Finite Group Databasebeta

← Group #13020631

Character table — Group #13020631

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
χ2122-222-2-2-22-22-2222-2-22-2-2-2-2222i−2i2i−2i2i−2i2i−2i00002-2-222222-2-2-2-22i−2i2i−2i000000002i2i−2i−2i0000000000000000000000000000
χ2222-222-2-2-22-22-2222-2-22-2-2-2-222−2i2i−2i2i−2i2i−2i2i00002-2-222222-2-2-2-2−2i2i−2i2i00000000−2i−2i2i2i0000000000000000000000000000
χ2322-222-2-2-22-22-22-2-2222-2-2-2-2222i−2i2i−2i2i−2i2i−2i00002-2-22-2-2-2-222222i−2i2i−2i00000000−2i−2i2i2i0000000000000000000000000000
χ2422-222-2-2-22-22-22-2-2222-2-2-2-222−2i2i−2i2i−2i2i−2i2i00002-2-22-2-2-2-22222−2i2i−2i2i000000002i2i−2i−2i0000000000000000000000000000
χ2522-222-2-2-2-22-22200002-2-2-2-2222i−2i2i−2i2i−2i2i−2i0000-222-200000000−2i2i−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
χ2622-222-2-2-2-22-22200002-2-2-2-2222i−2i2i−2i2i−2i2i−2i0000-222-200000000−2i2i−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
χ2722-222-2-2-2-22-22200002-2-2-2-222−2i2i−2i2i−2i2i−2i2i0000-222-2000000002i−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
χ2822-222-2-2-2-22-22200002-2-2-2-222−2i2i−2i2i−2i2i−2i2i0000-222-2000000002i−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
χ292-222-2-2-222-2-2220000-222-2-22-22i−2i−2i2i2i−2i−2i2i000022-2-2000000002i−2i−2i2i000000000000000000000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39
χ302-222-2-2-222-2-2220000-222-2-22-22i−2i−2i2i2i−2i−2i2i000022-2-2000000002i−2i−2i2i0000000000000000000000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39
χ312-222-2-2-222-2-2220000-222-2-22-2−2i2i2i−2i−2i2i2i−2i000022-2-200000000−2i2i2i−2i000000000000000000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37
χ322-222-2-2-222-2-2220000-222-2-22-2−2i2i2i−2i−2i2i2i−2i000022-2-200000000−2i2i2i−2i0000000000000000000000000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37
χ332-222-2-2-22-222-220000-222-2-22-22i−2i−2i2i2i−2i−2i2i002i−2i-2-22200000000−2i2i2i−2i00002i2i−2i−2i00000000000000000000002-200000000
χ342-222-2-2-22-222-220000-222-2-22-22i−2i−2i2i2i−2i−2i2i00−2i2i-2-22200000000−2i2i2i−2i0000−2i−2i2i2i0000000000000000000000-2200000000
χ352-222-2-2-22-222-220000-222-2-22-2−2i2i2i−2i−2i2i2i−2i002i−2i-2-222000000002i−2i−2i2i00002i2i−2i−2i0000000000000000000000-2200000000
χ362-222-2-2-22-222-220000-222-2-22-2−2i2i2i−2i−2i2i2i−2i00−2i2i-2-222000000002i−2i−2i2i0000−2i−2i2i2i00000000000000000000002-200000000
χ372-22-222-2-2000022−22−2-22-22-2-222i−2i2i−2i−2i2i−2i2i0000000022−2−222−2−2000000000000i2−i2i2−i2−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900001+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000
χ382-22-222-2-2000022−22−2-22-22-2-222i−2i2i−2i−2i2i−2i2i0000000022−2−222−2−2000000000000i2−i2i2−i22ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
χ392-22-222-2-2000022−22−2-22-22-2-22−2i2i−2i2i2i−2i2i−2i0000000022−2−222−2−2000000000000−i2i2−i2i2−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370000−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000
χ402-22-222-2-2000022−22−2-22-22-2-22−2i2i−2i2i2i−2i2i−2i0000000022−2−222−2−2000000000000−i2i2−i2i22ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700001−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
χ412-22-222-2-200002−22−22-22-22-2-222i−2i2i−2i−2i2i−2i2i00000000−2−222−2−222000000000000−i2i2−i2i2−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
χ422-22-222-2-200002−22−22-22-22-2-222i−2i2i−2i−2i2i−2i2i00000000−2−222−2−222000000000000−i2i2−i2i22ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900001+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000
χ432-22-222-2-200002−22−22-22-22-2-22−2i2i−2i2i2i−2i2i−2i00000000−2−222−2−222000000000000i2−i2i2−i2−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700001−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
χ442-22-222-2-200002−22−22-22-22-2-22−2i2i−2i2i2i−2i2i−2i00000000−2−222−2−222000000000000i2−i2i2−i22ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000
χ452-2-22-222-222-2-220000-2-2-2222-222-2-222-2-200002-22-20000000022-2-2000000000000000000000000000000002-22-20000
χ462-2-22-222-222-2-220000-2-2-2222-222-2-222-2-200002-22-20000000022-2-200000000000000000000000000000000-22-220000
χ472-2-22-222-222-2-220000-2-2-2222-2-2-222-2-22200002-22-200000000-2-222000000000000000000000000000000002i−2i−2i2i0000
χ482-2-22-222-222-2-220000-2-2-2222-2-2-222-2-22200002-22-200000000-2-22200000000000000000000000000000000−2i2i2i−2i0000
χ492-2-22-222-2-2-22220000-2-2-2222-222-2-222-2-22i−2i00-22-2200000000-2-2222i2i−2i−2i0000000000000000000000002i−2i0000000000
χ502-2-22-222-2-2-22220000-2-2-2222-222-2-222-2-2−2i2i00-22-2200000000-2-222−2i−2i2i2i000000000000000000000000−2i2i0000000000
χ512-2-22-222-2-2-22220000-2-2-2222-2-2-222-2-2222i−2i00-22-220000000022-2-22i2i−2i−2i000000000000000000000000−2i2i0000000000
χ522-2-22-222-2-2-22220000-2-2-2222-2-2-222-2-222−2i2i00-22-220000000022-2-2−2i−2i2i2i0000000000000000000000002i−2i0000000000
χ532-2-2-22-222000022−2−22-2-22-22-222222-2-2-2-20000000022−2−2−2−2220000000000002−2−2200002i−2i2i−2ii2−i2−i2i2i2−i2−i2i2000000000000
χ542-2-2-22-222000022−2−22-2-22-22-222222-2-2-2-20000000022−2−2−2−2220000000000002−2−220000−2i2i−2i2i−i2i2i2−i2−i2i2i2−i2000000000000
χ552-2-2-22-222000022−2−22-2-22-22-22-2-2-2-222220000000022−2−2−2−222000000000000−222−200002-2-222−2−22−222−2000000000000
χ562-2-2-22-222000022−2−22-2-22-22-22-2-2-2-222220000000022−2−2−2−222000000000000−222−20000-222-2−222−22−2−22000000000000
χ572-2-2-22-22200002−222−2-2-22-22-222222-2-2-2-200000000−2−22222−2−2000000000000−222−200002i−2i2i−2i−i2i2i2−i2−i2i2i2−i2000000000000
χ582-2-2-22-22200002−222−2-2-22-22-222222-2-2-2-200000000−2−22222−2−2000000000000−222−20000−2i2i−2i2ii2−i2−i2i2i2−i2−i2i2000000000000
χ592-2-2-22-22200002−222−2-2-22-22-22-2-2-2-2222200000000−2−22222−2−20000000000002−2−2200002-2-22−222−22−2−22000000000000
χ602-2-2-22-22200002−222−2-2-22-22-22-2-2-2-2222200000000−2−22222−2−20000000000002−2−220000-222-22−2−22−222−2000000000000
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
χ65444-4-4-44-400004000044-4-44-4-444-4-4-4-444000000000000000000000000000000000000000000000000000000000000
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χ6744-444-4-4-44-44-4-144-4-4-11111-1-1000000000000-111-1-1-1-1-1111100005−55−55−55−500000000000000000000000000000000
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χ7244-4-4-44-440000400004-444-4-4-4−4i4i4i−4i4i−4i−4i4i000000000000000000000000000000000000000000000000000000000000
χ734-444-4-4-44-444-4-100001-1-111-1100000000004i−4i11-1-15−55−55−55−50000i5−i5−i5i5−i−iii00000000000000000000000000000000
χ744-444-4-4-44-444-4-100001-1-111-1100000000004i−4i11-1-1−55−55−55−550000−i5i5i5−i5−i−iii00000000000000000000000000000000
χ754-444-4-4-44-444-4-100001-1-111-110000000000−4i4i11-1-15−55−55−55−50000−i5i5i5−i5ii−i−i00000000000000000000000000000000
χ764-444-4-4-44-444-4-100001-1-111-110000000000−4i4i11-1-1−55−55−55−550000i5−i5−i5i5ii−i−i00000000000000000000000000000000
χ774-4-44-444-4-4-444-10000111-1-1-11000000004i−4i001-11-15−55−5−55−550000−i−iiii5−i5−i5i500000000000000000000000000000000
χ784-4-44-444-4-4-444-10000111-1-1-11000000004i−4i001-11-1−55−555−55−50000−i−iii−i5i5i5−i500000000000000000000000000000000
χ794-4-44-444-4-4-444-10000111-1-1-1100000000−4i4i001-11-15−55−5−55−550000ii−i−i−i5i5i5−i500000000000000000000000000000000
χ804-4-44-444-4-4-444-10000111-1-1-1100000000−4i4i001-11-1−55−555−55−50000ii−i−ii5−i5−i5i500000000000000000000000000000000
χ8188888888-8-8-8-8-20000-2-2-2-2-2-2-200000000000022220000000000000000000000000000000000000000000000000000
χ82888-8-8-88-80000-20000-2-222-222000000000000000010−10−101010−10−101000000000000000000000000000000000000000000000
χ83888-8-8-88-80000-20000-2-222-2220000000000000000−101010−10−101010−1000000000000000000000000000000000000000000000
χ8488-888-8-8-8-88-88-20000-22222-2-20000000000002-2-220000000000000000000000000000000000000000000000000000
χ8588-8-8-88-880000-20000-22-2-2222000000000000000010−10−1010−101010−1000000000000000000000000000000000000000000000
χ8688-8-8-88-880000-20000-22-2-22220000000000000000−101010−1010−10−101000000000000000000000000000000000000000000000
χ878-888-8-8-888-8-88-200002-2-222-22000000000000-2-2220000000000000000000000000000000000000000000000000000
χ888-88-888-8-80000-242−4242−422-22-222-20000000000000000−2−222−2−22200000000000000000000000000000000000000000000
χ898-88-888-8-80000-2−4242−42422-22-222-2000000000000000022−2−222−2−200000000000000000000000000000000000000000000
χ908-8-88-888-888-8-8-20000222-2-2-22000000000000-22-220000000000000000000000000000000000000000000000000000
χ918-8-8-88-8880000-242−42−424222-22-22-20000000000000000−2−22222−2−200000000000000000000000000000000000000000000
χ928-8-8-88-8880000-2−424242−4222-22-22-2000000000000000022−2−2−2−22200000000000000000000000000000000000000000000

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