Finite Group Databasebeta

← Group #14300515

Character table — Group #14300515

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size11111111222222224444444444444455555555888888888888888888881010101010101010121212122020202020202020202020202020202020202020202020202020202020202424242424242424606060606060606060606060
order122222223666666644510101010101010121212124444444415202020203030303030303060606060606060601212121212121212444422666688888888242424242424242424242424242424242020202020202020224488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1iiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i11111111-1-1-1-1iiii−i−i−i−i
χ6111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiii11111111-1-1-1-1−i−i−i−iiiii
χ7111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1-1-1-1-11111−i−i−i−iiiii
χ8111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1-1-1-1-11111iiii−i−i−i−i
χ91111111111111111-1-111111111-1-1-1-1111111111-1-1-1-11111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1
χ101111111111111111-1-111111111-1-1-1-1111111111-1-1-1-11111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-111-1-111
χ111111111111111111-1-111111111-1-1-1-1111111111-1-1-1-11111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111
χ121111111111111111-1-111111111-1-1-1-1111111111-1-1-1-11111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-111-1-111-1-1
χ131111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-111-1-1ii−i−i−i−iii
χ141111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-111-1-1−i−iiiii−i−i
χ151111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111-1-111−i−iiiii−i−i
χ161111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111-1-111ii−i−i−i−iii
χ1722222222-1-1-1-1-1-1-1-12222222222-1-1-1-122222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000022-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ1822222222-1-1-1-1-1-1-1-12222222222-1-1-1-122222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000022-1-1-1-1-2-2-2-2-2-2-2-2111111111111111100000000000000000000
χ1922222222-1-1-1-1-1-1-1-12222222222-1-1-1-1-2-2-2-2-2-2-2-2-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111110000-2-211112i2i2i2i−2i−2i−2i−2i−i−i−i−i−i−i−i−iiiiiiiii00000000000000000000
χ2022222222-1-1-1-1-1-1-1-12222222222-1-1-1-1-2-2-2-2-2-2-2-2-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111110000-2-21111−2i−2i−2i−2i2i2i2i2iiiiiiiii−i−i−i−i−i−i−i−i00000000000000000000
χ2122222222-1-1-1-1-1-1-1-1-2-222222222111122222222-1-2-2-2-2-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-10000-2-2111122-2-222-2-2-1-1-1-11111-1-1-1-1111100000000000000000000
χ2222222222-1-1-1-1-1-1-1-1-2-222222222111122222222-1-2-2-2-2-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-10000-2-21111-2-222-2-2221111-1-1-1-11111-1-1-1-100000000000000000000
χ2322222222-1-1-1-1-1-1-1-1-2-2222222221111-2-2-2-2-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-11111111111111111000022-1-1-1-12i2i−2i−2i−2i−2i2i2i−i−i−i−iiiiiiiii−i−i−i−i00000000000000000000
χ2422222222-1-1-1-1-1-1-1-1-2-2222222221111-2-2-2-2-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-11111111111111111000022-1-1-1-1−2i−2i2i2i2i2i−2i−2iiiii−i−i−i−i−i−i−i−iiiii00000000000000000000
χ25222-2-22-2-22222-2-2-2-200222-2-2-22-200002i−2i2i−2i2i2i−2i−2i20000222-2-2-2-2000000002i2i2i−2i−2i−2i2i−2i002i−2i00000000000000000000000000000000002i2i−2i−2i2-20000000000
χ26222-2-22-2-22222-2-2-2-200222-2-2-22-200002i−2i2i−2i2i2i−2i−2i20000222-2-2-2-2000000002i2i2i−2i−2i−2i2i−2i00−2i2i0000000000000000000000000000000000−2i−2i2i2i-220000000000
χ27222-2-22-2-22222-2-2-2-200222-2-2-22-20000−2i2i−2i2i−2i−2i2i2i20000222-2-2-2-200000000−2i−2i−2i2i2i2i−2i2i002i−2i00000000000000000000000000000000002i2i−2i−2i-220000000000
χ28222-2-22-2-22222-2-2-2-200222-2-2-22-20000−2i2i−2i2i−2i−2i2i2i20000222-2-2-2-200000000−2i−2i−2i2i2i2i−2i2i00−2i2i0000000000000000000000000000000000−2i−2i2i2i2-20000000000
χ2922-22-2-22-222-2-22-2-220022-22-2-2-22000022-2-22-22-2200002-2-22-2-220000000022-222-2-2-20000000000002i−2i002i−2i00002i2i−2i−2i00002i2i−2i−2i00000000000000000000
χ3022-22-2-22-222-2-22-2-220022-22-2-2-22000022-2-22-22-2200002-2-22-2-220000000022-222-2-2-2000000000000−2i2i00−2i2i0000−2i−2i2i2i0000−2i−2i2i2i00000000000000000000
χ3122-22-2-22-222-2-22-2-220022-22-2-2-220000-2-222-22-22200002-2-22-2-2200000000-2-22-2-22220000000000002-200-22000022-2-20000-2-22200000000000000000000
χ3222-22-2-22-222-2-22-2-220022-22-2-2-220000-2-222-22-22200002-2-22-2-2200000000-2-22-2-2222000000000000-22002-20000-2-222000022-2-200000000000000000000
χ3322-22-2-22-2-1-111-111-10022-22-2-2-22−i3−i3i3i322-2-22-22-2-10000-111-111-1−i3−i3−i3−i3i3i3i3i3-1-11-1-1111000000−i3−i3i3i3002i−2i002i−2i33−3−3−i−iii33−3−3−i−iii00000000000000000000
χ3422-22-2-22-2-1-111-111-10022-22-2-2-22−i3−i3i3i322-2-22-22-2-10000-111-111-1−i3−i3−i3−i3i3i3i3i3-1-11-1-1111000000−i3−i3i3i300−2i2i00−2i2i−3−333ii−i−i−3−333ii−i−i00000000000000000000
χ3522-22-2-22-2-1-111-111-10022-22-2-2-22−i3−i3i3i3-2-222-22-22-10000-111-111-1−i3−i3−i3−i3i3i3i3i311-111-1-1-1000000i3i3−i3−i3002-200-22−i3−i3i3i3-1-111i3i3−i3−i311-1-100000000000000000000
χ3622-22-2-22-2-1-111-111-10022-22-2-2-22−i3−i3i3i3-2-222-22-22-10000-111-111-1−i3−i3−i3−i3i3i3i3i311-111-1-1-1000000i3i3−i3−i300-22002-2i3i3−i3−i311-1-1−i3−i3i3i3-1-11100000000000000000000
χ3722-22-2-22-2-1-111-111-10022-22-2-2-22i3i3−i3−i322-2-22-22-2-10000-111-111-1i3i3i3i3−i3−i3−i3−i3-1-11-1-1111000000i3i3−i3−i3002i−2i002i−2i−3−333−i−iii−3−333−i−iii00000000000000000000
χ3822-22-2-22-2-1-111-111-10022-22-2-2-22i3i3−i3−i322-2-22-22-2-10000-111-111-1i3i3i3i3−i3−i3−i3−i3-1-11-1-1111000000i3i3−i3−i300−2i2i00−2i2i33−3−3ii−i−i33−3−3ii−i−i00000000000000000000
χ3922-22-2-22-2-1-111-111-10022-22-2-2-22i3i3−i3−i3-2-222-22-22-10000-111-111-1i3i3i3i3−i3−i3−i3−i311-111-1-1-1000000−i3−i3i3i3002-200-22i3i3−i3−i3-1-111−i3−i3i3i311-1-100000000000000000000
χ4022-22-2-22-2-1-111-111-10022-22-2-2-22i3i3−i3−i3-2-222-22-22-10000-111-111-1i3i3i3i3−i3−i3−i3−i311-111-1-1-1000000−i3−i3i3i300-22002-2−i3−i3i3i311-1-1i3i3−i3−i3-1-11100000000000000000000
χ4122-2-22-2-2222-2-2-222-20022-2-222-2-200002i−2i−2i2i2i−2i−2i2i200002-2-2-222-2000000002i2i−2i−2i−2i2i−2i2i00000000000000000000000000000000000000000000002ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ11900−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ10900
χ4222-2-22-2-2222-2-2-222-20022-2-222-2-200002i−2i−2i2i2i−2i−2i2i200002-2-2-222-2000000002i2i−2i−2i−2i2i−2i2i0000000000000000000000000000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119002ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ10900
χ4322-2-22-2-2222-2-2-222-20022-2-222-2-20000−2i2i2i−2i−2i2i2i−2i200002-2-2-222-200000000−2i−2i2i2i2i−2i2i−2i0000000000000000000000000000000000000000000000−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109002ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ11900
χ4422-2-22-2-2222-2-2-222-20022-2-222-2-20000−2i2i2i−2i−2i2i2i−2i200002-2-2-222-200000000−2i−2i2i2i2i−2i2i−2i00000000000000000000000000000000000000000000002ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ10900−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ11900
χ452-222-2-2-222-22-222-2-2002-2222-2-2-200002i−2i−2i2i−2i2i2i−2i20000-22-222-2-2000000002i−2i2i2i−2i−2i−2i2i0000000000000000000000000000000000000000000000002ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ11900−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109
χ462-222-2-2-222-22-222-2-2002-2222-2-2-200002i−2i−2i2i−2i2i2i−2i20000-22-222-2-2000000002i−2i2i2i−2i−2i−2i2i000000000000000000000000000000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119002ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ109
χ472-222-2-2-222-22-222-2-2002-2222-2-2-20000−2i2i2i−2i2i−2i−2i2i20000-22-222-2-200000000−2i2i−2i−2i2i2i2i−2i000000000000000000000000000000000000000000000000−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109002ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ119
χ482-222-2-2-222-22-222-2-2002-2222-2-2-20000−2i2i2i−2i2i−2i−2i2i20000-22-222-2-200000000−2i2i−2i−2i2i2i2i−2i0000000000000000000000000000000000000000000000002ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ10900−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119
χ492-22-22-22-22-22-2-2-222002-22-2-22-22000022-2-2-22-2220000-22-2-2-222000000002-22-222-2-200000000002i−2i002i−2i002i−2i2i−2i00002i−2i2i−2i000000000000000000000000
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χ512-22-22-22-22-22-2-2-222002-22-2-22-220000-2-2222-22-220000-22-2-2-22200000000-22-22-2-22200000000002-200-22002-22-20000-22-22000000000000000000000000
χ522-22-22-22-22-22-2-2-222002-22-2-22-220000-2-2222-22-220000-22-2-2-22200000000-22-22-2-2220000000000-22002-200-22-2200002-22-2000000000000000000000000
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χ542-22-22-22-2-11-1111-1-1002-22-2-22-22−i3i3−i3i322-2-2-22-22-100001-1111-1-1−i3−i3i3i3−i3−i3i3i3-11-11-1-111000000−i3i3−i3i3−2i2i00−2i2i00i−ii−i−33−33i−ii−i−33−3300000000000000000000
χ552-22-22-22-2-11-1111-1-1002-22-2-22-22−i3i3−i3i3-2-2222-22-2-100001-1111-1-1−i3−i3i3i3−i3−i3i3i31-11-111-1-1000000i3−i3i3−i32-200-2200-11-11−i3i3−i3i31-11-1i3−i3i3−i300000000000000000000
χ562-22-22-22-2-11-1111-1-1002-22-2-22-22−i3i3−i3i3-2-2222-22-2-100001-1111-1-1−i3−i3i3i3−i3−i3i3i31-11-111-1-1000000i3−i3i3−i3-22002-2001-11-1i3−i3i3−i3-11-11−i3i3−i3i300000000000000000000
χ572-22-22-22-2-11-1111-1-1002-22-2-22-22i3−i3i3−i322-2-2-22-22-100001-1111-1-1i3i3−i3−i3i3i3−i3−i3-11-11-1-111000000i3−i3i3−i32i−2i002i−2i00−ii−ii−33−33−ii−ii−33−3300000000000000000000
χ582-22-22-22-2-11-1111-1-1002-22-2-22-22i3−i3i3−i322-2-2-22-22-100001-1111-1-1i3i3−i3−i3i3i3−i3−i3-11-11-1-111000000i3−i3i3−i3−2i2i00−2i2i00i−ii−i3−33−3i−ii−i3−33−300000000000000000000
χ592-22-22-22-2-11-1111-1-1002-22-2-22-22i3−i3i3−i3-2-2222-22-2-100001-1111-1-1i3i3−i3−i3i3i3−i3−i31-11-111-1-1000000−i3i3−i3i32-200-2200-11-11i3−i3i3−i31-11-1−i3i3−i3i300000000000000000000
χ602-22-22-22-2-11-1111-1-1002-22-2-22-22i3−i3i3−i3-2-2222-22-2-100001-1111-1-1i3i3−i3−i3i3i3−i3−i31-11-111-1-1000000−i3i3−i3i3-22002-2001-11-1−i3i3−i3i3-11-11i3−i3i3−i300000000000000000000
χ612-2-2222-2-22-2-222-22-2002-2-22-222-200002i−2i2i−2i−2i−2i2i2i20000-2-222-22-2000000002i−2i−2i2i−2i2i2i−2i2-20000000000000000000000000000000022-2-20000002i−2i00000000
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Here ζ is a primitive root of unity of order 120 (ζ120 = 1); i = ζ30.