Finite Group Databasebeta

← Group #14287230

Character table — Group #14287230

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222444444555588888888810101010101010101010121212121616161616161616202020202020202020202020242424244040404040404040404848606060606060606060606060
order122234466651010101212444426615202030303044888812121212448810103030303060608812122424242424242424404040404881212242424242020448888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-111111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-1-1111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1
χ611111111111111111111-1-1-11111111111111111-1-111-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ711111111111111111111-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-11111
χ811111111111111111111-1-1-111111111-1-1-1-11111-1-111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-111-1-11111-1-1-1-1111111-1-1-1-1
χ91111111111111111-1-1-1-1111111111-1-1ii−i−i-1-1-1-1111111111111i−i-1-1ii−i−iii−i−i1111-1i−i-1-1ii−i−i11-1-1-1-1ii−i−iii−i−i
χ101111111111111111-1-1-1-1111111111-1-1ii−i−i-1-1-1-1-1-1-1-111111111i−i-1-1ii−i−iii−i−i-1-1-1-1-1i−i-1-1ii−i−i-1-11111−i−iii−i−iii
χ111111111111111111-1-1-1-1111111111-1-1−i−iii-1-1-1-1111111111111−ii-1-1−i−iii−i−iii1111-1−ii-1-1−i−iii11-1-1-1-1−i−iii−i−iii
χ121111111111111111-1-1-1-1111111111-1-1−i−iii-1-1-1-1-1-1-1-111111111−ii-1-1−i−iii−i−iii-1-1-1-1-1−ii-1-1−i−iii-1-11111ii−i−iii−i−i
χ131111111111111111-1-1-1-1-1-1-1111111-1-1ii−i−i-1-1-1-111-1-1-1-1-1-1-1-111i−i-1-1ii−i−iii−i−i-1-1-1-11−ii11−i−iii11-1-111ii−i−i−i−iii
χ141111111111111111-1-1-1-1-1-1-1111111-1-1ii−i−i-1-1-1-1-1-111-1-1-1-1-1-111i−i-1-1ii−i−iii−i−i11111−ii11−i−iii-1-111-1-1−i−iiiii−i−i
χ151111111111111111-1-1-1-1-1-1-1111111-1-1−i−iii-1-1-1-111-1-1-1-1-1-1-1-111−ii-1-1−i−iii−i−iii-1-1-1-11i−i11ii−i−i11-1-111−i−iiiii−i−i
χ161111111111111111-1-1-1-1-1-1-1111111-1-1−i−iii-1-1-1-1-1-111-1-1-1-1-1-111−ii-1-1−i−iii−i−iii11111i−i11ii−i−i-1-111-1-1ii−i−i−i−iii
χ1722222-2-22222222-2-222220002-2-2222-2-2222222220000000000-2-2-2-2-2-22222-2-2-2-2000000000000000000000000000
χ1822222-2-22222222-2-222220002-2-2222-2-2-2-2-2-222220000000000-2-222-2-2-2-2-2-22222000000000000000000000000000
χ1922222-2-22222222-2-2-2-2-2-20002-2-2222222i2i−2i−2i-2-2-2-20000000000-2-2−2i2i222i2i−2i−2i−2i−2i2i2i000000000000000000000000000
χ2022222-2-22222222-2-2-2-2-2-20002-2-222222−2i−2i2i2i-2-2-2-20000000000-2-22i−2i22−2i−2i2i2i2i2i−2i−2i000000000000000000000000000
χ212222-122-1-1-12222-1-122222-1-1-122-1-1-1222222-1-1-1-1000022-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-10000222-1-1-1-1-1-100000000000000
χ222222-122-1-1-12222-1-122222-1-1-122-1-1-122-2-2-2-2-1-1-1-1000022-1-1-1-1-1-1-2-2-1-11111111100002-2-2-1-1111100000000000000
χ232222-122-1-1-12222-1-12222-211-122-1-1-1222222-1-1-1-10000-2-21111-1-122-1-1-1-1-1-1-1-1-1-10000-2-2-211111100000000000000
χ242222-122-1-1-12222-1-12222-211-122-1-1-122-2-2-2-2-1-1-1-10000-2-21111-1-1-2-2-1-1111111110000-22211-1-1-1-100000000000000
χ252222-122-1-1-12222-1-1-2-2-2-22-1-1-122-1-1-1-2-22i2i−2i−2i1111000022-1-1-1-1-1-12i−2i11−i−iii−i−iii0000-22i−2i11−i−iii00000000000000
χ262222-122-1-1-12222-1-1-2-2-2-22-1-1-122-1-1-1-2-2−2i−2i2i2i1111000022-1-1-1-1-1-1−2i2i11ii−i−iii−i−i0000-2−2i2i11ii−i−i00000000000000
χ272222-122-1-1-12222-1-1-2-2-2-2-211-122-1-1-1-2-22i2i−2i−2i11110000-2-21111-1-12i−2i11−i−iii−i−iii00002−2i2i-1-1ii−i−i00000000000000
χ282222-122-1-1-12222-1-1-2-2-2-2-211-122-1-1-1-2-2−2i−2i2i2i11110000-2-21111-1-1−2i2i11ii−i−iii−i−i000022i−2i-1-1−i−iii00000000000000
χ292222-1-2-2-1-1-122221122220−i3i3-1-2-2-1-1-1-2-22222-1-1-1-1000000−i3−i3i3i311-2-211-1-1-1-111110000000−i3i3−i3i3−i3i300000000000000
χ302222-1-2-2-1-1-122221122220−i3i3-1-2-2-1-1-1-2-2-2-2-2-2-1-1-1-1000000−i3−i3i3i31122111111-1-1-1-10000000−i3i3i3−i3i3−i300000000000000
χ312222-1-2-2-1-1-122221122220i3−i3-1-2-2-1-1-1-2-22222-1-1-1-1000000i3i3−i3−i311-2-211-1-1-1-111110000000i3−i3i3−i3i3−i300000000000000
χ322222-1-2-2-1-1-122221122220i3−i3-1-2-2-1-1-1-2-2-2-2-2-2-1-1-1-1000000i3i3−i3−i31122111111-1-1-1-10000000i3−i3−i3i3−i3i300000000000000
χ332222-1-2-2-1-1-1222211-2-2-2-20−i3i3-1-2-2-1-1-1222i2i−2i−2i1111000000−i3−i3i3i311−2i2i-1-1−i−iiiii−i−i0000000i3−i33−3−3300000000000000
χ342222-1-2-2-1-1-1222211-2-2-2-20−i3i3-1-2-2-1-1-122−2i−2i2i2i1111000000−i3−i3i3i3112i−2i-1-1ii−i−i−i−iii0000000i3−i3−333−300000000000000
χ352222-1-2-2-1-1-1222211-2-2-2-20i3−i3-1-2-2-1-1-1222i2i−2i−2i1111000000i3i3−i3−i311−2i2i-1-1−i−iiiii−i−i0000000−i3i3−333−300000000000000
χ362222-1-2-2-1-1-1222211-2-2-2-20i3−i3-1-2-2-1-1-122−2i−2i2i2i1111000000i3i3−i3−i3112i−2i-1-1ii−i−i−i−iii0000000−i3i33−3−3300000000000000
χ3722-2-2200-22-22-2-22002i−2i2i−2i0002002-2-2002ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ119−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ1092i−2i2i−2i002−20000000000002ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ119−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109000022−2−20000000000000−i2i200001+i−1−i1−i−1+i
χ3822-2-2200-22-22-2-22002i−2i2i−2i0002002-2-2002ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ119−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ1092i−2i2i−2i00−220000000000002ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ119−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ1090000−2−2220000000000000i2−i20000−1−i1+i−1+i1−i
χ3922-2-2200-22-22-2-22002i−2i2i−2i0002002-2-200−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ1192ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092i−2i2i−2i002−2000000000000−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ1192ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ109000022−2−20000000000000−i2i20000−1−i1+i−1+i1−i
χ4022-2-2200-22-22-2-22002i−2i2i−2i0002002-2-200−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ1192ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092i−2i2i−2i00−22000000000000−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ1192ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1090000−2−2220000000000000i2−i200001+i−1−i1−i−1+i
χ4122-2-2200-22-22-2-2200−2i2i−2i2i0002002-2-200−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ1092ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ119−2i2i−2i2i002−2000000000000−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ1092ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ119000022−2−20000000000000i2−i200001−i−1+i1+i−1−i
χ4222-2-2200-22-22-2-2200−2i2i−2i2i0002002-2-200−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ1092ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ119−2i2i−2i2i00−22000000000000−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ1092ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1190000−2−2220000000000000−i2i20000−1+i1−i−1−i1+i
χ4322-2-2200-22-22-2-2200−2i2i−2i2i0002002-2-2002ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ109−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2i2i−2i2i002−20000000000002ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ109−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119000022−2−20000000000000i2−i20000−1+i1−i−1−i1+i
χ4422-2-2200-22-22-2-2200−2i2i−2i2i0002002-2-2002ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ109−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2i2i−2i2i00−220000000000002ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ109−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ1190000−2−2220000000000000−i2i200001−i−1+i1+i−1−i
χ452-2-2222-22-2-22-22-22-22i−2i−2i2i0002-22-2-222i−2i00002i−2i−2i2i00000000002-2002i−2i000000000000000000000000000−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ1092ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1190000
χ462-2-2222-22-2-22-22-22-22i−2i−2i2i0002-22-2-222i−2i00002i−2i−2i2i00000000002-2002i−2i0000000000000000000000000002ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ109−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ1190000
χ472-2-2222-22-2-22-22-22-2−2i2i2i−2i0002-22-2-22−2i2i0000−2i2i2i−2i00000000002-200−2i2i0000000000000000000000000002ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ119−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ1090000
χ482-2-2222-22-2-22-22-22-2−2i2i2i−2i0002-22-2-22−2i2i0000−2i2i2i−2i00000000002-200−2i2i000000000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ1192ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1090000
χ492-2-222-222-2-22-22-2-222i−2i−2i2i00022-2-2-22−2i2i00002i−2i−2i2i2i−2i00000000-2200−2i2i0000000000000000000002i−2i2-20000000000
χ502-2-222-222-2-22-22-2-222i−2i−2i2i00022-2-2-22−2i2i00002i−2i−2i2i−2i2i00000000-2200−2i2i000000000000000000000−2i2i-220000000000
χ512-2-222-222-2-22-22-2-22−2i2i2i−2i00022-2-2-222i−2i0000−2i2i2i−2i2i−2i00000000-22002i−2i0000000000000000000002i−2i-220000000000
χ522-2-222-222-2-22-22-2-22−2i2i2i−2i00022-2-2-222i−2i0000−2i2i2i−2i−2i2i00000000-22002i−2i000000000000000000000−2i2i2-20000000000
χ534444444444-1-1-1-1440000444-1-1-1-1-1-100000000004444-1-1-1-1-1-1-1-1000000000000-1-1-1-1000000000-1-1000000000000
χ544444444444-1-1-1-1440000444-1-1-1-1-1-10000000000-4-4-4-4-1-1-1-1-1-1-1-1000000000000111100000000011000000000000
χ554444444444-1-1-1-1440000-4-4-4-1-1-1-1-1-1000000000044-4-4111111-1-10000000000001111000000000-1-1000000000000
χ564444444444-1-1-1-1440000-4-4-4-1-1-1-1-1-10000000000-4-444111111-1-1000000000000-1-1-1-100000000011000000000000
χ5744-4-4-2002-224-4-44004i−4i4i−4i000-200-222004ζ7+4ζ23+4ζ31+4ζ47+4ζ71+4ζ79+4ζ103+4ζ119−4ζ7−4ζ23−4ζ31−4ζ47−4ζ71−4ζ79−4ζ103−4ζ119−4ζ13−4ζ29−4ζ37−4ζ53−4ζ61−4ζ77−4ζ101−4ζ1094ζ13+4ζ29+4ζ37+4ζ53+4ζ61+4ζ77+4ζ101+4ζ109−2i2i−2i2i0000000000000000−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ1192ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1090000000000000000000000000000000
χ5844-4-4-2002-224-4-44004i−4i4i−4i000-200-22200−4ζ7−4ζ23−4ζ31−4ζ47−4ζ71−4ζ79−4ζ103−4ζ1194ζ7+4ζ23+4ζ31+4ζ47+4ζ71+4ζ79+4ζ103+4ζ1194ζ13+4ζ29+4ζ37+4ζ53+4ζ61+4ζ77+4ζ101+4ζ109−4ζ13−4ζ29−4ζ37−4ζ53−4ζ61−4ζ77−4ζ101−4ζ109−2i2i−2i2i00000000000000002ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ119−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ1090000000000000000000000000000000
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Here ζ is a primitive root of unity of order 120 (ζ120 = 1); i = ζ30.