Finite Group Databasebeta

← Group #14285850

Character table — Group #14285850

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111122222222444444444444444555588888888888888888888101010101010101012121212202020202020202424242424242424404040404040404040404040606060606060606060606060
order122234444666451010101212121212122020202044441520202020303030606060606060606060606060224412121212888846612121212404040404040404088882424242424242424888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-111111111ii−i−iiiii−i−i−i−i-1-1-1-1iiii−i−i−i−i
χ6111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-111111111−i−iii−i−i−i−iiiii-1-1-1-1−i−i−i−iiiii
χ7111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iiiii−i−i−i−i1111−i−i−i−iiiii
χ8111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−i−i−iiiii1111iiii−i−i−i−i
χ911111-1-111111-1111111-1-1-1-1111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1-11111-1-1-1-11-11-111-1-111-1-111-1-111-1-111-1-1
χ1011111-1-111111-1111111-1-1-1-1111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1-11111-1-1-1-1-11-11-1-111-1-11111-1-1-1-111-1-111
χ1111111-1-111111-1111111-1-1-1-1111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-111-1-1-1-1-1-111111-11-111-1-111-1-1-1-111-1-111-1-111
χ1211111-1-111111-1111111-1-1-1-1111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-111-1-1-1-1-1-11111-11-11-1-111-1-111-1-11111-1-111-1-1
χ1311111-1-111111-1111111-1-1-1-11111-1-1-1-11-1-1-1-11111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1111-1-1111111-1-1-1-1i−i−iiii−i−i−i−iii-1-111ii−i−i−i−iii
χ1411111-1-111111-1111111-1-1-1-11111-1-1-1-11-1-1-1-11111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1111-1-1111111-1-1-1-1−iii−i−i−iiiii−i−i-1-111−i−iiiii−i−i
χ1511111-1-111111-1111111-1-1-1-11111-1-1-1-11-1-1-1-11111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111-1-111-1-1-1-11111i−i−iiii−i−i−i−iii11-1-1−i−iiiii−i−i
χ1611111-1-111111-1111111-1-1-1-11111-1-1-1-11-1-1-1-11111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111-1-111-1-1-1-11111−iii−i−i−iiiii−i−i11-1-1ii−i−i−i−iii
χ172222222-2-2222-22222-2-222-2-2-2-2-2-22222222-2-2222-2-2-2-22222-2-2-2-222-2-222220000-222-2-2-2-200000000000000000000000000000000
χ182222222-2-2222-22222-2-222-2-2-2-2-2-2-2-2-2-2222-2-2222-2-2-2-22222-2-2-2-2-2-222-2-2-2-200002-2-2222200000000000000000000000000000000
χ1922222-2-2-2-222222222-2-2-2-222-2-2-2-222222-2-222222-2-2-2-2-2-2-2-22222-2-2-2-2222200002-2-2-2-22200000000000000000000000000000000
χ2022222-2-2-2-222222222-2-2-2-222-2-2-2-2-2-2-2-22-2-222222-2-2-2-2-2-2-2-222222222-2-2-2-20000-22222-2-200000000000000000000000000000000
χ212222-12222-1-1-122222-1-1-1-1-1-122222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-100002-1-1-1-1-1-1000000002222-1-1-1-1-1-1-1-1000000000000
χ222222-12222-1-1-122222-1-1-1-1-1-122222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-100002-1-1-1-1-1-100000000-2-2-2-211111111000000000000
χ232222-12222-1-1-122222-1-1-1-1-1-12222-2-2-2-2-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211110000-2111111000000002i2i−2i−2i−i−i−i−iiiii000000000000
χ242222-12222-1-1-122222-1-1-1-1-1-12222-2-2-2-2-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211110000-211111100000000−2i−2i2i2iiiii−i−i−i−i000000000000
χ252222-122-2-2-1-1-1-2222211-1-111-2-2-2-22222-122-2-2-1-1-11111-1-1-1-1111122-2-2-1-1-1-10000-2-1-11111000000000000−i3i3−i3i3−i3i3−i3i3000000000000
χ262222-122-2-2-1-1-1-2222211-1-111-2-2-2-22222-122-2-2-1-1-11111-1-1-1-1111122-2-2-1-1-1-10000-2-1-11111000000000000i3−i3i3−i3i3−i3i3−i3000000000000
χ272222-122-2-2-1-1-1-2222211-1-111-2-2-2-2-2-2-2-2-122-2-2-1-1-11111-1-1-1-11111-2-22211110000211-1-1-1-10000000000003−33−3−33−33000000000000
χ282222-122-2-2-1-1-1-2222211-1-111-2-2-2-2-2-2-2-2-122-2-2-1-1-11111-1-1-1-11111-2-22211110000211-1-1-1-1000000000000−33−333−33−3000000000000
χ292222-1-2-222-1-1-1-22222-1-1111122222222-1-2-2-2-2-1-1-1-1-1-1-111111111-2-222-1-1-1-10000-211-1-111000000002-22-2-1-111-1-111000000000000
χ302222-1-2-222-1-1-1-22222-1-1111122222222-1-2-2-2-2-1-1-1-1-1-1-111111111-2-222-1-1-1-10000-211-1-11100000000-22-2211-1-111-1-1000000000000
χ312222-1-2-222-1-1-1-22222-1-111112222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-11111111122-2-2111100002-1-111-1-1000000002i−2i−2i2i−i−iiiii−i−i000000000000
χ322222-1-2-222-1-1-1-22222-1-111112222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-11111111122-2-2111100002-1-111-1-100000000−2i2i2i−2iii−i−i−i−iii000000000000
χ332222-1-2-2-2-2-1-1-1222221111-1-1-2-2-2-22222-1-2-222-1-1-111111111-1-1-1-1-2-2-2-2-1-1-1-1000021111-1-1000000000000−i3i3i3−i3−i3i3i3−i3000000000000
χ342222-1-2-2-2-2-1-1-1222221111-1-1-2-2-2-22222-1-2-222-1-1-111111111-1-1-1-1-2-2-2-2-1-1-1-1000021111-1-1000000000000i3−i3−i3i3i3−i3−i3i3000000000000
χ352222-1-2-2-2-2-1-1-1222221111-1-1-2-2-2-2-2-2-2-2-1-2-222-1-1-111111111-1-1-1-1222211110000-2-1-1-1-1110000000000003−3−33−333−3000000000000
χ362222-1-2-2-2-2-1-1-1222221111-1-1-2-2-2-2-2-2-2-2-1-2-222-1-1-111111111-1-1-1-1222211110000-2-1-1-1-111000000000000−333−33−3−33000000000000
χ3722-2-22002-22-2-2022-2-22-20000-2-2222i−2i2i−2i200002-2-222-2-200000000002i−2i2i−2i2i−2i00000002i−2i00000000000000000000000000002ζ7+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
χ3822-2-22002-22-2-2022-2-22-20000-2-2222i−2i2i−2i200002-2-222-2-200000000002i−2i2i−2i2i−2i00000002i−2i0000000000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119002ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ109
χ3922-2-22002-22-2-2022-2-22-20000-2-222−2i2i−2i2i200002-2-222-2-20000000000−2i2i−2i2i−2i2i0000000−2i2i0000000000000000000000000000−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109002ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ119
χ4022-2-22002-22-2-2022-2-22-20000-2-222−2i2i−2i2i200002-2-222-2-20000000000−2i2i−2i2i−2i2i0000000−2i2i00000000000000000000000000002ζ13+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
χ4122-2-2200-222-2-2022-2-2-22000022-2-22i−2i2i−2i200002-2-2-2-2220000000000−2i2i2i−2i2i−2i0000000−2i2i00000000000000000000000000−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109002ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ11900
χ4222-2-2200-222-2-2022-2-2-22000022-2-22i−2i2i−2i200002-2-2-2-2220000000000−2i2i2i−2i2i−2i0000000−2i2i000000000000000000000000002ζ13+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
χ4322-2-2200-222-2-2022-2-2-22000022-2-2−2i2i−2i2i200002-2-2-2-22200000000002i−2i−2i2i−2i2i00000002i−2i000000000000000000000000002ζ7+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
χ4422-2-2200-222-2-2022-2-2-22000022-2-2−2i2i−2i2i200002-2-2-2-22200000000002i−2i−2i2i−2i2i00000002i−2i00000000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119002ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ10900
χ452-22-222-200-22-202-22-2002-200000022-2-222-200-22-2000022-2-200002-200-2-222−i2i2−i2i202-20000−i2−i2i2i2−i2−i2i2i2000000000000−i2i2−i2i200000000
χ462-22-222-200-22-202-22-2002-200000022-2-222-200-22-2000022-2-200002-200-2-222i2−i2i2−i202-20000i2i2−i2−i2i2i2−i2−i2000000000000i2−i2i2−i200000000
χ472-22-222-200-22-202-22-2002-2000000-2-22222-200-22-2000022-2-20000-220022-2-2−i2i2−i2i20-220000−i2−i2i2i2−i2−i2i2i2000000000000i2−i2i2−i200000000
χ482-22-222-200-22-202-22-2002-2000000-2-22222-200-22-2000022-2-20000-220022-2-2i2−i2i2−i20-220000i2i2−i2−i2i2i2−i2−i2000000000000−i2i2−i2i200000000
χ492-22-22-2200-22-202-22-200-2200000022-2-22-2200-22-20000-2-2220000-2200-2-222−i2i2i2−i20-220000−i2−i2i2i2i2i2−i2−i2000000000000−i2i2i2−i200000000
χ502-22-22-2200-22-202-22-200-2200000022-2-22-2200-22-20000-2-2220000-2200-2-222i2−i2−i2i20-220000i2i2−i2−i2−i2−i2i2i2000000000000i2−i2−i2i200000000
χ512-22-22-2200-22-202-22-200-22000000-2-2222-2200-22-20000-2-22200002-20022-2-2−i2i2i2−i202-20000−i2−i2i2i2i2i2−i2−i2000000000000i2−i2−i2i200000000
χ522-22-22-2200-22-202-22-200-22000000-2-2222-2200-22-20000-2-22200002-20022-2-2i2−i2−i2i202-20000i2i2−i2−i2−i2−i2i2i2000000000000−i2i2i2−i200000000
χ534444444444444-1-1-1-1444444-1-1-1-10000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000044440000000-1-1-1-1-1-1-1-1000000000000000000000000
χ544444444444444-1-1-1-1444444-1-1-1-10000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000-4-4-4-4000000011111111000000000000000000000000
χ554444444-4-4444-4-1-1-1-1-4-444-4-411110000-1-1-111-1-1-11111-1-1-1-111110000000000000000000−i5i5−i5i5−i5i5−i5i5000000000000000000000000
χ564444444-4-4444-4-1-1-1-1-4-444-4-411110000-1-1-111-1-1-11111-1-1-1-111110000000000000000000i5−i5i5−i5i5−i5i5−i5000000000000000000000000
χ5744444-4-444444-4-1-1-1-144-4-4-4-4-1-1-1-10000-11111-1-1-1-1-1-1-1111111110000000044-4-40000000-1-1-1-11111000000000000000000000000
χ5844444-4-444444-4-1-1-1-144-4-4-4-4-1-1-1-10000-11111-1-1-1-1-1-1-11111111100000000-4-44400000001111-1-1-1-1000000000000000000000000
χ5944444-4-4-4-44444-1-1-1-1-4-4-4-44411110000-111-1-1-1-1-111111111-1-1-1-10000000000000000000−i5i5−i5i5i5−i5i5−i5000000000000000000000000
χ6044444-4-4-4-44444-1-1-1-1-4-4-4-44411110000-111-1-1-1-1-111111111-1-1-1-10000000000000000000i5−i5i5−i5−i5i5−i5i5000000000000000000000000
χ6144-4-4-2004-4-222044-4-4-220000-4-4444i−4i4i−4i-20000-222-2-22200000000004i−4i−2i2i−2i2i0000000−2i2i0000000000000000000000000000000000
χ6244-4-4-2004-4-222044-4-4-220000-4-444−4i4i−4i4i-20000-222-2-2220000000000−4i4i2i−2i2i−2i00000002i−2i0000000000000000000000000000000000
χ6344-4-4-200-44-222044-4-42-2000044-4-44i−4i4i−4i-20000-22222-2-20000000000−4i4i−2i2i−2i2i00000002i−2i0000000000000000000000000000000000
χ6444-4-4-200-44-222044-4-42-2000044-4-4−4i4i−4i4i-20000-22222-2-200000000004i−4i2i−2i2i−2i0000000−2i2i0000000000000000000000000000000000
χ654-44-444-400-44-40-11-11004-400−i5i5−i5i50000-1-11−i5i51-11−i5i5−i5i5-1-111−i5−i5i5i500000000−2i22i2−2i22i20000000ζ7+ζ23+ζ29+ζ47+ζ61+ζ101+ζ103+ζ109ζ13+ζ31+ζ37+ζ53+ζ71+ζ77+ζ79+ζ119−ζ7−ζ23−ζ29−ζ47−ζ61−ζ101−ζ103−ζ109−ζ13−ζ31−ζ37−ζ53−ζ71−ζ77−ζ79−ζ119ζ7+ζ23+ζ29+ζ47+ζ61+ζ101+ζ103+ζ109ζ13+ζ31+ζ37+ζ53+ζ71+ζ77+ζ79+ζ119−ζ7−ζ23−ζ29−ζ47−ζ61−ζ101−ζ103−ζ109−ζ13−ζ31−ζ37−ζ53−ζ71−ζ77−ζ79−ζ119000000000000000000000000
χ664-44-444-400-44-40-11-11004-400−i5i5−i5i50000-1-11−i5i51-11−i5i5−i5i5-1-111−i5−i5i5i5000000002i2−2i22i2−2i20000000−ζ7−ζ23−ζ29−ζ47−ζ61−ζ101−ζ103−ζ109−ζ13−ζ31−ζ37−ζ53−ζ71−ζ77−ζ79−ζ119ζ7+ζ23+ζ29+ζ47+ζ61+ζ101+ζ103+ζ109ζ13+ζ31+ζ37+ζ53+ζ71+ζ77+ζ79+ζ119−ζ7−ζ23−ζ29−ζ47−ζ61−ζ101−ζ103−ζ109−ζ13−ζ31−ζ37−ζ53−ζ71−ζ77−ζ79−ζ119ζ7+ζ23+ζ29+ζ47+ζ61+ζ101+ζ103+ζ109ζ13+ζ31+ζ37+ζ53+ζ71+ζ77+ζ79+ζ119000000000000000000000000
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χ1028-8-88-4000044-40-222-200004i3−4i32i5−2i5−2i52i5000010000-1-11i5−i5−i5i5−151515−15−i3i3−i3i3000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 120 (ζ120 = 1); i = ζ30.