Finite Group Databasebeta

← Group #13018157

Character table — Group #13018157

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122224444444444445555555588888888888888881010101016161616161616162020202020202020202020202020202020202020404040404040404040404040
order12222222444444445101010101010104444444444442020202020202020202020204444202020202020202044448888888888888888444488888888
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
χ5111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-111111111-1-1-1-1iiiiiiii−i−i−i−i−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−i−i−i−i−iiiiiiiii-1-1-1-1−i−i−i−iiiii
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−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−i−i−i−i−iiiiiiiii1111iiii−i−i−i−i
χ9111111111111-1-1-1-1111111111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1
χ10111111111111-1-1-1-1111111111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111-1-111
χ11111111111111-1-1-1-11111111111111111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-111-1-111
χ12111111111111-1-1-1-11111111111111111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-111-1-1
χ13111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiii11-1-1ii−i−i−i−iii
χ14111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i11-1-1−i−iiiii−i−i
χ15111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-111−i−iiiii−i−i
χ16111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-111ii−i−i−i−iii
χ1722222222-2-2-2-222-2-222222222222222220000-2-2-2-22222-2-2-2-2-2-2-2-20000000022-2-20000000000000000000000000000
χ1822222222-2-2-2-222-2-222222222-2-2-2-2-2-2-2-20000-2-2-2-22222-2-2-2-2222200000000-2-2220000000000000000000000000000
χ1922222222-2-2-2-2-2-22222222222222222220000-2-2-2-2-2-2-2-22222-2-2-2-200000000-2-2220000000000000000000000000000
χ2022222222-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-20000-2-2-2-2-2-2-2-2222222220000000022-2-20000000000000000000000000000
χ21222-2-2-22-222-2-200002-2-2-222-222i2i−2i−2i2i2i−2i−2i000022-2-2000000002i−2i2i−2i0000000000000000−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ370000−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39000000000000
χ22222-2-2-22-222-2-200002-2-2-222-222i2i−2i−2i2i2i−2i−2i000022-2-2000000002i−2i2i−2i00000000000000002ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700002ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000000000
χ23222-2-2-22-222-2-200002-2-2-222-22−2i−2i2i2i−2i−2i2i2i000022-2-200000000−2i2i−2i2i0000000000000000−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ390000−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37000000000000
χ24222-2-2-22-222-2-200002-2-2-222-22−2i−2i2i2i−2i−2i2i2i000022-2-200000000−2i2i−2i2i00000000000000002ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900002ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000000000
χ25222-2-2-22-2-2-22200002-2-2-222-222i2i−2i−2i2i2i−2i−2i0000-2-22200000000−2i2i−2i2i000000000000−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ390000−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ370000000000000000
χ26222-2-2-22-2-2-22200002-2-2-222-222i2i−2i−2i2i2i−2i−2i0000-2-22200000000−2i2i−2i2i0000000000002ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900002ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000000000000000
χ27222-2-2-22-2-2-22200002-2-2-222-22−2i−2i2i2i−2i−2i2i2i0000-2-222000000002i−2i2i−2i000000000000−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ370000−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ390000000000000000
χ28222-2-2-22-2-2-22200002-2-2-222-22−2i−2i2i2i−2i−2i2i2i0000-2-222000000002i−2i2i−2i0000000000002ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700002ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000000000000000
χ292-222-22-2-20000002-222-2-2-2-2222i−2i2i−2i2i−2i2i−2i00000000000022-2-2000000000000002i−2i1+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i000000000000
χ302-222-22-2-20000002-222-2-2-2-2222i−2i2i−2i2i−2i2i−2i00000000000022-2-2000000000000002i−2i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i000000000000
χ312-222-22-2-20000002-222-2-2-2-222−2i2i−2i2i−2i2i−2i2i00000000000022-2-200000000000000−2i2i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i000000000000
χ322-222-22-2-20000002-222-2-2-2-222−2i2i−2i2i−2i2i−2i2i00000000000022-2-200000000000000−2i2i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i000000000000
χ332-222-22-2-2000000-2222-2-2-2-2222i−2i2i−2i2i−2i2i−2i000000000000-2-22200000000000000−2i2i1+i−1−i1+i−1−i−1−i1+i−1−i1+i1−i−1+i1−i−1+i−1+i1−i−1+i1−i000000000000
χ342-222-22-2-2000000-2222-2-2-2-2222i−2i2i−2i2i−2i2i−2i000000000000-2-22200000000000000−2i2i−1−i1+i−1−i1+i1+i−1−i1+i−1−i−1+i1−i−1+i1−i1−i−1+i1−i−1+i000000000000
χ352-222-22-2-2000000-2222-2-2-2-222−2i2i−2i2i−2i2i−2i2i000000000000-2-222000000000000002i−2i1−i−1+i1−i−1+i−1+i1−i−1+i1−i1+i−1−i1+i−1−i−1−i1+i−1−i1+i000000000000
χ362-222-22-2-2000000-2222-2-2-2-222−2i2i−2i2i−2i2i−2i2i000000000000-2-222000000000000002i−2i−1+i1−i−1+i1−i1−i−1+i1−i−1+i−1−i1+i−1−i1+i1+i−1−i1+i−1−i000000000000
χ372-22-22-2-2200002i−2i002-222-2-2-222-2-222-2-22000000002i2i−2i−2i00000000000000002i−2i00i2−i2−i2i22−2−22i2−i2−i2i2−222−2000000000000
χ382-22-22-2-2200002i−2i002-222-2-2-222-2-222-2-22000000002i2i−2i−2i00000000000000002i−2i00−i2i2i2−i2−222−2−i2i2i2−i22−2−22000000000000
χ392-22-22-2-2200002i−2i002-222-2-2-22-222-2-222-2000000002i2i−2i−2i0000000000000000−2i2i002−2−22−i2i2i2−i2−222−2−i2i2i2−i2000000000000
χ402-22-22-2-2200002i−2i002-222-2-2-22-222-2-222-2000000002i2i−2i−2i0000000000000000−2i2i00−222−2i2−i2−i2i22−2−22i2−i2−i2i2000000000000
χ412-22-22-2-220000−2i2i002-222-2-2-222-2-222-2-2200000000−2i−2i2i2i0000000000000000−2i2i00i2−i2−i2i2−222−2i2−i2−i2i22−2−22000000000000
χ422-22-22-2-220000−2i2i002-222-2-2-222-2-222-2-2200000000−2i−2i2i2i0000000000000000−2i2i00−i2i2i2−i22−2−22−i2i2i2−i2−222−2000000000000
χ432-22-22-2-220000−2i2i002-222-2-2-22-222-2-222-200000000−2i−2i2i2i00000000000000002i−2i002−2−22i2−i2−i2i2−222−2i2−i2−i2i2000000000000
χ442-22-22-2-220000−2i2i002-222-2-2-22-222-2-222-200000000−2i−2i2i2i00000000000000002i−2i00−222−2−i2i2i2−i22−2−22−i2i2i2−i2000000000000
χ452-2-22-2-2222-22-20000222-22-2-2-22i2i−2i−2i−2i−2i2i2i00002-22-2000000002i−2i−2i2i00000000000000000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900
χ462-2-22-2-2222-22-20000222-22-2-2-22i2i−2i−2i−2i−2i2i2i00002-22-2000000002i−2i−2i2i000000000000000000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900
χ472-2-22-2-2222-22-20000222-22-2-2-2−2i−2i2i2i2i2i−2i−2i00002-22-200000000−2i2i2i−2i00000000000000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700
χ482-2-22-2-2222-22-20000222-22-2-2-2−2i−2i2i2i2i2i−2i−2i00002-22-200000000−2i2i2i−2i000000000000000000000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700
χ492-2-22-2-222-22-220000222-22-2-2-22i2i−2i−2i−2i−2i2i2i0000-22-2200000000−2i2i2i−2i0000000000000000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37
χ502-2-22-2-222-22-220000222-22-2-2-22i2i−2i−2i−2i−2i2i2i0000-22-2200000000−2i2i2i−2i00000000000000000000000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37
χ512-2-22-2-222-22-220000222-22-2-2-2−2i−2i2i2i2i2i−2i−2i0000-22-22000000002i−2i−2i2i0000000000000000000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39
χ522-2-22-2-222-22-220000222-22-2-2-2−2i−2i2i2i2i2i−2i−2i0000-22-22000000002i−2i−2i2i00000000000000000000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39
χ532-2-2-2222-22-2-2200002-2-222-22-22222-2-2-2-2002-22-2-220000000022-2-222-2-20000000000000000000000002-20000000000
χ542-2-2-2222-22-2-2200002-2-222-22-22222-2-2-2-200-222-2-220000000022-2-2-2-222000000000000000000000000-220000000000
χ552-2-2-2222-22-2-2200002-2-222-22-2-2-2-2-22222002-22-2-2200000000-2-22222-2-2000000000000000000000000-220000000000
χ562-2-2-2222-22-2-2200002-2-222-22-2-2-2-2-2222200-222-2-2200000000-2-222-2-2220000000000000000000000002-20000000000
χ572-2-2-2222-2-222-200002-2-222-22-22222-2-2-2-22i−2i00-222-200000000-2-22200002i2i−2i−2i00000000000000000000002i−2i00000000
χ582-2-2-2222-2-222-200002-2-222-22-22222-2-2-2-2−2i2i00-222-200000000-2-2220000−2i−2i2i2i0000000000000000000000−2i2i00000000
χ592-2-2-2222-2-222-200002-2-222-22-2-2-2-2-222222i−2i00-222-20000000022-2-200002i2i−2i−2i0000000000000000000000−2i2i00000000
χ602-2-2-2222-2-222-200002-2-222-22-2-2-2-2-22222−2i2i00-222-20000000022-2-20000−2i−2i2i2i00000000000000000000002i−2i00000000
χ614444444444444444-1-1-1-1-1-1-1-1000000004444-1-1-1-1-1-1-1-1-1-1-1-10000-1-1-1-1-1-1-1-100000000000000000000000000000000
χ624444444444444444-1-1-1-1-1-1-1-100000000-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-100001111111100000000000000000000000000000000
χ63444444444444-4-4-4-4-1-1-1-1-1-1-1-10000000044-4-4-1-1-1-11111111100001111-1-1-1-100000000000000000000000000000000
χ64444444444444-4-4-4-4-1-1-1-1-1-1-1-100000000-4-444-1-1-1-1111111110000-1-1-1-1111100000000000000000000000000000000
χ6544444444-4-4-4-444-4-4-1-1-1-1-1-1-1-10000000000001111-1-1-1-1111100005−55−55−55−500000000000000000000000000000000
χ6644444444-4-4-4-444-4-4-1-1-1-1-1-1-1-10000000000001111-1-1-1-111110000−55−55−55−5500000000000000000000000000000000
χ6744444444-4-4-4-4-4-444-1-1-1-1-1-1-1-100000000000011111111-1-1-1-100005−55−5−55−5500000000000000000000000000000000
χ6844444444-4-4-4-4-4-444-1-1-1-1-1-1-1-100000000000011111111-1-1-1-10000−55−555−55−500000000000000000000000000000000
χ6944-444-4-4-40000000044-44-44-4-44-4-44-444-4000000000000000000000000000000000000000000000000000000000000
χ7044-444-4-4-40000000044-44-44-4-4-444-44-4-44000000000000000000000000000000000000000000000000000000000000
χ7144-4-4-44-44000000004-44-4-444-44i−4i4i−4i−4i4i−4i4i000000000000000000000000000000000000000000000000000000000000
χ7244-4-4-44-44000000004-44-4-444-4−4i4i−4i4i4i−4i4i−4i000000000000000000000000000000000000000000000000000000000000
χ734-4-4-4444-44-4-440000-111-1-11-1100000000004-4-111-1i5−i5i5−i5i5−i5i5−i50000-1-111i5−i5−i5i500000000000000000000000000000000
χ744-4-4-4444-44-4-440000-111-1-11-1100000000004-4-111-1−i5i5−i5i5−i5i5−i5i50000-1-111−i5i5i5−i500000000000000000000000000000000
χ754-4-4-4444-44-4-440000-111-1-11-110000000000-44-111-1i5−i5i5−i5i5−i5i5−i5000011-1-1−i5i5i5−i500000000000000000000000000000000
χ764-4-4-4444-44-4-440000-111-1-11-110000000000-44-111-1−i5i5−i5i5−i5i5−i5i5000011-1-1i5−i5−i5i500000000000000000000000000000000
χ774-4-4-4444-4-444-40000-111-1-11-11000000004i−4i001-1-11i5−i5i5−i5−i5i5−i5i500005−5−55−i−iii00000000000000000000000000000000
χ784-4-4-4444-4-444-40000-111-1-11-11000000004i−4i001-1-11−i5i5−i5i5i5−i5i5−i50000−555−5−i−iii00000000000000000000000000000000
χ794-4-4-4444-4-444-40000-111-1-11-1100000000−4i4i001-1-11i5−i5i5−i5−i5i5−i5i50000−555−5ii−i−i00000000000000000000000000000000
χ804-4-4-4444-4-444-40000-111-1-11-1100000000−4i4i001-1-11−i5i5−i5i5i5−i5i5−i500005−5−55ii−i−i00000000000000000000000000000000
χ81888-8-8-88-888-8-80000-2222-2-22-2000000000000-2-2220000000000000000000000000000000000000000000000000000
χ82888-8-8-88-8-8-8880000-2222-2-22-200000000000022-2-20000000000000000000000000000000000000000000000000000
χ8388-888-8-8-800000000-2-22-22-222000000000000000025−25−2525000000000000000000000000000000000000000000000000
χ8488-888-8-8-800000000-2-22-22-2220000000000000000−252525−25000000000000000000000000000000000000000000000000
χ8588-8-8-88-8800000000-22-222-2-22000000000000000000002i5−2i5−2i52i500000000000000000000000000000000000000000000
χ8688-8-8-88-8800000000-22-222-2-2200000000000000000000−2i52i52i5−2i500000000000000000000000000000000000000000000
χ878-888-88-8-80000008-8-2-22222-2-200000000000000000000-2-22200000000000000000000000000000000000000000000
χ888-888-88-8-8000000-88-2-22222-2-20000000000000000000022-2-200000000000000000000000000000000000000000000
χ898-88-88-8-8800008i−8i00-22-2-2222-20000000000000000−2i−2i2i2i000000000000000000000000000000000000000000000000
χ908-88-88-8-880000−8i8i00-22-2-2222-200000000000000002i2i−2i−2i000000000000000000000000000000000000000000000000
χ918-8-88-8-8888-88-80000-2-2-22-2222000000000000-22-220000000000000000000000000000000000000000000000000000
χ928-8-88-8-888-88-880000-2-2-22-22220000000000002-22-20000000000000000000000000000000000000000000000000000

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