Finite Group Databasebeta

← Group #14299562

Character table — Group #14299562

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size1111222222444444444444444455556688888888888888888888101010101010121212202020202020202020202020242424242424242430304040404040404040404060606060606060120120
order12223446665881010101212202020202424242444442215303030404040406060606012012012012012012012012022121212124886688888824242424101020204040404044882424242424242424288888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1
χ3111111111111111111111111111111-1-111111111111111111111111111-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-111111111111111111111111111-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1111-1-1-1-1ii−i−i-1-1-1-111111111-1-1i−iiiii−i−i−i−i-1-1-1ii−i−ii−i
χ611111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1111-1-1-1-1−i−iii-1-1-1-111111111-1-1−ii−i−i−i−iiiii-1-1-1−i−iii−ii
χ711111111111111111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i-1-1-1-1-1-1-1-1-1-1-1-111i−iiiii−i−i−i−i111−i−iii−ii
χ811111111111111111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii-1-1-1-1-1-1-1-1-1-1-1-111−ii−i−i−i−iiiii111ii−i−ii−i
χ911111111111-1-1111111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111-1-111-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-11-1-11111-1-1
χ1011111111111-1-1111111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1111-1-1-1-1-1-111
χ1111111111111-1-1111111111-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1-111-1-1-1-111
χ1211111111111-1-1111111111-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-111-1111111-1-1
χ1311111111111-1-1111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111ii−i−i11111111-1-1-1-1-1-1−iiii−i−i−i−iii-111ii−i−i−ii
χ1411111111111-1-1111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111−i−iii11111111-1-1-1-1-1-1i−i−i−iiiii−i−i-111−i−iiii−i
χ1511111111111-1-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111ii−i−i1111-1-1-1-1111111−iiii−i−i−i−iii1-1-1−i−iiii−i
χ1611111111111-1-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111−i−iii1111-1-1-1-1111111i−i−i−iiiii−i−i1-1-1ii−i−i−ii
χ1722222-2-2222200222-2-2-2-2-2-2000022222222220000-2-2-2-200000000-2-22222-200-2-2000000000022-2-20000220000000000-200000000
χ1822222-2-2222200222-2-2-2-2-2-200002222-2-222220000-2-2-2-200000000-2-22222200-2-20000000000-2-2220000-2-20000000000200000000
χ1922222-2-2222200222-2-2-2-2-2-20000-2-2-2-22222220000-2-2-2-20000000022-2-2-2-2-20022000000000022-2-20000-2-20000000000200000000
χ2022222-2-2222200222-2-2-2-2-2-20000-2-2-2-2-2-222220000-2-2-2-20000000022-2-2-2-2200220000000000-2-2220000220000000000-200000000
χ212222-122-1-1-1222222-1-12222-1-1-1-1222200-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1000-1-1222222-1-1-1-1000000000022-1-1-1-1-1-1-1-1000000000
χ222222-122-1-1-1222222-1-12222-1-1-1-1222200-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1000-1-122-2-2-2-2-1-1-1-10000000000-2-211111111000000000
χ232222-122-1-1-1222222-1-12222-1-1-1-1-2-2-2-200-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2111100011-2-22i2i−2i−2i111100000000002i−2i−i−i−i−iiiii000000000
χ242222-122-1-1-1222222-1-12222-1-1-1-1-2-2-2-200-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2111100011-2-2−2i−2i2i2i11110000000000−2i2iiiii−i−i−i−i000000000
χ252222-122-1-1-12-2-2222-1-122221111222200-1-1-1-1-2-2-2-2-1-1-1-11111111122-1-1-1-1000-1-1-2-2222211110000000000-2-2-1-111-1-111000000000
χ262222-122-1-1-12-2-2222-1-122221111222200-1-1-1-1-2-2-2-2-1-1-1-11111111122-1-1-1-1000-1-1-2-2-2-2-2-2111100000000002211-1-111-1-1000000000
χ272222-122-1-1-12-2-2222-1-122221111-2-2-2-200-1-1-1-1-2-2-2-2-1-1-1-111111111-2-2111100011222i2i−2i−2i-1-1-1-10000000000−2i2i−i−iiiii−i−i000000000
χ282222-122-1-1-12-2-2222-1-122221111-2-2-2-200-1-1-1-1-2-2-2-2-1-1-1-111111111-2-211110001122−2i−2i2i2i-1-1-1-100000000002i−2iii−i−i−i−iii000000000
χ2922-2-22002-2-222−22-2-200000022−2−22i−2i2i−2i2-222-2-222−2−200002222−2−2−2−2002i−2i2i−2i02−200−i2i20000−i2−i2i2i22-20022−2−22i−2i00000000000−i2i2000000
χ3022-2-22002-2-222−22-2-200000022−2−22i−2i2i−2i-2222-2-222−2−200002222−2−2−2−2002i−2i2i−2i0−2200−i2i20000−i2−i2i2i2-2200−2−222−2i2i00000000000i2−i2000000
χ3122-2-22002-2-222−22-2-200000022−2−2−2i2i−2i2i2-222-2-222−2−200002222−2−2−2−200−2i2i−2i2i02−200i2−i20000i2i2−i2−i22-20022−2−2−2i2i00000000000i2−i2000000
χ3222-2-22002-2-222−22-2-200000022−2−2−2i2i−2i2i-2222-2-222−2−200002222−2−2−2−200−2i2i−2i2i0−2200i2−i20000i2i2−i2−i2-2200−2−2222i−2i00000000000−i2i2000000
χ3322-2-22002-2-22−222-2-2000000−2−2222i−2i2i−2i2-222-2-2−2−2220000−2−2−2−22222002i−2i2i−2i0−2200i2−i20000i2i2−i2−i22-200−2−2222i−2i00000000000i2−i2000000
χ3422-2-22002-2-22−222-2-2000000−2−2222i−2i2i−2i-2222-2-2−2−2220000−2−2−2−22222002i−2i2i−2i02−200i2−i20000i2i2−i2−i2-220022−2−2−2i2i00000000000−i2i2000000
χ3522-2-22002-2-22−222-2-2000000−2−222−2i2i−2i2i2-222-2-2−2−2220000−2−2−2−2222200−2i2i−2i2i0−2200−i2i20000−i2−i2i2i22-200−2−222−2i2i00000000000−i2i2000000
χ3622-2-22002-2-22−222-2-2000000−2−222−2i2i−2i2i-2222-2-2−2−2220000−2−2−2−2222200−2i2i−2i2i02−200−i2i20000−i2−i2i2i2-220022−2−22i−2i00000000000i2−i2000000
χ372-2-2222-2-2-22200-2-22-2222-2-2000022-2-2002-2-220000-2-222000000002-222-2-20002-2002i−2i2i−2i00000000000000002i−2i002i−2i00000000000
χ382-2-2222-2-2-22200-2-22-2222-2-2000022-2-2002-2-220000-2-222000000002-222-2-20002-200−2i2i−2i2i0000000000000000−2i2i00−2i2i00000000000
χ392-2-2222-2-2-22200-2-22-2222-2-20000-2-222002-2-220000-2-22200000000-22-2-222000-22002-2-2200000000000000002-200-2200000000000
χ402-2-2222-2-2-22200-2-22-2222-2-20000-2-222002-2-220000-2-22200000000-22-2-222000-2200-222-20000000000000000-22002-200000000000
χ412-2-222-22-2-22200-2-222-2-2-222000022-2-2002-2-22000022-2-200000000-2222-2-2000-220000000000000000000000000000000002i−2i2i−2i00
χ422-2-222-22-2-22200-2-222-2-2-222000022-2-2002-2-22000022-2-200000000-2222-2-2000-22000000000000000000000000000000000−2i2i−2i2i00
χ432-2-222-22-2-22200-2-222-2-2-2220000-2-222002-2-22000022-2-2000000002-2-2-2220002-20000000000000000000000000000000002-2-2200
χ442-2-222-22-2-22200-2-222-2-2-2220000-2-222002-2-22000022-2-2000000002-2-2-2220002-2000000000000000000000000000000000-222-200
χ452-2-22-12-211-1200-2-221-122-2-2−i3i3−i3i322-2-200-111-1000011-1-1−i3−i3i3i3−i3−i3i3i32-2-1-111000-11002i−2i2i−2i−i3i3−i3i3000000000000−ii3−3−ii3−3000000000
χ462-2-22-12-211-1200-2-221-122-2-2−i3i3−i3i322-2-200-111-1000011-1-1−i3−i3i3i3−i3−i3i3i32-2-1-111000-1100−2i2i−2i2i−i3i3−i3i3000000000000i−i−33i−i−33000000000
χ472-2-22-12-211-1200-2-221-122-2-2−i3i3−i3i3-2-22200-111-1000011-1-1−i3−i3i3i3−i3−i3i3i3-2211-1-10001-1002-2-22i3−i3i3−i3000000000000-11−i3i31-1i3−i3000000000
χ482-2-22-12-211-1200-2-221-122-2-2−i3i3−i3i3-2-22200-111-1000011-1-1−i3−i3i3i3−i3−i3i3i3-2211-1-10001-100-222-2i3−i3i3−i30000000000001-1i3−i3-11−i3i3000000000
χ492-2-22-12-211-1200-2-221-122-2-2i3−i3i3−i322-2-200-111-1000011-1-1i3i3−i3−i3i3i3−i3−i32-2-1-111000-11002i−2i2i−2ii3−i3i3−i3000000000000−ii−33−ii−33000000000
χ502-2-22-12-211-1200-2-221-122-2-2i3−i3i3−i322-2-200-111-1000011-1-1i3i3−i3−i3i3i3−i3−i32-2-1-111000-1100−2i2i−2i2ii3−i3i3−i3000000000000i−i3−3i−i3−3000000000
χ512-2-22-12-211-1200-2-221-122-2-2i3−i3i3−i3-2-22200-111-1000011-1-1i3i3−i3−i3i3i3−i3−i3-2211-1-10001-1002-2-22−i3i3−i3i3000000000000-11i3−i31-1−i3i3000000000
χ522-2-22-12-211-1200-2-221-122-2-2i3−i3i3−i3-2-22200-111-1000011-1-1i3i3−i3−i3i3i3−i3−i3-2211-1-10001-100-222-2−i3i3−i3i30000000000001-1−i3i3-11i3−i3000000000
χ534444444444-144-1-1-144-1-1-1-14444000044-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000444000000000000-1-1-1-1-1-1-1-1000000000000000000000
χ544444444444-144-1-1-144-1-1-1-144440000-4-4-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000-4-4-400000000000011111111000000000000000000000
χ554444444444-1-4-4-1-1-144-1-1-1-1-4-4-4-4000044-1-1-1-11111-1-1-1-1111111110000004-4-4000000000000-1-1-1-11111000000000000000000000
χ564444444444-1-4-4-1-1-144-1-1-1-1-4-4-4-40000-4-4-1-1-1-11111-1-1-1-111111111000000-4440000000000001111-1-1-1-1000000000000000000000
χ5744444-4-4444-100-1-1-1-4-411110000000044-1-1-1-1−i5i5−i5i51111−i5i5−i5i5−i5i5−i5i5000000-400000000000000-1-111−i5i5−i5i5000000000000000000000
χ5844444-4-4444-100-1-1-1-4-411110000000044-1-1-1-1i5−i5i5−i51111i5−i5i5−i5i5−i5i5−i5000000-400000000000000-1-111i5−i5i5−i5000000000000000000000
χ5944444-4-4444-100-1-1-1-4-4111100000000-4-4-1-1-1-1−i5i5−i5i51111−i5i5−i5i5−i5i5−i5i500000040000000000000011-1-1i5−i5i5−i5000000000000000000000
χ6044444-4-4444-100-1-1-1-4-4111100000000-4-4-1-1-1-1i5−i5i5−i51111i5−i5i5−i5i5−i5i5−i500000040000000000000011-1-1−i5i5−i5i5000000000000000000000
χ614444-2-4-4-2-2-240044422-4-4-4-40000444400-2-2-2-20000222200000000-4-4-2-2-2-200022000000000000000000000000000000000000000
χ624444-2-4-4-2-2-240044422-4-4-4-40000-4-4-4-400-2-2-2-20000222200000000442222000-2-2000000000000000000000000000000000000000
χ6344-4-44004-4-4-122−22-11100−i5i5−i5i52222−22−2200004-4-1-111−ζ7−ζ23+ζ29−ζ47+ζ61+ζ101−ζ103+ζ109ζ13−ζ31+ζ37+ζ53−ζ71+ζ77−ζ79−ζ119ζ7+ζ23−ζ29+ζ47−ζ61−ζ101+ζ103−ζ109−ζ13+ζ31−ζ37−ζ53+ζ71−ζ77+ζ79+ζ119−i5i5−i5i5−ζ7−ζ23+ζ29−ζ47+ζ61+ζ101−ζ103+ζ109ζ13−ζ31+ζ37+ζ53−ζ71+ζ77−ζ79−ζ119−ζ7−ζ23+ζ29−ζ47+ζ61+ζ101−ζ103+ζ109ζ13−ζ31+ζ37+ζ53−ζ71+ζ77−ζ79−ζ119ζ7+ζ23−ζ29+ζ47−ζ61−ζ101+ζ103−ζ109−ζ13+ζ31−ζ37−ζ53+ζ71−ζ77+ζ79+ζ119ζ7+ζ23−ζ29+ζ47−ζ61−ζ101+ζ103−ζ109−ζ13+ζ31−ζ37−ζ53+ζ71−ζ77+ζ79+ζ119000000022−22000000000000-11−i5i5−ζ7−ζ23+ζ29−ζ47+ζ61+ζ101−ζ103+ζ109ζ13−ζ31+ζ37+ζ53−ζ71+ζ77−ζ79−ζ119ζ7+ζ23−ζ29+ζ47−ζ61−ζ101+ζ103−ζ109−ζ13+ζ31−ζ37−ζ53+ζ71−ζ77+ζ79+ζ119000000000000000000000
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Here ζ is a primitive root of unity of order 120 (ζ120 = 1); i = ζ30.