−1−i
χ3622-2-22-2002-22-2−2i−2i2i2i0000−22-2200−2i2i00000−2−222002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000i2−i20000000000−1+i1−i−1−i1+i
χ3744444444-1-1-1-10000444444-1-1-1-100-1-1-1-1-1-1-1-1-1000000-1-100000000000000000000
χ3844444444-1-1-1-1000044-4-4-4-4-1-1-1-100-111111111000000-1-100000000000000000000
χ3944444444-1-1-1-10000-4-444-4-4-1-1-1-100-1-1-1-1-111110000001100000000000000000000
χ4044444444-1-1-1-10000-4-4-4-444-1-1-1-100-11111-1-1-1-10000001100000000000000000000
χ414444-4-44-4-1-1-1-100004-40000111100-1i5i5−i5−i5i5−i5i5−i5000000-1100000000000000000000
χ424444-4-44-4-1-1-1-100004-40000111100-1−i5−i5i5i5−i5i5−i5i5000000-1100000000000000000000
χ434444-4-44-4-1-1-1-10000-440000111100-1i5i5−i5−i5−i5i5−i5i50000001-100000000000000000000
χ444444-4-44-4-1-1-1-10000-440000111100-1−i5−i5i5i5i5−i5i5−i50000001-100000000000000000000
χ4544-4-4-44004-44-44i4i−4i−4i0000004-400−4i4i0000000000000000000000000000000000000
χ4644-4-4-44004-44-4−4i−4i4i4i0000004-4004i−4i0000000000000000000000000000000000000
χ474-44-400004-4-444i−4i4i−4i00000000000000000000000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370000
χ484-44-400004-4-444i−4i4i−4i000000000000000000000000000000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000
χ494-44-400004-4-44−4i4i−4i4i00000000000000000000000000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000
χ504-44-400004-4-44−4i4i−4i4i000000000000000000000000000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000
χ514-4-44000044-4-44-4-44002i−2i0000000002i−2i2i−2i000000000000002i−2i0000000000000000
χ524-4-44000044-4-44-4-4400−2i2i000000000−2i2i−2i2i00000000000000−2i2i0000000000000000
χ534-4-44000044-4-4-444-4002i−2i0000000002i−2i2i−2i00000000000000−2i2i0000000000000000
χ544-4-44000044-4-4-444-400−2i2i000000000−2i2i−2i2i000000000000002i−2i0000000000000000
χ55888888-8-8-2-2-2-20000000000-2-222002000000000000000000000000000000000000
χ568888-8-8-88-2-2-2-2000000000022-2-2002000000000000000000000000000000000000
χ5788-8-88-800-22-220000000042−422-2000000000−2−2220000000000000000000000000000
χ5888-8-88-800-22-2200000000−42422-200000000022−2−20000000000000000000000000000
χ5988-8-8-8800-22-220000000000-22000000000i10−i10−i10i100000000000000000000000000000
χ6088-8-8-8800-22-220000000000-22000000000−i10i10i10−i100000000000000000000000000000
χ618-8-880000-2-2220000004i−4i00002i5−2i5000ζ4−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+ζ3800000000000000000000000000000000
χ628-8-880000-2-2220000004i−4i0000−2i52i5000−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+ζ3800000000000000000000000000000000
χ638-8-880000-2-222000000−4i4i00002i5−2i5000−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−ζ3800000000000000000000000000000000
χ648-8-880000-2-222000000−4i4i0000−2i52i5000ζ4+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−ζ3800000000000000000000000000000000
χ6516-1616-160000-444-400000000000000000000000000000000000000000000000000000

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