Finite Group Databasebeta

← Group #13019388

Character table — Group #13019388

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11112244444455558888888888101016161616161616161620202020202032324040404040404040404040404040404040404040
order12222244510101044442224881010202044101010102040404040448888102024448888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111-1-1-1-111111111111-1-1-1-1111111-1-1-111-1-1-111-1-1-1-11111-1-1-1-1
χ4111111111111111111-1-1-1-111111111111-1-1-1-111-1-1-1-1-1-1-111-1-1-1-1-11111-1-1-1-11111
χ51111111111111111-1-111-1-1111111-1-1-1-11-1-1-1-1111111111-1-11-1-1111111-1-1-1-1-1-1-1-1
χ61111111111111111-1-111-1-1111111-1-1-1-11-1-1-1-111-1-1-1-1111-1-11-1-1-1-1-1-1-1-111111111
χ71111111111111111-1-1-1-111111111-1-1-1-111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ81111111111111111-1-1-1-111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1
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
χ11111111111111-1-1-1-111-1-1-1-11111-1-111111-1-1-1-1-1-1ii−i−i-1-11-1-1111i−i−i−iiiii−i−i−i−iii
χ12111111111111-1-1-1-111-1-1-1-11111-1-111111-1-1-1-1-1-1−i−iii-1-11-1-1111−iiii−i−i−i−iiiii−i−i
χ13111111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-11-1-1-1-1-1-1ii−i−i11-111-111i−iii−i−i−i−iii−i−iii
χ14111111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-11-1-1-1-1-1-1−i−iii11-111-111−ii−i−iiiii−i−iii−i−i
χ15111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111-1-1ii−i−i-1-11111-1-1i−i−i−iii−i−iiiii−i−i
χ16111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111-1-1−i−iii-1-11111-1-1−iiii−i−iii−i−i−i−iii
χ17222222-2-22222222200000022-2-2220000-20000-2-2222200000000-2-2000000000000
χ18222222-2-22222222200000022-2-2220000-20000-2-2-2-2-2-20000000022000000000000
χ19222222-2-22222-2-2-2-200000022-2-2-2-20000-20000222i2i−2i−2i00000000−2i2i000000000000
χ20222222-2-22222-2-2-2-200000022-2-2-2-20000-2000022−2i−2i2i2i000000002i−2i000000000000
χ212222-2-22-222222222000000-2-2-2-2-2-2000020000-22000000000000002-22-200000000
χ222222-2-22-222222222000000-2-2-2-2-2-2000020000-2200000000000000-22-2200000000
χ232222-2-22-22222-2-2-2-2000000-2-2-2-2220000200002-2000000000000002i−2i−2i2i00000000
χ242222-2-22-22222-2-2-2-2000000-2-2-2-2220000200002-200000000000000−2i2i2i−2i00000000
χ252222-2-2-2222222222002-200-2-222-2-20000-200002-200002-2-20020000000000000000
χ262222-2-2-222222222200-2200-2-222-2-20000-200002-20000-22200-20000000000000000
χ272222-2-2-222222-2-2-2-2002-200-2-222220000-20000-2200002-2200-20000000000000000
χ282222-2-2-222222-2-2-2-200-2200-2-222220000-20000-220000-22-20020000000000000000
χ292-2-222-2002-22-222-2-200002−22-2002-20000022−2−2002i−2i2i−2i0000002−20000000000i2−i2i2−i2
χ302-2-222-2002-22-222-2-200002−22-2002-20000022−2−200−2i2i−2i2i0000002−20000000000−i2i2−i2i2
χ312-2-222-2002-22-222-2-20000−222-2002-200000−2−222002i−2i2i−2i000000−220000000000−i2i2−i2i2
χ322-2-222-2002-22-222-2-20000−222-2002-200000−2−22200−2i2i−2i2i000000−220000000000i2−i2i2−i2
χ332-2-222-2002-22-2-2-22200002−22-200-220000022−2−2002-2-22000000−2200000000002−2−22
χ342-2-222-2002-22-2-2-22200002−22-200-220000022−2−200-222-2000000−220000000000−222−2
χ352-2-222-2002-22-2-2-2220000−222-200-2200000−2−222002-2-220000002−20000000000−222−2
χ362-2-222-2002-22-2-2-2220000−222-200-2200000−2−22200-222-20000002−200000000002−2−22
χ3744444444-1-1-1-10000444444-1-1-1-100-1-1-1-1-1-1-1-1-1000000-1-100000000000000000000
χ3844444444-1-1-1-1000044-4-4-4-4-1-1-1-100-1-1-1-1-111110000001100000000000000000000
χ3944444444-1-1-1-10000-4-444-4-4-1-1-1-1001111-11111000000-1-100000000000000000000
χ4044444444-1-1-1-10000-4-4-4-444-1-1-1-1001111-1-1-1-1-10000001100000000000000000000
χ414444-4-4-44-1-1-1-10000004-40011-1-10055−5−515−55−5000000-1100000000000000000000
χ424444-4-4-44-1-1-1-10000004-40011-1-100−5−5551−55−55000000-1100000000000000000000
χ434444-4-4-44-1-1-1-1000000-440011-1-10055−5−51−55−550000001-100000000000000000000
χ444444-4-4-44-1-1-1-1000000-440011-1-100−5−55515−55−50000001-100000000000000000000
χ4544-4-400004-4-444i−4i4i−4i2-200000000002-22-2000000000000002i−2i00000000000000000
χ4644-4-400004-4-444i−4i4i−4i-220000000000-22-2200000000000000−2i2i00000000000000000
χ4744-4-400004-4-44−4i4i−4i4i2-200000000002-22-200000000000000−2i2i00000000000000000
χ4844-4-400004-4-44−4i4i−4i4i-220000000000-22-22000000000000002i−2i00000000000000000
χ494-44-4000044-4-44i−4i−4i4i00000000000000000000000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370000
χ504-44-4000044-4-44i−4i−4i4i000000000000000000000000000000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000
χ514-44-4000044-4-4−4i4i4i−4i00000000000000000000000000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000
χ524-44-4000044-4-4−4i4i4i−4i000000000000000000000000000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000
χ534-4-44-44004-44-444-4-4000000-4400-440000000000000000000000000000000000000
χ544-4-44-44004-44-4-4-444000000-44004-40000000000000000000000000000000000000
χ55888888-8-8-2-2-2-20000000000-2-222000000200000000000000000000000000000000
χ568888-8-88-8-2-2-2-200000000002222000000-200000000000000000000000000000000
χ5788-8-80000-222-200004-400000025−2500−1+51−5−1−51+5000000000000000000000000000000000
χ5888-8-80000-222-200004-4000000−252500−1−51+5−1+51−5000000000000000000000000000000000
χ5988-8-80000-222-20000-4400000025−25001−5−1+51+5−1−5000000000000000000000000000000000
χ6088-8-80000-222-20000-44000000−2525001+5−1−51−5−1+5000000000000000000000000000000000
χ618-8-888-800-22-220000000042−42-22000000000−2−2220000000000000000000000000000
χ628-8-888-800-22-2200000000−4242-2200000000022−2−20000000000000000000000000000
χ638-8-88-8800-22-2200000000002-200000000010−10−10100000000000000000000000000000
χ648-8-88-8800-22-2200000000002-2000000000−101010−100000000000000000000000000000
χ6516-1616-160000-4-44400000000000000000000000000000000000000000000000000000

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