Finite Group Databasebeta

← Group #13020637

Character table — Group #13020637

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122224444444444445555555588888888888888881010101016161616161616162020202020202020202020202020202020202020404040404040404040404040
order12222222444458888101010101010104444444444442020202040404040404040404444202020202020202088888888888888888888444488888888
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
χ5111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-111111111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−i-1-1-1-1ii−i−iii−i−i
χ6111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-111111111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii-1-1-1-1−i−iii−i−iii
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−iiiii−i−i−i−i1111−i−iii−i−iii
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−iii−i−iii−i−i−i−iiiii1111ii−i−iii−i−i
χ91111111111111-1-1-1-111111111111111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1
χ101111111111111-1-1-1-111111111111111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111
χ111111111111111-1-1-1-1111111111111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ121111111111111-1-1-1-1111111111111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-1-1-1
χ131111111111111-1-1-1-11111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111ii−i−iii−i−i−i−i−i−iiiii-1-111ii−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−iii−i−iiiiiii−i−i−i−i-1-111−i−iiiii−i−i
χ151111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111ii−i−iii−i−i−i−i−i−iiiii11-1-1−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−iii−i−iiiiiii−i−i−i−i11-1-1ii−i−i−i−iii
χ1722222222-2-2-2-2200002222222222222220000-2-2-2-200000000-2-2-2-20000000000002222-2-2-2-200000000000000000000
χ1822222222-2-2-2-2200002222222222222220000-2-2-2-200000000-2-2-2-2000000000000-2-2-2-2222200000000000000000000
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
χ21222-2-2-22-22-22-2200002-2-2-222-22i−2i2i−2i2i−2i2i−2i00002-2-22000000002i−2i2i−2i00000000000000000000−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39000000000000
χ22222-2-2-22-22-22-2200002-2-2-222-22i−2i2i−2i2i−2i2i−2i00002-2-22000000002i−2i2i−2i000000000000000000002ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000000000
χ23222-2-2-22-22-22-2200002-2-2-222-2−2i2i−2i2i−2i2i−2i2i00002-2-2200000000−2i2i−2i2i00000000000000000000−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37000000000000
χ24222-2-2-22-22-22-2200002-2-2-222-2−2i2i−2i2i−2i2i−2i2i00002-2-2200000000−2i2i−2i2i000000000000000000002ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000000000
χ25222-2-2-22-2-22-2222i2i−2i−2i2-2-2-222-22i−2i2i−2i2i−2i2i−2i0000-222-22i2i2i2i−2i−2i−2i−2i−2i2i−2i2i0000000022-2-20000000000000000000000000000
χ26222-2-2-22-2-22-2222i2i−2i−2i2-2-2-222-2−2i2i−2i2i−2i2i−2i2i0000-222-22i2i2i2i−2i−2i−2i−2i2i−2i2i−2i00000000-2-2220000000000000000000000000000
χ27222-2-2-22-2-22-222−2i−2i2i2i2-2-2-222-22i−2i2i−2i2i−2i2i−2i0000-222-2−2i−2i−2i−2i2i2i2i2i−2i2i−2i2i00000000-2-2220000000000000000000000000000
χ28222-2-2-22-2-22-222−2i−2i2i2i2-2-2-222-2−2i2i−2i2i−2i2i−2i2i0000-222-2−2i−2i−2i−2i2i2i2i2i2i−2i2i−2i0000000022-2-20000000000000000000000000000
χ2922-22-2-2-222-2-2220000-22-2-22-222i−2i−2i2i2i−2i−2i2i002-222-2-2000000002i−2i−2i2i000022-2-200000000000000000000002i−2i00000000
χ3022-22-2-2-222-2-2220000-22-2-22-222i−2i−2i2i2i−2i−2i2i00-2222-2-2000000002i−2i−2i2i0000-2-2220000000000000000000000−2i2i00000000
χ3122-22-2-2-222-2-2220000-22-2-22-22−2i2i2i−2i−2i2i2i−2i002-222-2-200000000−2i2i2i−2i000022-2-20000000000000000000000−2i2i00000000
χ3222-22-2-2-222-2-2220000-22-2-22-22−2i2i2i−2i−2i2i2i−2i00-2222-2-200000000−2i2i2i−2i0000-2-22200000000000000000000002i−2i00000000
χ3322-22-2-2-22-222-220000-22-2-22-222i−2i−2i2i2i−2i−2i2i0000-2-22200000000−2i2i2i−2i000000000000000000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37
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χ3522-22-2-2-22-222-220000-22-2-22-22−2i2i2i−2i−2i2i2i−2i0000-2-222000000002i−2i−2i2i000000000000000000000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39
χ3622-22-2-2-22-222-220000-22-2-22-22−2i2i2i−2i−2i2i2i−2i0000-2-222000000002i−2i−2i2i0000000000000000000000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39
χ3722-2-222-2-222-2-220000-2-2222-2-222-2-222-2-200002-22-20000000022-2-2000000000000000000000000000000002-22-20000
χ3822-2-222-2-222-2-220000-2-2222-2-222-2-222-2-200002-22-20000000022-2-200000000000000000000000000000000-22-220000
χ3922-2-222-2-222-2-220000-2-2222-2-2-2-222-2-22200002-22-200000000-2-222000000000000000000000000000000002i−2i−2i2i0000
χ4022-2-222-2-222-2-220000-2-2222-2-2-2-222-2-22200002-22-200000000-2-22200000000000000000000000000000000−2i2i2i−2i0000
χ4122-2-222-2-2-2-22220000-2-2222-2-222-2-222-2-22i−2i00-22-2200000000-2-2222i2i−2i−2i0000000000000000000000002i−2i0000000000
χ4222-2-222-2-2-2-22220000-2-2222-2-222-2-222-2-2−2i2i00-22-2200000000-2-222−2i−2i2i2i000000000000000000000000−2i2i0000000000
χ4322-2-222-2-2-2-22220000-2-2222-2-2-2-222-2-2222i−2i00-22-220000000022-2-22i2i−2i−2i000000000000000000000000−2i2i0000000000
χ4422-2-222-2-2-2-22220000-2-2222-2-2-2-222-2-222−2i2i00-22-220000000022-2-2−2i−2i2i2i0000000000000000000000002i−2i0000000000
χ452-2222-2-2-2000022−22−2-2-22-2-2222i−2i−2i2i−2i2i2i−2i0000000022−2−222−2−2000000000000i2−i2i2−i20000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ391+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000
χ462-2222-2-2-2000022−22−2-2-22-2-2222i−2i−2i2i−2i2i2i−2i0000000022−2−222−2−2000000000000i2−i2i2−i200002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
χ472-2222-2-2-2000022−22−2-2-22-2-222−2i2i2i−2i2i−2i−2i2i0000000022−2−222−2−2000000000000−i2i2−i2i20000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000
χ482-2222-2-2-2000022−22−2-2-22-2-222−2i2i2i−2i2i−2i−2i2i0000000022−2−222−2−2000000000000−i2i2−i2i200002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ371−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
χ492-2222-2-2-200002−22−22-2-22-2-2222i−2i−2i2i−2i2i2i−2i00000000−2−222−2−222000000000000−i2i2−i2i20000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
χ502-2222-2-2-200002−22−22-2-22-2-2222i−2i−2i2i−2i2i2i−2i00000000−2−222−2−222000000000000−i2i2−i2i200002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ391+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000
χ512-2222-2-2-200002−22−22-2-22-2-222−2i2i2i−2i2i−2i−2i2i00000000−2−222−2−222000000000000i2−i2i2−i20000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ371−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
χ522-2222-2-2-200002−22−22-2-22-2-222−2i2i2i−2i2i−2i−2i2i00000000−2−222−2−222000000000000i2−i2i2−i200002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000
χ532-22-2-22-2200002i2−i2−i2i2-22-22-22-222-2-2-2-22200000000i2i2−i2−i2−i2−i2i2i2000000000000−i2i2i2−i22i−2i2i−2i00002−2−22−222−2000000000000
χ542-22-2-22-2200002i2−i2−i2i2-22-22-22-222-2-2-2-22200000000i2i2−i2−i2−i2−i2i2i2000000000000−i2i2i2−i2−2i2i−2i2i0000−222−22−2−22000000000000
χ552-22-2-22-2200002i2−i2−i2i2-22-22-22-2-2-22222-2-200000000i2i2−i2−i2−i2−i2i2i2000000000000i2−i2−i2i22-2-220000−i2i2i2−i2−i2i2i2−i2000000000000
χ562-22-2-22-2200002i2−i2−i2i2-22-22-22-2-2-22222-2-200000000i2i2−i2−i2−i2−i2i2i2000000000000i2−i2−i2i2-222-20000i2−i2−i2i2i2−i2−i2i2000000000000
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χ582-22-2-22-2200002−i2i2i2−i2-22-22-22-222-2-2-2-22200000000−i2−i2i2i2i2i2−i2−i2000000000000i2−i2−i2i2−2i2i−2i2i00002−2−22−222−2000000000000
χ592-22-2-22-2200002−i2i2i2−i2-22-22-22-2-2-22222-2-200000000−i2−i2i2i2i2i2−i2−i2000000000000−i2i2i2−i22-2-220000i2−i2−i2i2i2−i2−i2i2000000000000
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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
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χ67444-4-4-44-4-44-44-1−4i−4i4i4i-1111-1-110000000000001-1-11iiii−i−i−i−i00005−55−5−i5i5−i5i500000000000000000000000000000000
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χ7144-44-4-4-444-4-44-100001-111-11-10000000000-44-1-111i5−i5i5−i5i5−i5i5−i50000−i5i5i5−i511-1-100000000000000000000000000000000
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χ898-8-88-888-80000-20000-222-222-20000000000000000i10−i10−i10i10i10−i10−i10i1000000000000000000000000000000000000000000000
χ908-8-88-888-80000-20000-222-222-20000000000000000−i10i10i10−i10−i10i10i10−i1000000000000000000000000000000000000000000000
χ918-8-8-88-8880000-20000-2-2-22222000000000000000010−10−1010−101010−1000000000000000000000000000000000000000000000
χ928-8-8-88-8880000-20000-2-2-222220000000000000000−101010−1010−10−101000000000000000000000000000000000000000000000

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