Finite Group Databasebeta

← Group #13103492

Character table — Group #13103492

Order 1600.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94
size1111222222224444444445555888888888888888888101010101010101010101010101020202020202020202020202020202020202020202020202040404040505050505050100100100
order12225510101010101045101010202020204444551010101010102020202020202020202044888820202020202020204488202020204040404040404040404040404040404020202020448888488
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11-1-1
χ31111111111111111111111111111111111111111111-1-1111111111111-111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111-1-1-1-1-1-111111111-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111
χ5111111111111111111111-1-1-1-111111111111111111111ii−i−i-1-1-1-1-1-1-1-11-1i−i-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1ii−i−i-1i−i
χ6111111111111111111111-1-1-1-111111111111111111111−i−iii-1-1-1-1-1-1-1-11-1−ii-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1111-1-1−i−iii-1−ii
χ7111111111111111111111-1-1-1-1111111111111111111-1-1ii−i−i-1-1-1-1-1-1-1-1-1-1i−i-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-111−i−iii1−ii
χ8111111111111111111111-1-1-1-1111111111111111111-1-1−i−iii-1-1-1-1-1-1-1-1-1-1−ii-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-111ii−i−i1i−i
χ9111111111111-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1111111-1-1-1
χ10111111111111-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-1-111
χ11111111111111-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1111
χ12111111111111-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111111-1-1
χ13111111111111-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111ii−i−i-1-1-1-1-1-1-1-1-11−ii1111iiii−i−i−i−i−i−i−i−iiiii11-1-1-1-1ii−i−i1−ii
χ14111111111111-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111−i−iii-1-1-1-1-1-1-1-1-11i−i1111−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-1−i−iii1i−i
χ15111111111111-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i-1-1-1-1-1-1-1-111−ii1111iiii−i−i−i−i−i−i−i−iiiii-1-11111−i−iii-1i−i
χ16111111111111-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−iii-1-1-1-1-1-1-1-111i−i1111−i−i−i−iiiiiiiii−i−i−i−i-1-11111ii−i−i-1−ii
χ172222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−5222222−1+52−1+52−1−52−1−522222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−5222−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52002222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−520222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−520000000000000
χ182222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−5222222−1+52−1+52−1−52−1−522222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−5222−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−5200-2-2-2-2−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5202-2-2−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+521−521−521+521+521−521−521+521+520000000000000
χ192222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−5222222−1+52−1+52−1−52−1−52-2-2-2-2−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−5222−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52002i2i−2i−2i1−521−521+521+521−521−521+521+520-22i−2i1−521−521+521+52−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ140000000000000
χ202222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−5222222−1+52−1+52−1−52−1−52-2-2-2-2−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−5222−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−5200−2i−2i2i2i1−521−521+521+521−521−521+521+520-2−2i2i1−521−521+521+52ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ140000000000000
χ212222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52-222221−521−521+521+522222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-2-21−521−521−521−521+521+521+521+52002222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−520-2-2-21−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+520000000000000
χ222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52-222221−521−521+521+522222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-2-21−521−521−521−521+521+521+521+5200-2-2-2-2−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−520-2221−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−520000000000000
χ232222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52-222221−521−521+521+52-2-2-2-2−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-2-21−521−521−521−521+521+521+521+52002i2i−2i−2i1−521−521+521+521−521−521+521+5202−2i2i−1+52−1+52−1−52−1−52−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ140000000000000
χ242222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52-222221−521−521+521+52-2-2-2-2−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-2-21−521−521−521−521+521+521+521+5200−2i−2i2i2i1−521−521+521+521−521−521+521+52022i−2i−1+52−1+52−1−52−1−52ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ140000000000000
χ252222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+5222222−1−52−1−52−1+52−1+522222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+5222−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52002222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+520222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+520000000000000
χ262222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+5222222−1−52−1−52−1+52−1+522222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+5222−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+5200-2-2-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5202-2-2−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−521+521+521−521−521+521+521−521−520000000000000
χ272222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+5222222−1−52−1−52−1+52−1+52-2-2-2-2−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+5222−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52002i2i−2i−2i1+521+521−521−521+521+521−521−520-22i−2i1+521+521−521−52−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ380000000000000
χ282222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+5222222−1−52−1−52−1+52−1+52-2-2-2-2−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+5222−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+5200−2i−2i2i2i1+521+521−521−521+521+521−521−520-2−2i2i1+521+521−521−52ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ380000000000000
χ292222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52-222221+521+521−521−522222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52-2-21+521+521+521+521−521−521−521−52002222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+520-2-2-21+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−520000000000000
χ302222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52-222221+521+521−521−522222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52-2-21+521+521+521+521−521−521−521−5200-2-2-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+520-2221+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+52−1+520000000000000
χ312222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52-222221+521+521−521−52-2-2-2-2−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52-2-21+521+521+521+521−521−521−521−52002i2i−2i−2i1+521+521−521−521+521+521−521−5202−2i2i−1−52−1−52−1+52−1+52−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ380000000000000
χ322222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52-222221+521+521−521−52-2-2-2-2−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52-2-21+521+521+521+521−521−521−521−5200−2i−2i2i2i1+521+521−521−521+521+521−521−52022i−2i−1−52−1−52−1+52−1+52ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ380000000000000
χ3322-2-222-2-22-22-2022-2-2000022-2-2222-22-2-2-200000000000000002222-2-2-2-20000000000000000000000000000002-22-2000
χ3422-2-222-2-22-22-2022-2-2000022-2-2222-22-2-2-200000000000000002222-2-2-2-2000000000000000000000000000000-22-22000
χ3522-2-222-2-22-22-2022-2-20000-2-222222-22-2-2-20000000000000000-2-2-2-222220000000000000000000000000000002i−2i−2i2i000
χ3622-2-222-2-22-22-2022-2-20000-2-222222-22-2-2-20000000000000000-2-2-2-22222000000000000000000000000000000−2i2i2i−2i000
χ372-22-22222-2-2-2-202-2-2200002i−2i2i−2i22-2-2-2-22200000000002-200002i−2i2i−2i2i−2i2i−2i0000000000000000000000002-2002i−2i0000000
χ382-22-22222-2-2-2-202-2-2200002i−2i2i−2i22-2-2-2-2220000000000-2200002i−2i2i−2i2i−2i2i−2i000000000000000000000000-2200−2i2i0000000
χ392-22-22222-2-2-2-202-2-220000−2i2i−2i2i22-2-2-2-22200000000002-20000−2i2i−2i2i−2i2i−2i2i0000000000000000000000002-200−2i2i0000000
χ402-22-22222-2-2-2-202-2-220000−2i2i−2i2i22-2-2-2-2220000000000-220000−2i2i−2i2i−2i2i−2i2i000000000000000000000000-22002i−2i0000000
χ412-2-2222-2-2-22-2202-22-200002i−2i−2i2i22-22-22-2-2000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372i−2i2i−2i−2i2i−2i2i00000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700000000000000000
χ422-2-2222-2-2-22-2202-22-200002i−2i−2i2i22-22-22-2-20000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372i−2i2i−2i−2i2i−2i2i000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700000000000000000
χ432-2-2222-2-2-22-2202-22-20000−2i2i2i−2i22-22-22-2-2000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2i2i−2i2i2i−2i2i−2i00000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900000000000000000
χ442-2-2222-2-2-22-2202-22-20000−2i2i2i−2i22-22-22-2-20000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2i2i−2i2i2i−2i2i−2i000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900000000000000000
χ452-2-22−1+52−1−521−521+521−52−1+521+52−1−5202-22-2−ζ22+ζ38ζ22−ζ38ζ6−ζ14−ζ6+ζ142i−2i−2i2i−1+52−1−521−52−1+521+52−1−521−521+5200−ζ22+ζ38−ζ22+ζ38ζ22−ζ38ζ22−ζ38ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ6+ζ1400−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−ζ22−ζ38ζ22+ζ38−ζ6−ζ14ζ6+ζ14ζ22+ζ38−ζ22−ζ38ζ6+ζ14−ζ6−ζ140000ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36ζ7+ζ23−ζ7−ζ23ζ31+ζ39−ζ31−ζ39−ζ13+ζ37ζ13−ζ37−ζ21+ζ29ζ21−ζ29ζ13+ζ37−ζ13−ζ37ζ21+ζ29−ζ21−ζ29ζ7−ζ23−ζ7+ζ23−ζ31+ζ39ζ31−ζ390000000000000
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χ878-88-8−2+25−2−25−2+25−2−252−252−252+252+250-222-2000000001−521+52−1+52−1+52−1−52−1−521−521+52−2525−5+525−52−5+525−525+52−5−525+52−5−52000000000000000000000000000000000000000000000000000
χ888-88-8−2−25−2+25−2−25−2+252+252+252−252−250-222-2000000001+521−52−1−52−1−52−1+52−1+521+521−5225−25−5−525+52−5−525+525−52−5+525−52−5+52000000000000000000000000000000000000000000000000000
χ898-88-8−2−25−2+25−2−25−2+252+252+252−252−250-222-2000000001+521−52−1−52−1−52−1+52−1+521+521−52−25255+52−5−525+52−5−52−5+525−52−5+525−52000000000000000000000000000000000000000000000000000
χ908-8-8888-8-8-88-880-22-2200000000-2-22-22-2220000000000000000000000000000000000000000000000000000000000000
χ918-8-88−2+25−2−252−252+252−25−2+252+25−2−250-22-22−4ζ22+4ζ384ζ22−4ζ384ζ6−4ζ14−4ζ6+4ζ1400001−521+52−1+521−52−1−521+52−1+52−1−5200ζ22−ζ38ζ22−ζ38−ζ22+ζ38−ζ22+ζ38−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ6−ζ14000000000000000000000000000000000000000000000000000
χ928-8-88−2+25−2−252−252+252−25−2+252+25−2−250-22-224ζ22−4ζ38−4ζ22+4ζ38−4ζ6+4ζ144ζ6−4ζ1400001−521+52−1+521−52−1−521+52−1+52−1−5200−ζ22+ζ38−ζ22+ζ38ζ22−ζ38ζ22−ζ38ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ6+ζ14000000000000000000000000000000000000000000000000000
χ938-8-88−2−25−2+252+252−252+25−2−252−25−2+250-22-224ζ6−4ζ14−4ζ6+4ζ144ζ22−4ζ38−4ζ22+4ζ3800001+521−52−1−521+52−1+521−52−1−52−1+5200−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ6−ζ14−ζ22+ζ38−ζ22+ζ38ζ22−ζ38ζ22−ζ38000000000000000000000000000000000000000000000000000
χ948-8-88−2−25−2+252+252−252+25−2−252−25−2+250-22-22−4ζ6+4ζ144ζ6−4ζ14−4ζ22+4ζ384ζ22−4ζ3800001+521−52−1−521+52−1+521−52−1−52−1+5200ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ6+ζ14ζ22−ζ38ζ22−ζ38−ζ22+ζ38−ζ22+ζ38000000000000000000000000000000000000000000000000000

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