Finite Group Databasebeta

← Group #13019986

Character table — Group #13019986

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112244444488888888101010101010161616161616161616162020202020202020203232404040404040404040404040808080
order12222244510101024881010202022444421010101020404040402888888881020444444888888488
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11-1-1
χ311111111111111111111-1-1-1-1-1-11111111111-1iiii−i−i−i−i11-1-1ii−i−i-1-1ii−i−i-1i−i
χ411111111111111111111-1-1-1-1-1-11111111111-1−i−i−i−iiiii11-1-1−i−iii-1-1−i−iii-1−ii
χ511111111111111-1-11111111111-1-1-1-1-11-1-1-1-11111111111111-1-1-1-1-1-11111-1-1-1
χ611111111111111-1-11111111111-1-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-111
χ711111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1iiii−i−i−i−i11-1-1−i−iii11ii−i−i1−ii
χ811111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1−i−i−i−iiiii11-1-1ii−i−i11−i−iii1i−i
χ9111111111111-1-1111111111111-1-1-1-1-111111111-1-111-1-1-1-1-1-11111111-11-1-1-1-1
χ10111111111111-1-1111111111111-1-1-1-1-1111111-1-111-1-111-1-1-1-1-1-1-1-111-11-11-111
χ11111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-111111-1ii−i−i−i−iii-1-111ii−i−i-1-1i−i−ii1−ii
χ12111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-111111-1−i−iiiii−i−i-1-111−i−iii-1-1−iii−i1i−i
χ13111111111111-1-1-1-11111111111111111-1-1-1-1111-1-111-1-1-1-1-1-1-1-1-1-1-1-11-11-1111
χ14111111111111-1-1-1-11111111111111111-1-1-1-11-1-111-1-111-1-1-1-11111-1-1-11-111-1-1
χ15111111111111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1ii−i−i−i−iii-1-111−i−iii11i−i−ii-1i−i
χ16111111111111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1−i−iiiii−i−i-1-111ii−i−i11−iii−i-1−ii
χ17222222-2-22222000022-2-222-2-2-2-200000-2000022i2i00−2i−2i000000000000−2i02i0000
χ18222222-2-22222000022-2-222-2-2-2-200000-200002−2i−2i002i2i0000000000002i0−2i0000
χ19222222-2-22222000022-2-2-2-2222200000-20000-2220022000000000000-20-20000
χ20222222-2-22222000022-2-2-2-2222200000-20000-2-2-200-2-20000000000002020000
χ212222-2-22-222220000-2-2-2-222-2-2220000020000-20022002200000000000-20-2000
χ222222-2-22-222220000-2-2-2-222-2-2220000020000-200-2-200-2-200000000000202000
χ232222-2-22-222220000-2-2-2-2-2-222-2-200000200002002i2i00−2i−2i00000000000−2i02i000
χ242222-2-22-222220000-2-2-2-2-2-222-2-20000020000200−2i−2i002i2i000000000002i0−2i000
χ252222-2-2-2222222-200-2-2222222-2-200000-20000-2000000002-2-220000000000000
χ262222-2-2-2222222-200-2-222-2-2-2-22200000-200002000000002-22-20000000000000
χ272222-2-2-222222-2200-2-2222222-2-200000-20000-200000000-222-20000000000000
χ282222-2-2-222222-2200-2-222-2-2-2-22200000-20000200000000-22-220000000000000
χ2922-2-22-2002-22-2002−22-200002i−2i2i−2i00000022−2−20−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000001+i−1−i1−i−1+ii2−i20000000
χ3022-2-22-2002-22-2002−22-200002i−2i2i−2i00000022−2−202ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000−1−i1+i−1+i1−ii2−i20000000
χ3122-2-22-2002-22-2002−22-20000−2i2i−2i2i00000022−2−20−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000−1+i1−i−1−i1+i−i2i20000000
χ3222-2-22-2002-22-2002−22-20000−2i2i−2i2i00000022−2−202ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000001−i−1+i1+i−1−i−i2i20000000
χ3322-2-22-2002-22-200−222-200002i−2i2i−2i000000−2−2220−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000−1−i1+i−1+i1−i−i2i20000000
χ3422-2-22-2002-22-200−222-200002i−2i2i−2i000000−2−22202ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000001+i−1−i1−i−1+i−i2i20000000
χ3522-2-22-2002-22-200−222-20000−2i2i−2i2i000000−2−2220−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370000001−i−1+i1+i−1−ii2−i20000000
χ3622-2-22-2002-22-200−222-20000−2i2i−2i2i000000−2−22202ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000−1+i1−i−1−i1+ii2−i20000000
χ3744444444-1-1-1-14444-1-1-1-10000004-1-1-1-1-1-1-1-1-1000000000-1-1000000000000000
χ3844444444-1-1-1-144-4-4-1-1-1-1000000-41111-11111000000000-1-1000000000000000
χ3944444444-1-1-1-1-4-444-1-1-1-1000000-41111-1-1-1-1-100000000011000000000000000
χ4044444444-1-1-1-1-4-4-4-4-1-1-1-10000004-1-1-1-1-1111100000000011000000000000000
χ414444-4-4-44-1-1-1-14-40011-1-1000000055−5−515−55−5000000000-11000000000000000
χ424444-4-4-44-1-1-1-14-40011-1-10000000−5−5551−55−55000000000-11000000000000000
χ434444-4-4-44-1-1-1-1-440011-1-1000000055−5−51−55−550000000001-1000000000000000
χ444444-4-4-44-1-1-1-1-440011-1-10000000−5−55515−55−50000000001-1000000000000000
χ4544-4-4-44004-44-40000-4400004i−4i−4i4i000000000000000000000000000000000000
χ4644-4-4-44004-44-40000-440000−4i4i4i−4i000000000000000000000000000000000000
χ474-4-44000044-4-4000000004-4000000000000000002i2−2i2002i2−2i200000000000000000
χ484-4-44000044-4-4000000004-400000000000000000−2i22i200−2i22i200000000000000000
χ494-4-44000044-4-400000000-440000000000000000022−2200−222200000000000000000
χ504-4-44000044-4-400000000-4400000000000000000−22220022−2200000000000000000
χ51888888-8-8-2-2-2-20000-2-222000000000002000000000000000000000000000000
χ528888-8-88-8-2-2-2-20000222200000000000-2000000000000000000000000000000
χ5388-8-88-800-22-220042−42-2200000000000000−2−22200000000000000000000000000
χ5488-8-88-800-22-2200−4242-220000000000000022−2−200000000000000000000000000
χ5588-8-8-8800-22-2200002-20000000000000010−10−101000000000000000000000000000
χ5688-8-8-8800-22-2200002-200000000000000−101010−1000000000000000000000000000
χ578-88-800008-8-8800000000000000000000000000000000000000000000000000
χ588-88-80000-222-200000025−2500000002ζ12−2ζ28−2ζ12+2ζ28−2ζ4+2ζ362ζ4−2ζ360000000000000000000000000000000
χ598-88-80000-222-200000025−250000000−2ζ12+2ζ282ζ12−2ζ282ζ4−2ζ36−2ζ4+2ζ360000000000000000000000000000000
χ608-88-80000-222-2000000−25250000000−2ζ4+2ζ362ζ4−2ζ36−2ζ12+2ζ282ζ12−2ζ280000000000000000000000000000000
χ618-88-80000-222-2000000−252500000002ζ4−2ζ36−2ζ4+2ζ362ζ12−2ζ28−2ζ12+2ζ280000000000000000000000000000000
χ6216-16-16160000-4-44400000000000000000000000000000000000000000000000000

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