Finite Group Databasebeta

← Group #13030066

Character table — Group #13030066

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95
size111122222222444444444555588888888888888810101010101010101010101010101010161616161616161616202020202020202020202020202020202020202020404040404040404040
order12224444444422444510101044444441010101020202020202020202244444488888888202020202020202020224448888888888888888244888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1
χ3111111111111111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1iiii−i−i−i−i111111111-1-1-1-1-1ii−i−iiiiiii−i−i−i−i−i−i-1-1-1iii−i−i−i
χ4111111111111111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii111111111-1-1-1-1-1−i−iii−i−i−i−i−i−iiiiiii-1-1-1−i−i−iiii
χ5111111111111-1-111111111111-1-1-1-1-1-1-111111111111111111111111111-1-11-1-1-1-111-1-11-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1
χ6111111111111-1-111111111111-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-11-1-1-1-111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ7111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1iiii−i−i−i−i11-1-11-1-1-1-1-1-111-1−i−iiiiiiiii−i−i−i−i−i−i111−i−i−iiii
χ8111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii11-1-11-1-1-1-1-1-111-1ii−i−i−i−i−i−i−i−iiiiiii111iii−i−i−i
χ9111111-1-1-1-11111-11-1111111111-1-1111111-1-111-1-1-1-111-1-111111111111-1-1-1-111-1-11-111-1111111-1-1-1-111-1-1-1-1-11-11-1-11-1-1
χ10111111-1-1-1-11111-11-1111111111-1-1111111-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-11-1-1-1-111-1-11-111-1-1-1-1-1-1-11111-1-11111-11-1-111-111
χ11111111-1-1-1-11111-11-11111-1-1-1-11-1-1111111-1-111-1-111-1-111-1-1iiii−i−i−i−i1-1-1-1-111-1-1-11-1-11ii−i−iii−i−i−i−i−i−iiiii1-11i−i−i−iii
χ12111111-1-1-1-11111-11-11111-1-1-1-11-1-1111111-1-111-1-111-1-111-1-1−i−i−i−iiiii1-1-1-1-111-1-1-11-1-11−i−iii−i−iiiiiii−i−i−i−i1-11−iiii−i−i
χ13111111-1-1-1-111-1-1-11-111111111-111-1-1-1-111-1-111-1-1-1-111-1-111111111111-111-1-1-1111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11-11-111-111
χ14111111-1-1-1-111-1-1-11-111111111-111-1-1-1-111-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-11-111-1-1-1111-1-1-1-11111-1-11111-1-111111-111-1-11-1-1
χ15111111-1-1-1-111-1-1-11-11111-1-1-1-1-111-1-1-1-111-1-111-1-111-1-111-1-1iiii−i−i−i−i1-111-1-1-111-11111−i−iiiii−i−i−i−i−i−iiiii-11-1−iiii−i−i
χ16111111-1-1-1-111-1-1-11-11111-1-1-1-1-111-1-1-1-111-1-111-1-111-1-111-1-1−i−i−i−iiiii1-111-1-1-111-11111ii−i−i−i−iiiiiii−i−i−i−i-11-1i−i−i−iii
χ171111-1-111-1-11111-1-1111111111-11-1111111-1-1-1-111-1-1-1-1111111111111-11-1-1-1-1-111-1111-11111-1-111-1-1-1-111-1-1-1-11-11-1-11-1
χ181111-1-111-1-11111-1-1111111111-11-1111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-11-1-1-1-1-111-1111-1-1-1-1-111-1-11111-1-111-1-111-111-11
χ191111-1-111-1-11111-1-111111-1-1-1-1-11-1111111-1-1-1-1111111-1-1-1-1iiii−i−i−i−i-11-1-1-1-1-1111-1-1-11ii−i−i−i−iii−i−iii−i−iii11-1−ii−ii−ii
χ201111-1-111-1-11111-1-111111-1-1-1-1-11-1111111-1-1-1-1111111-1-1-1-1−i−i−i−iiiii-11-1-1-1-1-1111-1-1-11−i−iiiii−i−iii−i−iii−i−i11-1i−ii−ii−i
χ211111-1-111-1-111-1-1-1-11111111111-11-1-1-1-111-1-1-1-111-1-1-1-1111111111111-1111-111-1-1-11-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111-11-111-11
χ221111-1-111-1-111-1-1-1-11111111111-11-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1111-111-1-1-11-1-1-1111111-1-11111-1-11111-1-11-1-11-1
χ231111-1-111-1-111-1-1-1-111111-1-1-1-11-11-1-1-1-111-1-1-1-1111111-1-1-1-1iiii−i−i−i−i-1111-111-1-11-1111−i−iii−i−iii−i−iii−i−iii-1-11i−ii−ii−i
χ241111-1-111-1-111-1-1-1-111111-1-1-1-11-11-1-1-1-111-1-1-1-1111111-1-1-1-1−i−i−i−iiiii-1111-111-1-11-1111ii−i−iii−i−iii−i−iii−i−i-1-11−ii−ii−ii
χ251111-1-1-1-11111111-1-111111111-1-1111111111-1-1-1-111-1-1-1-11111111111-1-1111-1-1-1-1-1-11111111-1-1-1-111-1-1-1-1111-1-1-1-11-1-11
χ261111-1-1-1-11111111-1-111111111-1-1111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1111-1-1-1-11111-1-11111-1-11-1-111-111-1
χ271111-1-1-1-11111111-1-11111-1-1-1-1-1-1111111111-1-1-1-1-1-11111-1-1iiii−i−i−i−i-1-1111-1-1-1-111-1-1-1ii−i−i−i−i−i−iiiiiii−i−i-111−i−iiii−i
χ281111-1-1-1-11111111-1-11111-1-1-1-1-1-1111111111-1-1-1-1-1-11111-1-1−i−i−i−iiiii-1-1111-1-1-1-111-1-1-1−i−iiiiiii−i−i−i−i−i−iii-111ii−i−i−ii
χ291111-1-1-1-11111-1-11-1-11111111111-1-1-1-1-11111-1-1-1-111-1-1-1-11111111111-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-111-11111-111-1
χ301111-1-1-1-11111-1-11-1-11111111111-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1111111111-1-11111-1-1-111-1-11-1-11
χ311111-1-1-1-11111-1-11-1-11111-1-1-1-111-1-1-1-1-11111-1-1-1-1-1-11111-1-1iiii−i−i−i−i-1-1-1-1111111111-1−i−iii−i−i−i−iiiiiii−i−i1-1-1ii−i−i−ii
χ321111-1-1-1-11111-1-11-1-11111-1-1-1-111-1-1-1-1-11111-1-1-1-1-1-11111-1-1−i−i−i−iiiii-1-1-1-1111111111-1ii−i−iiiii−i−i−i−i−i−iii1-1-1−i−iiii−i
χ332222222222-2-200-2-2-2222222220000000-2-2222222222222-2-200000000-2-200-20000-2-200-20000000000000000000000000
χ342222222222-2-200-2-2-22222-2-2-2-20000000-2-2222222-2-2-2-2-2-22200000000-2-200-20000220020000000000000000000000000
χ35222222-2-2-2-2-2-2002-22222222220000000-2-2-2-222-2-2-2-222-2-2-2-200000000-220020000-220020000000000000000000000000
χ36222222-2-2-2-2-2-2002-222222-2-2-2-20000000-2-2-2-222-2-222-2-2222200000000-2200200002-200-20000000000000000000000000
χ372222-2-222-2-2-2-20022-2222222220000000-2-2-2-2-2-222-2-2-2-222-2-2000000002-200200002-20020000000000000000000000000
χ382222-2-222-2-2-2-20022-22222-2-2-2-20000000-2-2-2-2-2-2222222-2-222000000002-20020000-2200-20000000000000000000000000
χ392222-2-2-2-222-2-200-222222222220000000-2-222-2-2-2-222-2-2-2-2-2-2000000002200-200002200-20000000000000000000000000
χ402222-2-2-2-222-2-200-2222222-2-2-2-20000000-2-222-2-2-2-2-2-2222222000000002200-20000-2-20020000000000000000000000000
χ412-22-22i−2i2i−2i2-200000002-22-222-2-20000000002-22i−2i2i−2i2-22i−2i2i−2i00i2i2−i2−i2i2i2−i2−i20000000000000000002−22−2i2−i22−22−2i2−i2000000000
χ422-22-22i−2i2i−2i2-200000002-22-222-2-20000000002-22i−2i2i−2i2-22i−2i2i−2i00−i2−i2i2i2−i2−i2i2i2000000000000000000−22−22−i2i2−22−22−i2i2000000000
χ432-22-22i−2i2i−2i2-200000002-22-2-2-2220000000002-22i−2i2i−2i-22−2i2i−2i2i0022−2−2−2−222000000000000000000−i2i2−i2i22−2i2−i2i2−i2−22000000000
χ442-22-22i−2i2i−2i2-200000002-22-2-2-2220000000002-22i−2i2i−2i-22−2i2i−2i2i00−2−22222−2−2000000000000000000i2−i2i2−i2−22−i2i2−i2i22−2000000000
χ452-22-22i−2i−2i2i-2200000002-22-222-2-2000000000-222i−2i−2i2i-222i−2i−2i2i00i2i2−i2−i2i2i2−i2−i20000000000000000002−2−22−i2i22−2−22−i2i2000000000
χ462-22-22i−2i−2i2i-2200000002-22-222-2-2000000000-222i−2i−2i2i-222i−2i−2i2i00−i2−i2i2i2−i2−i2i2i2000000000000000000−222−2i2−i2−222−2i2−i2000000000
χ472-22-22i−2i−2i2i-2200000002-22-2-2-222000000000-222i−2i−2i2i2-2−2i2i2i−2i0022−2−2−2−222000000000000000000−i2i2i2−i2−22i2−i2−i2i22−2000000000
χ482-22-22i−2i−2i2i-2200000002-22-2-2-222000000000-222i−2i−2i2i2-2−2i2i2i−2i00−2−22222−2−2000000000000000000i2−i2−i2i22−2−i2i2i2−i2−22000000000
χ492-22-2−2i2i2i−2i-2200000002-22-222-2-2000000000-22−2i2i2i−2i-22−2i2i2i−2i00i2i2−i2−i2i2i2−i2−i2000000000000000000−222−2−i2i2−222−2−i2i2000000000
χ502-22-2−2i2i2i−2i-2200000002-22-222-2-2000000000-22−2i2i2i−2i-22−2i2i2i−2i00−i2−i2i2i2−i2−i2i2i20000000000000000002−2−22i2−i22−2−22i2−i2000000000
χ512-22-2−2i2i2i−2i-2200000002-22-2-2-222000000000-22−2i2i2i−2i2-22i−2i−2i2i0022−2−2−2−222000000000000000000i2−i2−i2i2−22−i2i2i2−i22−2000000000
χ522-22-2−2i2i2i−2i-2200000002-22-2-2-222000000000-22−2i2i2i−2i2-22i−2i−2i2i00−2−22222−2−2000000000000000000−i2i2i2−i22−2i2−i2−i2i2−22000000000
χ532-22-2−2i2i−2i2i2-200000002-22-222-2-20000000002-2−2i2i−2i2i2-2−2i2i−2i2i00i2i2−i2−i2i2i2−i2−i2000000000000000000−22−22i2−i2−22−22i2−i2000000000
χ542-22-2−2i2i−2i2i2-200000002-22-222-2-20000000002-2−2i2i−2i2i2-2−2i2i−2i2i00−i2−i2i2i2−i2−i2i2i20000000000000000002−22−2−i2i22−22−2−i2i2000000000
χ552-22-2−2i2i−2i2i2-200000002-22-2-2-2220000000002-2−2i2i−2i2i-222i−2i2i−2i0022−2−2−2−222000000000000000000i2−i2i2−i22−2−i2i2−i2i2−22000000000
χ562-22-2−2i2i−2i2i2-200000002-22-2-2-2220000000002-2−2i2i−2i2i-222i−2i2i−2i00−2−22222−2−2000000000000000000−i2i2−i2i2−22i2−i2i2−i22−2000000000
χ572-2-220000002-22-200022-2-22i−2i2i−2i00022-2-22-20000000000002i−2i−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000000002i−2i0−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000000000000000000
χ582-2-220000002-22-200022-2-22i−2i2i−2i00022-2-22-20000000000002i−2i2ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000000002i−2i02ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000000000000000000
χ592-2-220000002-22-200022-2-2−2i2i−2i2i00022-2-22-2000000000000−2i2i−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700000000000−2i2i0−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000000000000000000
χ602-2-220000002-22-200022-2-2−2i2i−2i2i00022-2-22-2000000000000−2i2i2ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700000000000−2i2i02ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000000000000000000
χ612-2-220000002-2-2200022-2-22i−2i2i−2i000-2-2222-20000000000002i−2i−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900000000000−2i2i02ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000000000000000000
χ622-2-220000002-2-2200022-2-22i−2i2i−2i000-2-2222-20000000000002i−2i2ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900000000000−2i2i0−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000000000000000000
χ632-2-220000002-2-2200022-2-2−2i2i−2i2i000-2-2222-2000000000000−2i2i−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000000002i−2i02ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000000000000000000
χ642-2-220000002-2-2200022-2-2−2i2i−2i2i000-2-2222-2000000000000−2i2i2ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000000002i−2i0−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000000000000000000
χ6544444444444444444-1-1-1-10000444-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-1-1-1-1-1-1-1-1-1000000000000000000000000000000
χ66444444444444-4-4444-1-1-1-10000-4-4-41111-1-1-1-1-1-1-1-10000000000000000-1-111-11111000000000000000000000000000000
χ674444444444-4-400-4-4-4-1-1-1-100000005−55−511-1-1-1-1-1-10000000000000000115−515−55−5000000000000000000000000000000
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χ70444444-4-4-4-444-4-4-44-4-1-1-1-10000-4441111-1-111-1-1110000000000000000-11-1-1111-1-1000000000000000000000000000000
χ71444444-4-4-4-4-4-4004-44-1-1-1-100000005−55−51111-1-11100000000000000001-1−55-15−5−55000000000000000000000000000000
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χ734444-4-444-4-44444-4-44-1-1-1-10000-44-4-1-1-1-1-1-11111-1-100000000000000001-111111-1-1000000000000000000000000000000
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χ794444-4-4-4-444-4-400-444-1-1-1-100000005−55−511-1-111110000000000000000-1-15−51−55−55000000000000000000000000000000
χ804444-4-4-4-444-4-400-444-1-1-1-10000000−55−5511-1-111110000000000000000-1-1−5515−55−5000000000000000000000000000000
χ8144-4-400000000000004-4-444i−4i−4i4i000000000000000000000002−2i−2+2i−2+2i2−2i2+2i−2−2i−2−2i2+2i000000000000000000000000000000000000000
χ8244-4-400000000000004-4-444i−4i−4i4i00000000000000000000000−2+2i2−2i2−2i−2+2i−2−2i2+2i2+2i−2−2i000000000000000000000000000000000000000
χ8344-4-400000000000004-4-44−4i4i4i−4i000000000000000000000002+2i−2−2i−2−2i2+2i2−2i−2+2i−2+2i2−2i000000000000000000000000000000000000000
χ8444-4-400000000000004-4-44−4i4i4i−4i00000000000000000000000−2−2i2+2i2+2i−2−2i−2+2i2−2i2−2i−2+2i000000000000000000000000000000000000000
χ854-4-44000000-440000044-4-44i−4i4i−4i0000000-44000000000000−4i4i00000000000000000000000000000000000000000000000
χ864-4-44000000-440000044-4-4−4i4i−4i4i0000000-440000000000004i−4i00000000000000000000000000000000000000000000000
χ878-88-88i−8i8i−8i8-80000000-22-220000000000000-22−2i2i−2i2i0000000000000000000000000000000000000000000000000000000
χ888-88-88i−8i−8i8i-880000000-22-2200000000000002-2−2i2i2i−2i0000000000000000000000000000000000000000000000000000000
χ898-88-8−8i8i8i−8i-880000000-22-2200000000000002-22i−2i−2i2i0000000000000000000000000000000000000000000000000000000
χ908-88-8−8i8i−8i8i8-80000000-22-220000000000000-222i−2i2i−2i0000000000000000000000000000000000000000000000000000000
χ918-8-880000008-88-8000-2-2220000000-2-222-220000000000000000000000000000000000000000000000000000000000000
χ928-8-880000008-8-88000-2-222000000022-2-2-220000000000000000000000000000000000000000000000000000000000000
χ938-8-88000000-8800000-2-222000000025−25−25252-20000000000000000000000000000000000000000000000000000000000000
χ948-8-88000000-8800000-2-2220000000−252525−252-20000000000000000000000000000000000000000000000000000000000000
χ951616-16-160000000000000-444-400000000000000000000000000000000000000000000000000000000000000000000000000

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