Finite Group Databasebeta

← Group #13020921

Character table — Group #13020921

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122224444444444445555555588888888888888881010101016161616161616162020202020202020202020202020202020202020404040404040404040404040
order12222222444444445101010101010104444444444442020202020202020202020204444202020202020202044448888888888888888224488888888
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
χ9111111111111-1-1-1-1111111111111111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-1
χ10111111111111-1-1-1-1111111111111111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-111
χ11111111111111-1-1-1-11111111111111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111
χ12111111111111-1-1-1-11111111111111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-111-1-1
χ13111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-111ii−i−i−i−iii
χ14111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-111−i−iiiii−i−i
χ15111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiii11-1-1−i−iiiii−i−i
χ16111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i11-1-1ii−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
χ21222-2-2-2-2222-2-200002-2-2222-2-22i2i−2i−2i2i2i−2i−2i002i−2i22-2-2000000002i2i−2i−2i00002i2i−2i−2i00000000000000000000002-200000000
χ22222-2-2-2-2222-2-200002-2-2222-2-22i2i−2i−2i2i2i−2i−2i00−2i2i22-2-2000000002i2i−2i−2i0000−2i−2i2i2i0000000000000000000000-2200000000
χ23222-2-2-2-2222-2-200002-2-2222-2-2−2i−2i2i2i−2i−2i2i2i002i−2i22-2-200000000−2i−2i2i2i00002i2i−2i−2i0000000000000000000000-2200000000
χ24222-2-2-2-2222-2-200002-2-2222-2-2−2i−2i2i2i−2i−2i2i2i00−2i2i22-2-200000000−2i−2i2i2i0000−2i−2i2i2i00000000000000000000002-200000000
χ25222-2-2-2-22-2-22200002-2-2222-2-22i2i−2i−2i2i2i−2i−2i2i−2i00-2-22200000000−2i−2i2i2i2i2i−2i−2i0000000000000000000000002-20000000000
χ26222-2-2-2-22-2-22200002-2-2222-2-22i2i−2i−2i2i2i−2i−2i−2i2i00-2-22200000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000-220000000000
χ27222-2-2-2-22-2-22200002-2-2222-2-2−2i−2i2i2i−2i−2i2i2i2i−2i00-2-222000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000-220000000000
χ28222-2-2-2-22-2-22200002-2-2222-2-2−2i−2i2i2i−2i−2i2i2i−2i2i00-2-222000000002i2i−2i−2i−2i−2i2i2i0000000000000000000000002-20000000000
χ2922-22-22-2-20000002i−2i22-22-2-22-22-22-22-22-20000000000002i2i−2i−2i000000000000002i−2ii2i2−i2−i222−2−2i2i2−i2−i222−2−2000000000000
χ3022-22-22-2-20000002i−2i22-22-2-22-22-22-22-22-20000000000002i2i−2i−2i000000000000002i−2i−i2−i2i2i2−2−222−i2−i2i2i2−2−222000000000000
χ3122-22-22-2-20000002i−2i22-22-2-22-2-22-22-22-220000000000002i2i−2i−2i00000000000000−2i2i22−2−2−i2−i2i2i2−2−222i2i2−i2−i2000000000000
χ3222-22-22-2-20000002i−2i22-22-2-22-2-22-22-22-220000000000002i2i−2i−2i00000000000000−2i2i−2−222i2i2−i2−i222−2−2−i2−i2i2i2000000000000
χ3322-22-22-2-2000000−2i2i22-22-2-22-22-22-22-22-2000000000000−2i−2i2i2i00000000000000−2i2ii2i2−i2−i2−2−222i2i2−i2−i2−2−222000000000000
χ3422-22-22-2-2000000−2i2i22-22-2-22-22-22-22-22-2000000000000−2i−2i2i2i00000000000000−2i2i−i2−i2i2i222−2−2−i2−i2i2i222−2−2000000000000
χ3522-22-22-2-2000000−2i2i22-22-2-22-2-22-22-22-22000000000000−2i−2i2i2i000000000000002i−2i22−2−2i2i2−i2−i2−2−222−i2−i2i2i2000000000000
χ3622-22-22-2-2000000−2i2i22-22-2-22-2-22-22-22-22000000000000−2i−2i2i2i000000000000002i−2i−2−222−i2−i2i2i222−2−2i2i2−i2−i2000000000000
χ372-22-222-2-200002i−2i002-22-22-22-22-22-2-22-22000000002i2i−2i−2i00000000000000002i−2i002−22−2i2−i2i2−i22−22−2i2−i2i2−i2000000000000
χ382-22-222-2-200002i−2i002-22-22-22-22-22-2-22-22000000002i2i−2i−2i00000000000000002i−2i00−22−22−i2i2−i2i2−22−22−i2i2−i2i2000000000000
χ392-22-222-2-200002i−2i002-22-22-22-2-22-222-22-2000000002i2i−2i−2i0000000000000000−2i2i00i2−i2i2−i2−22−22−i2i2−i2i22−22−2000000000000
χ402-22-222-2-200002i−2i002-22-22-22-2-22-222-22-2000000002i2i−2i−2i0000000000000000−2i2i00−i2i2−i2i22−22−2i2−i2i2−i2−22−22000000000000
χ412-22-222-2-20000−2i2i002-22-22-22-22-22-2-22-2200000000−2i−2i2i2i0000000000000000−2i2i002−22−2−i2i2−i2i22−22−2−i2i2−i2i2000000000000
χ422-22-222-2-20000−2i2i002-22-22-22-22-22-2-22-2200000000−2i−2i2i2i0000000000000000−2i2i00−22−22i2−i2i2−i2−22−22i2−i2i2−i2000000000000
χ432-22-222-2-20000−2i2i002-22-22-22-2-22-222-22-200000000−2i−2i2i2i00000000000000002i−2i00i2−i2i2−i22−22−2−i2i2−i2i2−22−22000000000000
χ442-22-222-2-20000−2i2i002-22-22-22-2-22-222-22-200000000−2i−2i2i2i00000000000000002i−2i00−i2i2−i2i2−22−22i2−i2i2−i22−22−2000000000000
χ452-2-222-2-222-22-20000222-2-22-2-22i2i−2i−2i−2i−2i2i2i00002-22-2000000002i−2i2i−2i00000000000000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700
χ462-2-222-2-222-22-20000222-2-22-2-22i2i−2i−2i−2i−2i2i2i00002-22-2000000002i−2i2i−2i000000000000000000000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700
χ472-2-222-2-222-22-20000222-2-22-2-2−2i−2i2i2i2i2i−2i−2i00002-22-200000000−2i2i−2i2i00000000000000000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900
χ482-2-222-2-222-22-20000222-2-22-2-2−2i−2i2i2i2i2i−2i−2i00002-22-200000000−2i2i−2i2i000000000000000000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900
χ492-2-222-2-22-22-220000222-2-22-2-22i2i−2i−2i−2i−2i2i2i0000-22-2200000000−2i2i−2i2i0000000000000000000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39
χ502-2-222-2-22-22-220000222-2-22-2-22i2i−2i−2i−2i−2i2i2i0000-22-2200000000−2i2i−2i2i00000000000000000000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39
χ512-2-222-2-22-22-220000222-2-22-2-2−2i−2i2i2i2i2i−2i−2i0000-22-22000000002i−2i2i−2i0000000000000000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37
χ522-2-222-2-22-22-220000222-2-22-2-2−2i−2i2i2i2i2i−2i−2i0000-22-22000000002i−2i2i−2i00000000000000000000000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37
χ532-2-2-2-22222-2-2200002-2-2-2-22222222-2-2-2-200002-2-22000000002-2-2200000000000000002i−2i−2i2i00002i−2i−2i2i000000000000
χ542-2-2-2-22222-2-2200002-2-2-2-22222222-2-2-2-200002-2-22000000002-2-220000000000000000−2i2i2i−2i0000−2i2i2i−2i000000000000
χ552-2-2-2-22222-2-2200002-2-2-2-2222-2-2-2-2222200002-2-2200000000-222-200000000000000002-2-220000-222-2000000000000
χ562-2-2-2-22222-2-2200002-2-2-2-2222-2-2-2-2222200002-2-2200000000-222-20000000000000000-222-200002-2-22000000000000
χ572-2-2-2-2222-222-200002-2-2-2-22222222-2-2-2-20000-222-200000000-222-20000000000002i−2i−2i2i00002i−2i−2i2i0000000000000000
χ582-2-2-2-2222-222-200002-2-2-2-22222222-2-2-2-20000-222-200000000-222-2000000000000−2i2i2i−2i0000−2i2i2i−2i0000000000000000
χ592-2-2-2-2222-222-200002-2-2-2-2222-2-2-2-222220000-222-2000000002-2-220000000000002-2-220000-222-20000000000000000
χ602-2-2-2-2222-222-200002-2-2-2-2222-2-2-2-222220000-222-2000000002-2-22000000000000-222-200002-2-220000000000000000
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
χ63444444444444-4-4-4-4-1-1-1-1-1-1-1-10000000044-4-4-1-1-1-1111111110000-1-1-1-1111100000000000000000000000000000000
χ64444444444444-4-4-4-4-1-1-1-1-1-1-1-100000000-4-444-1-1-1-11111111100001111-1-1-1-100000000000000000000000000000000
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
χ69444-4-4-4-4444-4-40000-111-1-1-11100000000004i−4i-1-1115−55−55−55−50000i5−i5−i5i5−i−iii00000000000000000000000000000000
χ70444-4-4-4-4444-4-40000-111-1-1-11100000000004i−4i-1-111−55−55−55−550000−i5i5i5−i5−i−iii00000000000000000000000000000000
χ71444-4-4-4-4444-4-40000-111-1-1-1110000000000−4i4i-1-1115−55−55−55−50000−i5i5i5−i5ii−i−i00000000000000000000000000000000
χ72444-4-4-4-4444-4-40000-111-1-1-1110000000000−4i4i-1-111−55−55−55−550000i5−i5−i5i5ii−i−i00000000000000000000000000000000
χ73444-4-4-4-44-4-4440000-111-1-1-111000000004i−4i0011-1-15−55−5−55−550000−i−iiii5−i5−i5i500000000000000000000000000000000
χ74444-4-4-4-44-4-4440000-111-1-1-111000000004i−4i0011-1-1−55−555−55−50000−i−iii−i5i5i5−i500000000000000000000000000000000
χ75444-4-4-4-44-4-4440000-111-1-1-11100000000−4i4i0011-1-15−55−5−55−550000ii−i−i−i5i5i5−i500000000000000000000000000000000
χ76444-4-4-4-44-4-4440000-111-1-1-11100000000−4i4i0011-1-1−55−555−55−50000ii−i−ii5−i5−i5i500000000000000000000000000000000
χ7744-4-44-44-4000000004-444-4-4-444i−4i−4i4i4i−4i−4i4i000000000000000000000000000000000000000000000000000000000000
χ7844-4-44-44-4000000004-444-4-4-44−4i4i4i−4i−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000
χ794-444-4-44-40000000044-4-44-4-444i−4i−4i4i−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000
χ804-444-4-44-40000000044-4-44-4-44−4i4i4i−4i4i−4i−4i4i000000000000000000000000000000000000000000000000000000000000
χ8188-88-88-8-80000008i−8i-2-22-222-2200000000000000000000−2i−2i2i2i00000000000000000000000000000000000000000000
χ8288-88-88-8-8000000−8i8i-2-22-222-22000000000000000000002i2i−2i−2i00000000000000000000000000000000000000000000
χ8388-8-88-88-800000000-22-2-2222-2000000000000000000002i5−2i5−2i52i500000000000000000000000000000000000000000000
χ8488-8-88-88-800000000-22-2-2222-200000000000000000000−2i52i52i5−2i500000000000000000000000000000000000000000000
χ858-888-8-88-800000000-2-222-222-200000000000000002i5−2i5−2i52i5000000000000000000000000000000000000000000000000
χ868-888-8-88-800000000-2-222-222-20000000000000000−2i52i52i5−2i5000000000000000000000000000000000000000000000000
χ878-88-888-8-800008i−8i00-22-22-22-220000000000000000−2i−2i2i2i000000000000000000000000000000000000000000000000
χ888-88-888-8-80000−8i8i00-22-22-22-2200000000000000002i2i−2i−2i000000000000000000000000000000000000000000000000
χ898-8-888-8-888-88-80000-2-2-222-222000000000000-22-220000000000000000000000000000000000000000000000000000
χ908-8-888-8-88-88-880000-2-2-222-2220000000000002-22-20000000000000000000000000000000000000000000000000000
χ918-8-8-8-88888-8-880000-22222-2-2-2000000000000-222-20000000000000000000000000000000000000000000000000000
χ928-8-8-8-8888-888-80000-22222-2-2-20000000000002-2-220000000000000000000000000000000000000000000000000000

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