Finite Group Databasebeta

← Group #13022822

Character table — Group #13022822

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122224444444444445555555588888888888888881010101016161616161616162020202020202020202020202020202020202020404040404040404040404040
order12222222444458888101010101010104444444444442020202040404040404040402222202020202020202044444444888888888888444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
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
χ411111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-111111111iiii−i−i−i−i-1-1-1-1iiii−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−i−i−i−iiiii-1-1-1-1−i−i−i−iiiii-1-1-1-1−i−iii−i−iii
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i-1-1-1-1iiii−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−i−i−i−iiiii-1-1-1-1−i−i−i−iiiii1111ii−i−iii−i−i
χ91111111111111-1-1-1-111111111111111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1
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
χ111111111111111-1-1-1-1111111111111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
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
χ131111111111111-1-1-1-11111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−i1111−i−i−i−iiiii-1-111ii−i−i−i−iii
χ141111111111111-1-1-1-11111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii1111iiii−i−i−i−i-1-111−i−iiiii−i−i
χ151111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i1111−i−i−i−iiiii11-1-1−i−iiiii−i−i
χ161111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiii1111iiii−i−i−i−i11-1-1ii−i−i−i−iii
χ1722222222-2-2-2-2200002222222222222220000-2-2-2-200000000-2-2-2-20000000000000000000022-2-222-2-2000000000000
χ1822222222-2-2-2-2200002222222222222220000-2-2-2-200000000-2-2-2-200000000000000000000-2-222-2-222000000000000
χ1922222222-2-2-2-2200002222222-2-2-2-2-2-2-2-20000-2-2-2-2000000002222000000000000000000002i2i−2i−2i−2i−2i2i2i000000000000
χ2022222222-2-2-2-2200002222222-2-2-2-2-2-2-2-20000-2-2-2-200000000222200000000000000000000−2i−2i2i2i2i2i−2i−2i000000000000
χ21222-2-22-2-222-2-22000022-2-22-2-222-2-222-2-2000022-2-20000000022-2-2000000000000000000000000000000002-22-20000
χ22222-2-22-2-222-2-22000022-2-22-2-222-2-222-2-2000022-2-20000000022-2-200000000000000000000000000000000-22-220000
χ23222-2-22-2-222-2-22000022-2-22-2-2-2-222-2-222000022-2-200000000-2-222000000000000000000000000000000002i−2i−2i2i0000
χ24222-2-22-2-222-2-22000022-2-22-2-2-2-222-2-222000022-2-200000000-2-22200000000000000000000000000000000−2i2i2i−2i0000
χ25222-2-22-2-2-2-2222000022-2-22-2-222-2-222-2-2002i−2i-2-22200000000-2-22200002i2i−2i−2i00000000000000000000002i−2i00000000
χ26222-2-22-2-2-2-2222000022-2-22-2-222-2-222-2-200−2i2i-2-22200000000-2-2220000−2i−2i2i2i0000000000000000000000−2i2i00000000
χ27222-2-22-2-2-2-2222000022-2-22-2-2-2-222-2-222002i−2i-2-2220000000022-2-200002i2i−2i−2i0000000000000000000000−2i2i00000000
χ28222-2-22-2-2-2-2222000022-2-22-2-2-2-222-2-22200−2i2i-2-2220000000022-2-20000−2i−2i2i2i00000000000000000000002i−2i00000000
χ2922-222-2-2-20000222−2−22-2-2-2-2222i−2i2i−2i2i−2i2i−2i000000002222−2−2−2−20000000000001+i1+i−1−i−1−i1−i1−i−1+i−1+ii2i2−i2−i200−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000000000
χ3022-222-2-2-20000222−2−22-2-2-2-2222i−2i2i−2i2i−2i2i−2i000000002222−2−2−2−2000000000000−1−i−1−i1+i1+i−1+i−1+i1−i1−ii2i2−i2−i2002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000000000
χ3122-222-2-2-20000222−2−22-2-2-2-222−2i2i−2i2i−2i2i−2i2i000000002222−2−2−2−20000000000001−i1−i−1+i−1+i1+i1+i−1−i−1−i−i2−i2i2i2002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000000000
χ3222-222-2-2-20000222−2−22-2-2-2-222−2i2i−2i2i−2i2i−2i2i000000002222−2−2−2−2000000000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i−i2−i2i2i200−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000000000
χ3322-222-2-2-200002−2−2222-2-2-2-2222i−2i2i−2i2i−2i2i−2i00000000−2−2−2−222220000000000001+i1+i−1−i−1−i1−i1−i−1+i−1+i−i2−i2i2i2002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000000000
χ3422-222-2-2-200002−2−2222-2-2-2-2222i−2i2i−2i2i−2i2i−2i00000000−2−2−2−22222000000000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i−i2−i2i2i200−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000000000
χ3522-222-2-2-200002−2−2222-2-2-2-222−2i2i−2i2i−2i2i−2i2i00000000−2−2−2−222220000000000001−i1−i−1+i−1+i1+i1+i−1−i−1−ii2i2−i2−i200−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000000000
χ3622-222-2-2-200002−2−2222-2-2-2-222−2i2i−2i2i−2i2i−2i2i00000000−2−2−2−22222000000000000−1+i−1+i1−i1−i−1−i−1−i1+i1+ii2i2−i2−i2002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000000000
χ372-222-2-22-200002i2−i2i2−i2-222-2-22-22i−2i−2i2i−2i2i2i−2i00000000i2i2−i2−i2i2i2−i2−i20000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i2−22−2−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700000000000000
χ382-222-2-22-200002i2−i2i2−i2-222-2-22-22i−2i−2i2i−2i2i2i−2i00000000i2i2−i2−i2i2i2−i2−i2000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i2−22−22ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700000000000000
χ392-222-2-22-200002i2−i2i2−i2-222-2-22-2−2i2i2i−2i2i−2i−2i2i00000000i2i2−i2−i2i2i2−i2−i20000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i−22−22−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900000000000000
χ402-222-2-22-200002i2−i2i2−i2-222-2-22-2−2i2i2i−2i2i−2i−2i2i00000000i2i2−i2−i2i2i2−i2−i2000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i−22−222ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900000000000000
χ412-222-2-22-200002−i2i2−i2i2-222-2-22-22i−2i−2i2i−2i2i2i−2i00000000−i2−i2i2i2−i2−i2i2i20000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i−22−222ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700000000000000
χ422-222-2-22-200002−i2i2−i2i2-222-2-22-22i−2i−2i2i−2i2i2i−2i00000000−i2−i2i2i2−i2−i2i2i2000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i−22−22−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700000000000000
χ432-222-2-22-200002−i2i2−i2i2-222-2-22-2−2i2i2i−2i2i−2i−2i2i00000000−i2−i2i2i2−i2−i2i2i20000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i2−22−22ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900000000000000
χ442-222-2-22-200002−i2i2−i2i2-222-2-22-2−2i2i2i−2i2i−2i−2i2i00000000−i2−i2i2i2−i2−i2i2i2000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i2−22−2−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900000000000000
χ452-2-22-22-222-22-222i−2i−2i2i-2-2-2222-222-2-2-2-22200002-22-22i2i−2i−2i−2i−2i2i2i2-22-20000000000000000−2i2i2i−2i00000000000000000000
χ462-2-22-22-222-22-222i−2i−2i2i-2-2-2222-2-2-22222-2-200002-22-22i2i−2i−2i−2i−2i2i2i-22-2200000000000000002i−2i−2i2i00000000000000000000
χ472-2-22-22-222-22-22−2i2i2i−2i-2-2-2222-222-2-2-2-22200002-22-2−2i−2i2i2i2i2i−2i−2i2-22-200000000000000002i−2i−2i2i00000000000000000000
χ482-2-22-22-222-22-22−2i2i2i−2i-2-2-2222-2-2-22222-2-200002-22-2−2i−2i2i2i2i2i−2i−2i-22-220000000000000000−2i2i2i−2i00000000000000000000
χ492-2-22-22-22-22-2220000-2-2-2222-222-2-2-2-2220000-22-2200000000-22-22000000002-2-222-2-22000000000000000000000000
χ502-2-22-22-22-22-2220000-2-2-2222-222-2-2-2-2220000-22-2200000000-22-2200000000-222-2-222-2000000000000000000000000
χ512-2-22-22-22-22-2220000-2-2-2222-2-2-22222-2-20000-22-22000000002-22-2000000002i−2i−2i2i−2i2i2i−2i000000000000000000000000
χ522-2-22-22-22-22-2220000-2-2-2222-2-2-22222-2-20000-22-22000000002-22-200000000−2i2i2i−2i2i−2i−2i2i000000000000000000000000
χ532-2-2-2222-22-2-2220000-2-22-22-222222-2-2-2-200002-2-22000000002-2-220000000000000000000000000000000000002i−2i2i−2i
χ542-2-2-2222-22-2-2220000-2-22-22-222222-2-2-2-200002-2-22000000002-2-22000000000000000000000000000000000000−2i2i−2i2i
χ552-2-2-2222-22-2-2220000-2-22-22-22-2-2-2-2222200002-2-2200000000-222-20000000000000000000000000000000000002-2-22
χ562-2-2-2222-22-2-2220000-2-22-22-22-2-2-2-2222200002-2-2200000000-222-2000000000000000000000000000000000000-222-2
χ572-2-2-2222-2-222-220000-2-22-22-222222-2-2-2-22-200-222-200000000-222-222-2-20000000000000000000000002-20000000000
χ582-2-2-2222-2-222-220000-2-22-22-222222-2-2-2-2-2200-222-200000000-222-2-2-222000000000000000000000000-220000000000
χ592-2-2-2222-2-222-220000-2-22-22-22-2-2-2-222222-200-222-2000000002-2-2222-2-2000000000000000000000000-220000000000
χ602-2-2-2222-2-222-220000-2-22-22-22-2-2-2-22222-2200-222-2000000002-2-22-2-2220000000000000000000000002-20000000000
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
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χ64444444444444-1-4-4-4-4-1-1-1-1-1-1-100000000-4-444-1-1-1-11111111100001111-1-1-1-100000000000000000000000000000000
χ65444-4-44-4-4-4-444-10000-1-111-11100000000004i−4i11-1-15−55−55−55−50000i5−i5i5−i5−i−iii00000000000000000000000000000000
χ66444-4-44-4-4-4-444-10000-1-111-11100000000004i−4i11-1-1−55−55−55−550000−i5i5−i5i5−i−iii00000000000000000000000000000000
χ67444-4-44-4-4-4-444-10000-1-111-1110000000000−4i4i11-1-15−55−55−55−50000−i5i5−i5i5ii−i−i00000000000000000000000000000000
χ68444-4-44-4-4-4-444-10000-1-111-1110000000000−4i4i11-1-1−55−55−55−550000i5−i5i5−i5ii−i−i00000000000000000000000000000000
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χ754-4-44-44-444-44-4-1−4i4i4i−4i111-1-1-11000000000000-11-11ii−i−i−i−iii0000i5−i5−i5i5−55−5500000000000000000000000000000000
χ764-4-44-44-444-44-4-1−4i4i4i−4i111-1-1-11000000000000-11-11ii−i−i−i−iii0000−i5i5i5−i55−55−500000000000000000000000000000000
χ774-4-4-4444-4-444-4-1000011-11-11-1000000004-4001-1-11i5−i5−i5i5−i5i5i5−i50000-1-111−i5i5i5−i500000000000000000000000000000000
χ784-4-4-4444-4-444-4-1000011-11-11-1000000004-4001-1-11−i5i5i5−i5i5−i5−i5i50000-1-111i5−i5−i5i500000000000000000000000000000000
χ794-4-4-4444-4-444-4-1000011-11-11-100000000-44001-1-11i5−i5−i5i5−i5i5i5−i5000011-1-1i5−i5−i5i500000000000000000000000000000000
χ804-4-4-4444-4-444-4-1000011-11-11-100000000-44001-1-11−i5i5i5−i5i5−i5−i5i5000011-1-1−i5i5i5−i500000000000000000000000000000000
χ8188888888-8-8-8-8-20000-2-2-2-2-2-2-200000000000022220000000000000000000000000000000000000000000000000000
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χ8388-888-8-8-80000-24242−42−42-22222-2-20000000000000000−2−2−2−2222200000000000000000000000000000000000000000000
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χ888-888-8-88-80000-2−4i24i2−4i24i22-2-222-220000000000000000i2i2−i2−i2i2i2−i2−i200000000000000000000000000000000000000000000
χ898-88-88-8-880000-200002-22-222-20000000000000000i10−i10−i10i10i10−i10−i10i1000000000000000000000000000000000000000000000
χ908-88-88-8-880000-200002-22-222-20000000000000000−i10i10i10−i10−i10i10i10−i1000000000000000000000000000000000000000000000
χ918-8-88-88-88-88-88-20000222-2-2-220000000000002-22-20000000000000000000000000000000000000000000000000000
χ928-8-8-8888-88-8-88-2000022-22-22-2000000000000-222-20000000000000000000000000000000000000000000000000000

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