Finite Group Databasebeta

← Group #13032441

Character table — Group #13032441

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89
size1111222244444444444555588888881010101010101010101010101010101010101010161616161616161616202020202020202020202020202020202020203232404040404040404040
order12224444444588881010104444244202020204444888888888888888820202020204040404024488888888888888881020244888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1
χ31111111111111111111-1-1-1-11111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i111111111-1-1-1-1-1-1-1iiii−i−i−i−iii−i−i11-1-1-1iii−i−i−i
χ41111111111111111111-1-1-1-11111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii111111111-1-1-1-1-1-1-1−i−i−i−iiiii−i−iii11-1-1-1−i−i−iiii
χ5111111111111-1-1-1-11111111-1-111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1111-1-1-1-111-1-111-1-1-1-1-1-1-1-11-1-111-111-1
χ6111111111111-1-1-1-11111111-1-1111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1111-1-1-1-1-1-111-1-1111111-1-11-1-1-1-11-1-11
χ7111111111111-1-1-1-1111-1-1-1-1-1-111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii11111-1-1-1-1-1-1-11111ii−i−i−i−iii−i−iii-1-1-111ii−i−i−ii
χ8111111111111-1-1-1-1111-1-1-1-1-1-111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i11111-1-1-1-1-1-1-11111−i−iiiii−i−iii−i−i-1-1-111−i−iiii−i
χ911111111-1-11111111111111-1-1-11111111111111111111111111-1-1-1-111111-1-1111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1
χ1011111111-1-11111111111111-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111111-1-11111-1-111-1-111-1-1-1-1-1-1-1-1-1111111
χ1111111111-1-1111111111-1-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-1-1-1-11111-111-1-1-1-1ii−i−i−i−iiiii−i−i-1-1111−i−i−iiii
χ1211111111-1-1111111111-1-1-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-1-1-1-11111-111-1-1-1-1−i−iiiii−i−i−i−iii-1-1111iii−i−i−i
χ1311111111-1-111-1-1-1-1111111111-11111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11-1-1-1-1-1-111111111-1-1-1-111-111-1-11-1-11
χ1411111111-1-111-1-1-1-1111111111-111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-11111-111-1
χ1511111111-1-111-1-1-1-1111-1-1-1-111-11111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii1-1-1-1-1-1-1-1-1-1111111iiii−i−i−i−i−i−iii111-1-1−i−iiii−i
χ1611111111-1-111-1-1-1-1111-1-1-1-111-11111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i1-1-1-1-1-1-1-1-1-1111111−i−i−i−iiiiiii−i−i111-1-1ii−i−i−ii
χ171111-1-11111-1111-1-111111111-1-1-1-111-1-11111-1-111-1-111111111-1-1-11111-1-1-11111-1-11-1111-111-1-1-1-11-1-11-11-1-11-1-1
χ181111-1-11111-1111-1-111111111-1-1-1-111-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-11111-1-1-11111-1-1-11-1-1-11-1-111111-1-11-1-111-111
χ191111-1-11111-1111-1-1111-1-1-1-11-1-1-1-11111-1-1ii−i−i−i−iiiiiii−i−i−i−i-1-1-11111-1-11-1-1-1-111i−iii−ii−i−i−i−iii1-11-11i−i−i−iii
χ201111-1-11111-1111-1-1111-1-1-1-11-1-1-1-11111-1-1−i−iiiii−i−i−i−i−i−iiiii-1-1-11111-1-11-1-1-1-111−ii−i−ii−iiiii−i−i1-11-11−iiii−i−i
χ211111-1-11111-11-1-1111111111-11-1-1-111-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-111-1-1111-1-1-11-1-1-11111-11-1-111-111-11
χ221111-1-11111-11-1-1111111111-11-1-1-111-1-111-1-111-1-11111111111-1-1-111-1-111-111-1-111-1111-1111-1-1-1-1-11-1-11-11-1-11-1
χ231111-1-11111-11-1-111111-1-1-1-1-11-1-1-11111-1-1ii−i−i−i−iii−i−i−i−iiiii-1-1-111-1-1111-1-111-1-1i−i−i−i−iiiiii−i−i-1111-1i−ii−ii−i
χ241111-1-11111-11-1-111111-1-1-1-1-11-1-1-11111-1-1−i−iiiii−i−iiiii−i−i−i−i-1-1-111-1-1111-1-111-1-1−iiiii−i−i−i−i−iii-1111-1−ii−ii−ii
χ251111-1-111-1-1-1111-1-11111111-111-1-111-1-11111-1-111-1-111111111-111-1-111-1-1-1-1-111-1-11-1-1-11-1-1-1-1-1-1-1-111-11-111-111
χ261111-1-111-1-1-1111-1-11111111-111-1-111-1-111-1-111-1-111-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-111-1-1-1111-11111111-111-111-1-11-1-1
χ271111-1-111-1-1-1111-1-1111-1-1-1-1-111-1-11111-1-1ii−i−i−i−iiiiiii−i−i−i−i-111-1-111-1-1111-1-111i−i−i−i−iiii−i−iii-11-11-1−iiii−i−i
χ281111-1-111-1-1-1111-1-1111-1-1-1-1-111-1-11111-1-1−i−iiiii−i−i−i−i−i−iiiii-111-1-111-1-1111-1-111−iiiii−i−i−iii−i−i-11-11-1i−i−i−iii
χ291111-1-111-1-1-11-1-11111111111-11-1-111-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1111-1111-11111111-111-1-11-1-11-1
χ301111-1-111-1-1-11-1-11111111111-11-1-111-1-111-1-111-1-11111111111-111-1-1-1-111-1-1-1-1-111-11-1-1-11-1-1-1-1-1-11-111-11-111-11
χ311111-1-111-1-1-11-1-111111-1-1-1-11-11-1-11111-1-1ii−i−i−i−iii−i−i−i−iiiii-111-1-1-1-11111111-1-1i−iii−ii−i−iii−i−i1-1-1-11−ii−ii−ii
χ321111-1-111-1-1-11-1-111111-1-1-1-11-11-1-11111-1-1−i−iiiii−i−iiiii−i−i−i−i-111-1-1-1-11111111-1-1−ii−i−ii−iii−i−iii1-1-1-11i−ii−ii−i
χ33222222-2-200-220000222222200022-2-222-2-22222222200000000-200000000-2000000-2-200-2-200000000000000000
χ34222222-2-200-220000222222200022-2-222-2-2-2-2-2-2-2-2-2-200000000-200000000-200000022002200000000000000000
χ35222222-2-200-220000222-2-2-2-200022-2-2-2-2222i2i2i2i−2i−2i−2i−2i00000000-2000000002000000−2i−2i002i2i00000000000000000
χ36222222-2-200-220000222-2-2-2-200022-2-2-2-222−2i−2i−2i−2i2i2i2i2i00000000-20000000020000002i2i00−2i−2i00000000000000000
χ372222-2-2-2-2002200002222222000-2-2-2-2-2-2-2-222-2-222-2-2000000002000000002000000-2200-2200000000000000000
χ382222-2-2-2-2002200002222222000-2-2-2-2-2-2-2-2-2-222-2-2220000000020000000020000002-2002-200000000000000000
χ392222-2-2-2-200220000222-2-2-2-2000-2-2-2-222222i2i−2i−2i−2i−2i2i2i00000000200000000-2000000−2i2i002i−2i00000000000000000
χ402222-2-2-2-200220000222-2-2-2-2000-2-2-2-22222−2i−2i2i2i2i2i−2i−2i00000000200000000-20000002i−2i00−2i2i00000000000000000
χ4122-2-2002-22-2020000-2-222i2i−2i−2i00000-22002i−2i00000000−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ390002-2000002i−2i000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000000000000
χ4222-2-2002-22-2020000-2-222i2i−2i−2i00000-22002i−2i000000002ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ390002-2000002i−2i0000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000000000000
χ4322-2-2002-22-2020000-2-22−2i−2i2i2i00000-2200−2i2i00000000−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ370002-200000−2i2i000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000000000000
χ4422-2-2002-22-2020000-2-22−2i−2i2i2i00000-2200−2i2i000000002ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ370002-200000−2i2i0000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000000000000
χ4522-2-2002-2-22020000-2-222i2i−2i−2i00000-22002i−2i00000000−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39000-2200000−2i2i0000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000000000000
χ4622-2-2002-2-22020000-2-222i2i−2i−2i00000-22002i−2i000000002ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000-2200000−2i2i000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000000000000
χ4722-2-2002-2-22020000-2-22−2i−2i2i2i00000-2200−2i2i00000000−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37000-22000002i−2i0000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000000000000
χ4822-2-2002-2-22020000-2-22−2i−2i2i2i00000-2200−2i2i000000002ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000-22000002i−2i000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000000000000
χ492-22-22i−2i000002i2−i22−2-22-22-22-20002i−2i002i−2i002-22i−2i2-22i−2ii2−i2i2−i2i2−i2i2−i200000i2−i22−2000i2−i22−2000000002−22−200000000000
χ502-22-22i−2i000002i2−i22−2-22-22-22-20002i−2i002i−2i00-22−2i2i-22−2i2i−i2i2−i2i2−i2i2−i2i200000i2−i22−2000i2−i22−200000000−22−2200000000000
χ512-22-22i−2i000002i2−i22−2-22-2-22-220002i−2i00−2i2i002i−2i-22−2i2i2-2−22−222−22−200000i2−i22−2000−i2i2−2200000000i2−i2−i2i200000000000
χ522-22-22i−2i000002i2−i22−2-22-2-22-220002i−2i00−2i2i00−2i2i2-22i−2i-222−22−2−22−2200000i2−i22−2000−i2i2−2200000000−i2i2i2−i200000000000
χ532-22-22i−2i000002−i2i2−22-22-22-22-20002i−2i002i−2i002-22i−2i2-22i−2i−i2i2−i2i2−i2i2−i2i200000−i2i2−22000−i2i2−2200000000−22−2200000000000
χ542-22-22i−2i000002−i2i2−22-22-22-22-20002i−2i002i−2i00-22−2i2i-22−2i2ii2−i2i2−i2i2−i2i2−i200000−i2i2−22000−i2i2−22000000002−22−200000000000
χ552-22-22i−2i000002−i2i2−22-22-2-22-220002i−2i00−2i2i002i−2i-22−2i2i2-22−22−2−22−2200000−i2i2−22000i2−i22−200000000−i2i2i2−i200000000000
χ562-22-22i−2i000002−i2i2−22-22-2-22-220002i−2i00−2i2i00−2i2i2-22i−2i-22−22−222−22−200000−i2i2−22000i2−i22−200000000i2−i2−i2i200000000000
χ572-22-2−2i2i000002i2−i2−22-22-22-22-2000−2i2i00−2i2i002-2−2i2i2-2−2i2ii2−i2i2−i2i2−i2i2−i200000i2−i2−22000i2−i2−2200000000−22−2200000000000
χ582-22-2−2i2i000002i2−i2−22-22-22-22-2000−2i2i00−2i2i00-222i−2i-222i−2i−i2i2−i2i2−i2i2−i2i200000i2−i2−22000i2−i2−22000000002−22−200000000000
χ592-22-2−2i2i000002i2−i2−22-22-2-22-22000−2i2i002i−2i002i−2i2-2−2i2i-22−22−222−22−200000i2−i2−22000−i2i22−200000000−i2i2i2−i200000000000
χ602-22-2−2i2i000002i2−i2−22-22-2-22-22000−2i2i002i−2i00−2i2i-222i−2i2-22−22−2−22−2200000i2−i2−22000−i2i22−200000000i2−i2−i2i200000000000
χ612-22-2−2i2i000002−i2i22−2-22-22-22-2000−2i2i00−2i2i002-2−2i2i2-2−2i2i−i2i2−i2i2−i2i2−i2i200000−i2i22−2000−i2i22−2000000002−22−200000000000
χ622-22-2−2i2i000002−i2i22−2-22-22-22-2000−2i2i00−2i2i00-222i−2i-222i−2ii2−i2i2−i2i2−i2i2−i200000−i2i22−2000−i2i22−200000000−22−2200000000000
χ632-22-2−2i2i000002−i2i22−2-22-2-22-22000−2i2i002i−2i002i−2i2-2−2i2i-222−22−2−22−2200000−i2i22−2000i2−i2−2200000000i2−i2−i2i200000000000
χ642-22-2−2i2i000002−i2i22−2-22-2-22-22000−2i2i002i−2i00−2i2i-222i−2i2-2−22−222−22−200000−i2i22−2000i2−i2−2200000000−i2i2i2−i200000000000
χ6544444444444-14444-1-1-10000444-1-1-1-100000000000000000000-1-1-1-1-1-1-1-1-10000000000000000000-1-1000000000
χ6644444444444-1-4-4-4-4-1-1-10000-4-44-1-1-1-100000000000000000000-1-1-1-1-11111000000000000000000011000000000
χ6744444444-4-44-14444-1-1-10000-4-4-4-1-1-1-100000000000000000000-11111-1-1-1-1000000000000000000011000000000
χ6844444444-4-44-1-4-4-4-4-1-1-1000044-4-1-1-1-100000000000000000000-1111111110000000000000000000-1-1000000000
χ694444-4-44444-4-144-4-4-1-1-100004-4-411-1-100000000000000000000111-1-1-1-1110000000000000000000-11000000000
χ704444-4-44444-4-1-4-444-1-1-10000-44-411-1-100000000000000000000111-1-111-1-100000000000000000001-1000000000
χ714444-4-444-4-4-4-144-4-4-1-1-10000-44411-1-1000000000000000000001-1-111-1-11100000000000000000001-1000000000
χ724444-4-444-4-4-4-1-4-444-1-1-100004-4411-1-1000000000000000000001-1-11111-1-10000000000000000000-11000000000
χ7344-4-400-4400040000-4-444i4i−4i−4i000004-400−4i4i0000000000000000000000000000000000000000000000000000000
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χ764-4-440000000400004-4-44i−4i−4i4i0000000000000000000−2+2i2−2i2−2i−2+2i−2−2i2+2i2+2i−2−2i000000000000000000000000000000000000000
χ774-4-440000000400004-4-4−4i4i4i−4i00000000000000000002+2i−2−2i−2−2i2+2i2−2i−2+2i−2+2i2−2i000000000000000000000000000000000000000
χ784-4-440000000400004-4-4−4i4i4i−4i0000000000000000000−2−2i2+2i2+2i−2−2i−2+2i2−2i2−2i−2+2i000000000000000000000000000000000000000
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χ878-88-8−8i8i00000-24i2−4i2−42422-2200000002i−2i000000000000000000000000000−i2i22−2000000000000000000000000000000
χ888-88-8−8i8i00000-2−4i24i242−422-2200000002i−2i000000000000000000000000000i2−i2−22000000000000000000000000000000
χ8916-16-16160000000-40000-4440000000000000000000000000000000000000000000000000000000000000000000000

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