Finite Group Databasebeta

← Group #13020980

Character table — Group #13020980

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122224444444444445555555588888888888888881010101016161616161616162020202020202020202020202020202020202020404040404040404040404040
order12222222444458888101010101010104444444422442020202040404040404040404444101010102020202088888888888888888888224488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-111111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-1iiii−i−i−i−i
χ6111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-111111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-1−i−i−i−iiiii
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1111−i−i−i−iiiii
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1111iiii−i−i−i−i
χ91111111111111-1-1-1-111111111111111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1
χ101111111111111-1-1-1-111111111111111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-111
χ111111111111111-1-1-1-1111111111111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111
χ121111111111111-1-1-1-1111111111111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-111-1-1
χ131111111111111-1-1-1-11111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii11-1-1ii−i−i−i−iii
χ141111111111111-1-1-1-11111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i11-1-1−i−iiiii−i−i
χ151111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiii-1-111−i−iiiii−i−i
χ161111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i-1-111ii−i−i−i−iii
χ1722222222-2-2-2-2200002222222222222220000-2-2-2-200000000-2-2-2-200000000000022-2-222-2-200000000000000000000
χ1822222222-2-2-2-2200002222222222222220000-2-2-2-200000000-2-2-2-2000000000000-2-222-2-22200000000000000000000
χ1922222222-2-2-2-2200002222222-2-2-2-2-2-2-2-20000-2-2-2-20000000022220000000000002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ2022222222-2-2-2-2200002222222-2-2-2-2-2-2-2-20000-2-2-2-2000000002222000000000000−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ21222-2-22-2-22-22-22000022-2-2-22-22i−2i2i2i−2i−2i2i−2i00002-2-22000000002i−2i2i−2i0000000000000000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37
χ22222-2-22-2-22-22-22000022-2-2-22-22i−2i2i2i−2i−2i2i−2i00002-2-22000000002i−2i2i−2i00000000000000000000000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37
χ23222-2-22-2-22-22-22000022-2-2-22-2−2i2i−2i−2i2i2i−2i2i00002-2-2200000000−2i2i−2i2i0000000000000000000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39
χ24222-2-22-2-22-22-22000022-2-2-22-2−2i2i−2i−2i2i2i−2i2i00002-2-2200000000−2i2i−2i2i00000000000000000000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39
χ25222-2-22-2-2-22-222000022-2-2-22-22i−2i2i2i−2i−2i2i−2i002i−2i-222-200000000−2i2i−2i2i00002i2i−2i−2i000000000000000000002-20000000000
χ26222-2-22-2-2-22-222000022-2-2-22-22i−2i2i2i−2i−2i2i−2i00−2i2i-222-200000000−2i2i−2i2i0000−2i−2i2i2i00000000000000000000-220000000000
χ27222-2-22-2-2-22-222000022-2-2-22-2−2i2i−2i−2i2i2i−2i2i002i−2i-222-2000000002i−2i2i−2i00002i2i−2i−2i00000000000000000000-220000000000
χ28222-2-22-2-2-22-222000022-2-2-22-2−2i2i−2i−2i2i2i−2i2i00−2i2i-222-2000000002i−2i2i−2i0000−2i−2i2i2i000000000000000000002-20000000000
χ2922-22-2-2-220000222−2−22-22-2-2-22222-22-2-2-2000000002222−2−2−2−200000000000022−2−2002i−2i002i−2ii2i2−i2−i2i2i2−i2−i2000000000000
χ3022-22-2-2-220000222−2−22-22-2-2-22222-22-2-2-2000000002222−2−2−2−200000000000022−2−200−2i2i00−2i2i−i2−i2i2i2−i2−i2i2i2000000000000
χ3122-22-2-2-220000222−2−22-22-2-2-22-2-2-22-2222000000002222−2−2−2−2000000000000−2−222002-200-2222−2−2−2−222000000000000
χ3222-22-2-2-220000222−2−22-22-2-2-22-2-2-22-2222000000002222−2−2−2−2000000000000−2−22200-22002-2−2−22222−2−2000000000000
χ3322-22-2-2-2200002−2−2222-22-2-2-22222-22-2-2-200000000−2−2−2−22222000000000000−2−222002i−2i002i−2i−i2−i2i2i2−i2−i2i2i2000000000000
χ3422-22-2-2-2200002−2−2222-22-2-2-22222-22-2-2-200000000−2−2−2−22222000000000000−2−22200−2i2i00−2i2ii2i2−i2−i2i2i2−i2−i2000000000000
χ3522-22-2-2-2200002−2−2222-22-2-2-22-2-2-22-222200000000−2−2−2−2222200000000000022−2−2002-200-22−2−22222−2−2000000000000
χ3622-22-2-2-2200002−2−2222-22-2-2-22-2-2-22-222200000000−2−2−2−2222200000000000022−2−200-22002-222−2−2−2−222000000000000
χ372-22-22-2-22000022−22−2-22-22-2-2222-22-22-2-20000000022−2−222−2−20000000000002−22−22i−2i002i−2i00i2−i2i2−i2i2−i2i2−i2000000000000
χ382-22-22-2-22000022−22−2-22-22-2-2222-22-22-2-20000000022−2−222−2−20000000000002−22−2−2i2i00−2i2i00−i2i2−i2i2−i2i2−i2i2000000000000
χ392-22-22-2-22000022−22−2-22-22-2-22-2-22-22-2220000000022−2−222−2−2000000000000−22−222-200-22002−22−2−22−22000000000000
χ402-22-22-2-22000022−22−2-22-22-2-22-2-22-22-2220000000022−2−222−2−2000000000000−22−22-22002-200−22−222−22−2000000000000
χ412-22-22-2-2200002−22−22-22-22-2-2222-22-22-2-200000000−2−222−2−222000000000000−22−222i−2i002i−2i00−i2i2−i2i2−i2i2−i2i2000000000000
χ422-22-22-2-2200002−22−22-22-22-2-2222-22-22-2-200000000−2−222−2−222000000000000−22−22−2i2i00−2i2i00i2−i2i2−i2i2−i2i2−i2000000000000
χ432-22-22-2-2200002−22−22-22-22-2-22-2-22-22-22200000000−2−222−2−2220000000000002−22−22-200-2200−22−222−22−2000000000000
χ442-22-22-2-2200002−22−22-22-22-2-22-2-22-22-22200000000−2−222−2−2220000000000002−22−2-22002-2002−22−2−22−22000000000000
χ452-2-2222-2-22-2-2220000-2-222-22-22i−2i−2i−2i2i2i2i−2i2-20022-2-200000000−2i2i2i−2i22-2-2000000000000000000000000002i−2i00000000
χ462-2-2222-2-22-2-2220000-2-222-22-22i−2i−2i−2i2i2i2i−2i-220022-2-200000000−2i2i2i−2i-2-22200000000000000000000000000−2i2i00000000
χ472-2-2222-2-22-2-2220000-2-222-22-2−2i2i2i2i−2i−2i−2i2i2-20022-2-2000000002i−2i−2i2i22-2-200000000000000000000000000−2i2i00000000
χ482-2-2222-2-22-2-2220000-2-222-22-2−2i2i2i2i−2i−2i−2i2i-220022-2-2000000002i−2i−2i2i-2-222000000000000000000000000002i−2i00000000
χ492-2-2222-2-2-222-220000-2-222-22-22i−2i−2i−2i2i2i2i−2i0000-2-222000000002i−2i−2i2i00000000000000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700
χ502-2-2222-2-2-222-220000-2-222-22-22i−2i−2i−2i2i2i2i−2i0000-2-222000000002i−2i−2i2i000000000000000000000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700
χ512-2-2222-2-2-222-220000-2-222-22-2−2i2i2i2i−2i−2i−2i2i0000-2-22200000000−2i2i2i−2i00000000000000000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900
χ522-2-2222-2-2-222-220000-2-222-22-2−2i2i2i2i−2i−2i−2i2i0000-2-22200000000−2i2i2i−2i000000000000000000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900
χ532-2-2-2-222222-2-220000-2-2-2-222222-2-2-2-22200002-22-200000000-2-222000000000000000000002-2-222-2-22000000000000
χ542-2-2-2-222222-2-220000-2-2-2-222222-2-2-2-22200002-22-200000000-2-22200000000000000000000-222-2-222-2000000000000
χ552-2-2-2-222222-2-220000-2-2-2-2222-2-22222-2-200002-22-20000000022-2-2000000000000000000002i−2i−2i2i−2i2i2i−2i000000000000
χ562-2-2-2-222222-2-220000-2-2-2-2222-2-22222-2-200002-22-20000000022-2-200000000000000000000−2i2i2i−2i2i−2i−2i2i000000000000
χ572-2-2-2-2222-2-22222-2-22-2-2-2-222222-2-2-2-2220000-22-2222-2-2-2-22222-2-2000000002-2-220000000000000000000000000000
χ582-2-2-2-2222-2-22222-2-22-2-2-2-2222-2-22222-2-20000-22-2222-2-2-2-222-2-22200000000-222-20000000000000000000000000000
χ592-2-2-2-2222-2-2222-222-2-2-2-2-222222-2-2-2-2220000-22-22-2-22222-2-222-2-200000000-222-20000000000000000000000000000
χ602-2-2-2-2222-2-2222-222-2-2-2-2-2222-2-22222-2-20000-22-22-2-22222-2-2-2-222000000002-2-220000000000000000000000000000
χ61444444444444-14444-1-1-1-1-1-1-1000000004444-1-1-1-1-1-1-1-1-1-1-1-10000-1-1-1-1-1-1-1-100000000000000000000000000000000
χ62444444444444-14444-1-1-1-1-1-1-100000000-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-100001111111100000000000000000000000000000000
χ63444444444444-1-4-4-4-4-1-1-1-1-1-1-10000000044-4-4-1-1-1-1111111110000-1-1-1-1111100000000000000000000000000000000
χ64444444444444-1-4-4-4-4-1-1-1-1-1-1-100000000-4-444-1-1-1-11111111100001111-1-1-1-100000000000000000000000000000000
χ65444-4-44-4-4-44-44-10000-1-1111-1100000000004i−4i1-1-11i5−i5i5−i5i5−i5i5−i500005−55−5−i−iii00000000000000000000000000000000
χ66444-4-44-4-4-44-44-10000-1-1111-1100000000004i−4i1-1-11−i5i5−i5i5−i5i5−i5i50000−55−55−i−iii00000000000000000000000000000000
χ67444-4-44-4-4-44-44-10000-1-1111-110000000000−4i4i1-1-11i5−i5i5−i5i5−i5i5−i50000−55−55ii−i−i00000000000000000000000000000000
χ68444-4-44-4-4-44-44-10000-1-1111-110000000000−4i4i1-1-11−i5i5−i5i5−i5i5−i5i500005−55−5ii−i−i00000000000000000000000000000000
χ6944-4-44-44-40000400004-4-444-4-44i−4i4i−4i−4i4i−4i4i000000000000000000000000000000000000000000000000000000000000
χ7044-4-44-44-40000400004-4-444-4-4−4i4i−4i4i4i−4i4i−4i000000000000000000000000000000000000000000000000000000000000
χ714-444-4-44-4000040000-444-44-4-44i−4i−4i4i4i−4i−4i4i000000000000000000000000000000000000000000000000000000000000
χ724-444-4-44-4000040000-444-44-4-4−4i4i4i−4i−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000
χ734-4-4444-4-44-4-44-1000011-1-11-11000000004-400-1-111i5−i5−i5i5−i5i5i5−i50000-1-111i5−i5i5−i500000000000000000000000000000000
χ744-4-4444-4-44-4-44-1000011-1-11-11000000004-400-1-111−i5i5i5−i5i5−i5−i5i50000-1-111−i5i5−i5i500000000000000000000000000000000
χ754-4-4444-4-44-4-44-1000011-1-11-1100000000-4400-1-111i5−i5−i5i5−i5i5i5−i5000011-1-1−i5i5−i5i500000000000000000000000000000000
χ764-4-4444-4-44-4-44-1000011-1-11-1100000000-4400-1-111−i5i5i5−i5i5−i5−i5i5000011-1-1i5−i5i5−i500000000000000000000000000000000
χ774-4-4-4-4444-4-444-14-4-441111-1-1-10000000000001-11-1-1-11111-1-100005−5−555−5−5500000000000000000000000000000000
χ784-4-4-4-4444-4-444-14-4-441111-1-1-10000000000001-11-1-1-11111-1-10000−555−5−555−500000000000000000000000000000000
χ794-4-4-4-4444-4-444-1-444-41111-1-1-10000000000001-11-111-1-1-1-11100005−5−55−555−500000000000000000000000000000000
χ804-4-4-4-4444-4-444-1-444-41111-1-1-10000000000001-11-111-1-1-1-1110000−555−55−5−5500000000000000000000000000000000
χ8188888888-8-8-8-8-20000-2-2-2-2-2-2-200000000000022220000000000000000000000000000000000000000000000000000
χ82888-8-88-8-88-88-8-20000-2-2222-22000000000000-222-20000000000000000000000000000000000000000000000000000
χ8388-88-8-8-880000-24242−42−42-22-2222-20000000000000000−2−2−2−2222200000000000000000000000000000000000000000000
χ8488-88-8-8-880000-2−42−424242-22-2222-200000000000000002222−2−2−2−200000000000000000000000000000000000000000000
χ8588-8-88-88-80000-20000-222-2-2220000000000000000i10−i10i10−i10−i10i10−i10i1000000000000000000000000000000000000000000000
χ8688-8-88-88-80000-20000-222-2-2220000000000000000−i10i10−i10i10i10−i10i10−i1000000000000000000000000000000000000000000000
χ878-888-8-88-80000-200002-2-22-2220000000000000000i10−i10−i10i10i10−i10−i10i1000000000000000000000000000000000000000000000
χ888-888-8-88-80000-200002-2-22-2220000000000000000−i10i10i10−i10−i10i10i10−i1000000000000000000000000000000000000000000000
χ898-88-88-8-880000-242−4242−422-22-222-20000000000000000−2−222−2−22200000000000000000000000000000000000000000000
χ908-88-88-8-880000-2−4242−42422-22-222-2000000000000000022−2−222−2−200000000000000000000000000000000000000000000
χ918-8-8888-8-8-888-8-2000022-2-22-2200000000000022-2-20000000000000000000000000000000000000000000000000000
χ928-8-8-8-888888-8-8-200002222-2-2-2000000000000-22-220000000000000000000000000000000000000000000000000000

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