Finite Group Databasebeta

← Group #13017842

Character table — Group #13017842

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111224444448888888888881010101016161616161616161616161620202020202040404040404040404040404080808080
order12222244510101024444410102020202044441010202020202020202020204444442444888888888888
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−iii−i−i
χ4111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii−i−iii
χ511111111111111-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11-11-1
χ611111111111111-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-11-11
χ711111111111111-1-1-1-1111111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-111ii−i−i−i−iiii−i−ii
χ811111111111111-1-1-1-1111111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-111−i−iiiii−i−i−iii−i
χ9111111111111-1-111-1-11111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1
χ10111111111111-1-111-1-11111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ11111111111111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111ii−i−iii−i−i−i−iii
χ12111111111111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111−i−iii−i−iiiii−i−i
χ13111111111111-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-11-11
χ14111111111111-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111111-11-1
χ15111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1ii−i−i−i−iii−iii−i
χ16111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1−i−iiiii−i−ii−i−ii
χ17222222-2-22222002-20022-2-2-2-222220000000022-2-222-2-2-2-20000000000000000
χ18222222-2-22222002-20022-2-2-2-2-2-2-2-20000000022-2-2-2-222220000000000000000
χ19222222-2-2222200-220022-2-2-2-2222200000000-2-222-2-222-2-20000000000000000
χ20222222-2-2222200-220022-2-2-2-2-2-2-2-200000000-2-22222-2-2220000000000000000
χ212222-2-22-2222200002-2-2-222-2-22-2-220022-2-200000000002-2002-2000000000000
χ222222-2-22-2222200002-2-2-222-2-2-222-20022-2-20000000000-2200-22000000000000
χ232222-2-22-222220000-22-2-222-2-22-2-2200-2-22200000000002-200-22000000000000
χ242222-2-22-222220000-22-2-222-2-2-222-200-2-2220000000000-22002-2000000000000
χ252222-2-2-2222222-20000-2-2-2-2222-2-22220000-2-200000000-222-200000000000000
χ262222-2-2-2222222-20000-2-2-2-222-222-2220000-2-2000000002-2-2200000000000000
χ272222-2-2-222222-220000-2-2-2-2222-2-22-2-200002200000000-22-2200000000000000
χ282222-2-2-222222-220000-2-2-2-222-222-2-2-2000022000000002-22-200000000000000
χ2944444444-1-1-1-1444444-1-1-1-1-1-10000-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000
χ3044444444-1-1-1-144-4-4-4-4-1-1-1-1-1-10000-1-11111-1-111110000000000000000000000
χ3144444444-1-1-1-1-4-444-4-4-1-1-1-1-1-1000011111111-1-1-1-10000000000000000000000
χ3244444444-1-1-1-1-4-4-4-444-1-1-1-1-1-1000011-1-1-1-11111110000000000000000000000
χ33444444-4-4-1-1-1-1004-400-1-1111100005−55−55−55−5-1-1110000000000000000000000
χ34444444-4-4-1-1-1-1004-400-1-111110000−55−55−55−55-1-1110000000000000000000000
χ35444444-4-4-1-1-1-100-4400-1-1111100005−5−55−555−511-1-10000000000000000000000
χ36444444-4-4-1-1-1-100-4400-1-111110000−555−55−5−5511-1-10000000000000000000000
χ374444-4-44-4-1-1-1-100004-411-1-11100005−5-1-111−555−55−50000000000000000000000
χ384444-4-44-4-1-1-1-100004-411-1-1110000−55-1-1115−5−55−550000000000000000000000
χ394444-4-44-4-1-1-1-10000-4411-1-11100005−511-1-1−55−55−550000000000000000000000
χ404444-4-44-4-1-1-1-10000-4411-1-1110000−5511-1-15−55−55−50000000000000000000000
χ414444-4-4-44-1-1-1-14-400001111-1-10000-1-15−5−55115−5−550000000000000000000000
χ424444-4-4-44-1-1-1-14-400001111-1-10000-1-1−555−511−555−50000000000000000000000
χ434444-4-4-44-1-1-1-1-4400001111-1-10000115−5−55-1-1−555−50000000000000000000000
χ444444-4-4-44-1-1-1-1-4400001111-1-1000011−555−5-1-15−5−550000000000000000000000
χ4544-4-44-4004-4-440000004-400000000000000000000004i−4i000000000000000000
χ4644-4-44-4004-4-440000004-40000000000000000000000−4i4i000000000000000000
χ4744-4-4-44004-4-44000000-44000000000000000000004i−4i00000000000000000000
χ4844-4-4-44004-4-44000000-4400000000000000000000−4i4i00000000000000000000
χ494-44-4000044-4-4000000000000400-400000000000000000000002-22-200000000
χ504-44-4000044-4-4000000000000400-40000000000000000000000-22-2200000000
χ514-44-4000044-4-4000000000000-400400000000000000000000002i−2i−2i2i00000000
χ524-44-4000044-4-4000000000000-40040000000000000000000000−2i2i2i−2i00000000
χ534-4-4400004-44-400000000000004i−4i000000000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370000
χ544-4-4400004-44-400000000000004i−4i0000000000000000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000
χ554-4-4400004-44-40000000000000−4i4i000000000000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000
χ564-4-4400004-44-40000000000000−4i4i0000000000000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000
χ5788-8-88-800-222-2000000-2225−2525−2500000000000000000000000000000000000000
χ5888-8-88-800-222-2000000-22−2525−252500000000000000000000000000000000000000
χ5988-8-8-8800-222-20000002-225−25−252500000000000000000000000000000000000000
χ6088-8-8-8800-222-20000002-2−252525−2500000000000000000000000000000000000000
χ6116-1616-160000-4-44400000000000000000000000000000000000000000000000000
χ6216-16-16160000-44-4400000000000000000000000000000000000000000000000000

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