Finite Group Databasebeta

← Group #13017848

Character table — Group #13017848

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111224444448888888888881010101016161616161616161616161620202020202040404040404040404040404080808080
order12222244510101044444410102020202044442020202020202020202020202244442244888888884444
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iii−i−i
χ4111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−iii
χ511111111111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1111111-1-1-1-111111111-1-1-1-1
χ611111111111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ711111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−iii
χ811111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiiiii−i−i
χ9111111111111-1-11-11-1111111111111-1-1-1-1-1-111-1-111-1-1-1-11-11-111-1-111-1-11-11-1
χ10111111111111-1-11-11-1111111111111-1-1-1-1-1-111-1-111-1-1-1-11-11-1-1-111-1-111-11-11
χ11111111111111-1-11-11-1111111-1-1-1-111-1-1-1-1-1-111-1-1-1-11111-11-11ii−i−i−i−iiii−i−ii
χ12111111111111-1-11-11-1111111-1-1-1-111-1-1-1-1-1-111-1-1-1-11111-11-11−i−iiiii−i−i−iii−i
χ13111111111111-1-1-11-111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-11-1111-1-111-1-1-11-11
χ14111111111111-1-1-11-111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-11-11-1-111-1-1111-11-1
χ15111111111111-1-1-11-11111111-1-1-1-1-1-111-1-1-1-1-1-111-1-111111-11-1ii−i−i−i−iii−iii−i
χ16111111111111-1-1-11-11111111-1-1-1-1-1-111-1-1-1-1-1-111-1-111111-11-1−i−iiiii−i−ii−i−ii
χ17222222-2-222222-2000022-2-2-2-22222000022-2-20000-2-222-2-20000000000000000
χ18222222-2-222222-2000022-2-2-2-2-2-2-2-2000022-2-2000022-2-2220000000000000000
χ19222222-2-22222-22000022-2-2-2-222220000-2-2220000-2-2-2-2220000000000000000
χ20222222-2-22222-22000022-2-2-2-2-2-2-2-20000-2-22200002222-2-20000000000000000
χ212222-2-22-2222200020-2-2-222-2-222-2-200-2-2000000222-20000020-2000000000000
χ222222-2-22-2222200020-2-2-222-2-2-2-22200-2-200000022-2200000-202000000000000
χ232222-2-22-22222000-202-2-222-2-222-2-20022000000-2-22-200000-202000000000000
χ242222-2-22-22222000-202-2-222-2-2-2-2220022000000-2-2-220000020-2000000000000
χ252222-2-2-2222220020-20-2-2-2-22222-2-2-2-20000002200-22000020-20000000000000
χ262222-2-2-2222220020-20-2-2-2-222-2-222-2-200000022002-20000-2020000000000000
χ272222-2-2-22222200-2020-2-2-2-22222-2-222000000-2-200-220000-2020000000000000
χ282222-2-2-22222200-2020-2-2-2-222-2-22222000000-2-2002-2000020-20000000000000
χ2944444444-1-1-1-1444444-1-1-1-1-1-10000-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000
χ3044444444-1-1-1-144-4-4-4-4-1-1-1-1-1-100001111-1-1-1-111110000000000000000000000
χ3144444444-1-1-1-1-4-44-44-4-1-1-1-1-1-10000-1-1111111-1-1110000000000000000000000
χ3244444444-1-1-1-1-4-4-44-44-1-1-1-1-1-1000011-1-1111111-1-10000000000000000000000
χ33444444-4-4-1-1-1-14-40000-1-1111100005−55−5-1-1115−55−50000000000000000000000
χ34444444-4-4-1-1-1-14-40000-1-111110000−55−55-1-111−55−550000000000000000000000
χ35444444-4-4-1-1-1-1-440000-1-1111100005−5−5511-1-15−5−550000000000000000000000
χ36444444-4-4-1-1-1-1-440000-1-111110000−555−511-1-1−555−50000000000000000000000
χ374444-4-44-4-1-1-1-100040-411-1-11100005−5115−55−5−55-1-10000000000000000000000
χ384444-4-44-4-1-1-1-100040-411-1-1110000−5511−55−555−5-1-10000000000000000000000
χ394444-4-44-4-1-1-1-1000-40411-1-11100005−5-1-1−55−55−55110000000000000000000000
χ404444-4-44-4-1-1-1-1000-40411-1-1110000−55-1-15−55−55−5110000000000000000000000
χ414444-4-4-44-1-1-1-10040-401111-1-10000115−55−5−55-1-1−550000000000000000000000
χ424444-4-4-44-1-1-1-10040-401111-1-1000011−55−555−5-1-15−50000000000000000000000
χ434444-4-4-44-1-1-1-100-40401111-1-10000-1-15−5−555−511−550000000000000000000000
χ444444-4-4-44-1-1-1-100-40401111-1-10000-1-1−555−5−55115−50000000000000000000000
χ4544-4-400004-4-44000000000000004i−4i0000000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000
χ4644-4-400004-4-44000000000000004i−4i00000000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000
χ4744-4-400004-4-4400000000000000−4i4i0000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000
χ4844-4-400004-4-4400000000000000−4i4i00000000000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000
χ494-44-400004-44-40000000000004i−4i00000000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370000
χ504-44-400004-44-40000000000004i−4i000000000000000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000
χ514-44-400004-44-4000000000000−4i4i00000000000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000
χ524-44-400004-44-4000000000000−4i4i000000000000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000
χ534-4-444-40044-4-40000004-40000000000000000000000004i−4i0000000000000000
χ544-4-444-40044-4-40000004-4000000000000000000000000−4i4i0000000000000000
χ554-4-44-440044-4-4000000-4400000000000000000000004i−4i000000000000000000
χ564-4-44-440044-4-4000000-440000000000000000000000−4i4i000000000000000000
χ578-8-888-800-2-222000000-2225−2525−2500000000000000000000000000000000000000
χ588-8-888-800-2-222000000-22−2525−252500000000000000000000000000000000000000
χ598-8-88-8800-2-2220000002-225−25−252500000000000000000000000000000000000000
χ608-8-88-8800-2-2220000002-2−252525−2500000000000000000000000000000000000000
χ611616-16-160000-444-400000000000000000000000000000000000000000000000000
χ6216-1616-160000-44-4400000000000000000000000000000000000000000000000000

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