Finite Group Databasebeta

← Group #13019399

Character table — Group #13019399

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11112244444455558888888888101016161616161616161620202020202032324040404040404040404040404040404040404040
order12222244510101044444444881010202044202020202040404040448888202022248888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1111111111-1-11-1-1111111-1-1-1-1-1-1-1-1
χ4111111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-111-1-1-1-1111-1-11-1-1-1-1-1-1-1-111111111
χ51111111111111111-1-111-1-111111111111-1-1-1-1111111-1-1-111-1-1-1-1-111-1-11111-1-1-1-1
χ61111111111111111-1-111-1-111111111111-1-1-1-111-1-1-1-1-1-1-111-1-1-111-1-111-1-1-1-11111
χ71111111111111111-1-1-1-1111111111-1-1-1-11111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-11111
χ81111111111111111-1-1-1-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1
χ9111111111111-1-1-1-11111111111-1-1111111111-1-1ii−i−i11-1-1-1-1-1-1i−ii−ii−iii−i−iii−i−i
χ10111111111111-1-1-1-11111111111-1-1111111111-1-1−i−iii11-1-1-1-1-1-1−ii−ii−ii−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−i11-111-111i−ii−ii−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−iii11-111-111−ii−ii−iiii−i−iii−i−i
χ13111111111111-1-1-1-1-1-111-1-11111-1-111111-1-1-1-1-1-1ii−i−i-1-11-1-1111−iii−i−iiii−i−i−i−iii
χ14111111111111-1-1-1-1-1-111-1-11111-1-111111-1-1-1-1-1-1−i−iii-1-11-1-1111i−i−iii−i−i−iiiii−i−i
χ15111111111111-1-1-1-1-1-1-1-1111111-1-11-1-1-1-11111-1-1ii−i−i-1-11111-1-1−iii−i−ii−i−iiiii−i−i
χ16111111111111-1-1-1-1-1-1-1-1111111-1-11-1-1-1-11111-1-1−i−iii-1-11111-1-1i−i−iii−iii−i−i−i−iii
χ17222222-2-22222222200000022-2-222-200000000-2-222220000000000-2-20000000000
χ18222222-2-22222222200000022-2-222-200000000-2-2-2-2-2-20000000000220000000000
χ19222222-2-22222-2-2-2-200000022-2-2-2-2-200000000222i2i−2i−2i0000000000−2i2i0000000000
χ20222222-2-22222-2-2-2-200000022-2-2-2-2-20000000022−2i−2i2i2i00000000002i−2i0000000000
χ212222-2-22-222222222000000-2-2-2-2-2-2200000000-220000000000002200-2-200000000
χ222222-2-22-222222222000000-2-2-2-2-2-2200000000-22000000000000-2-2002200000000
χ232222-2-22-22222-2-2-2-2000000-2-2-2-2222000000002-20000000000002i−2i00−2i2i00000000
χ242222-2-22-22222-2-2-2-2000000-2-2-2-2222000000002-2000000000000−2i2i002i−2i00000000
χ252222-2-2-22222222222-20000-2-222-2-2-2000000002-200002-2-20020000000000000000
χ262222-2-2-2222222222-220000-2-222-2-2-2000000002-20000-22200-20000000000000000
χ272222-2-2-222222-2-2-2-22-20000-2-22222-200000000-2200002-2200-20000000000000000
χ282222-2-2-222222-2-2-2-2-220000-2-22222-200000000-220000-22-20020000000000000000
χ292-2-222-20022-2-22i−2i2i−2i00002−22-2002i−2i0000022−2−200−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000i2−i200000000001+i−1−i1−i−1+i
χ302-2-222-20022-2-22i−2i2i−2i00002−22-2002i−2i0000022−2−2002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000i2−i20000000000−1−i1+i−1+i1−i
χ312-2-222-20022-2-22i−2i2i−2i0000−222-2002i−2i00000−2−22200−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000−i2i20000000000−1−i1+i−1+i1−i
χ322-2-222-20022-2-22i−2i2i−2i0000−222-2002i−2i00000−2−222002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000−i2i200000000001+i−1−i1−i−1+i
χ332-2-222-20022-2-2−2i2i−2i2i00002−22-200−2i2i0000022−2−200−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000−i2i20000000000−1+i1−i−1−i1+i
χ342-2-222-20022-2-2−2i2i−2i2i00002−22-200−2i2i0000022−2−2002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000−i2i200000000001−i−1+i1+i−1−i
χ352-2-222-20022-2-2−2i2i−2i2i0000−222-200−2i2i00000−2−22200−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000i2−i200000000001−i−1+i1+i−1−i
χ362-2-222-20022-2-2−2i2i−2i2i0000−222-200−2i2i00000−2−222002ζ7+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
χ414444-4-4-44-1-1-1-100004-4000011-1-100155−5−55−55−5000000-1100000000000000000000
χ424444-4-4-44-1-1-1-100004-4000011-1-1001−5−555−55−55000000-1100000000000000000000
χ434444-4-4-44-1-1-1-10000-44000011-1-100155−5−5−55−550000001-100000000000000000000
χ444444-4-4-44-1-1-1-10000-44000011-1-1001−5−5555−55−50000001-100000000000000000000
χ4544-4-400004-44-44i−4i−4i4i002i−2i0000000002i−2i2i−2i00000000000002-200000000000000000
χ4644-4-400004-44-44i−4i−4i4i00−2i2i000000000−2i2i−2i2i0000000000000-2200000000000000000
χ4744-4-400004-44-4−4i4i4i−4i002i−2i0000000002i−2i2i−2i0000000000000-2200000000000000000
χ4844-4-400004-44-4−4i4i4i−4i00−2i2i000000000−2i2i−2i2i00000000000002-200000000000000000
χ494-44-400004-4-4444-4-4000000000000000000000000000000000000000002i−2i2i−2i0000
χ504-44-400004-4-4444-4-400000000000000000000000000000000000000000−2i2i−2i2i0000
χ514-44-400004-4-44-4-444000000000000000000000000000000000000000002-2-220000
χ524-44-400004-4-44-4-44400000000000000000000000000000000000000000-222-20000
χ534-4-44-440044-4-44i−4i4i−4i000000-4400−4i4i0000000000000000000000000000000000000
χ544-4-44-440044-4-4−4i4i−4i4i000000-44004i−4i0000000000000000000000000000000000000
χ55888888-8-8-2-2-2-20000000000-2-222002000000000000000000000000000000000000
χ568888-8-88-8-2-2-2-20000000000222200-2000000000000000000000000000000000000
χ5788-8-80000-22-220000004i−4i000025−25000−2ζ6−2ζ142ζ6+2ζ14−2ζ22−2ζ382ζ22+2ζ3800000000000000000000000000000000
χ5888-8-80000-22-220000004i−4i0000−2525000−2ζ22−2ζ382ζ22+2ζ38−2ζ6−2ζ142ζ6+2ζ1400000000000000000000000000000000
χ5988-8-80000-22-22000000−4i4i000025−250002ζ6+2ζ14−2ζ6−2ζ142ζ22+2ζ38−2ζ22−2ζ3800000000000000000000000000000000
χ6088-8-80000-22-22000000−4i4i0000−25250002ζ22+2ζ38−2ζ22−2ζ382ζ6+2ζ14−2ζ6−2ζ1400000000000000000000000000000000
χ618-8-888-800-2-2220000000042−42-22000000000−2−2220000000000000000000000000000
χ628-8-888-800-2-22200000000−4242-2200000000022−2−20000000000000000000000000000
χ638-8-88-8800-2-22200000000002-200000000010−10−10100000000000000000000000000000
χ648-8-88-8800-2-22200000000002-2000000000−101010−100000000000000000000000000000
χ6516-1616-160000-444-400000000000000000000000000000000000000000000000000000

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