Finite Group Databasebeta

← Group #14414882

Character table — Group #14414882

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132
size1111222244444445555668888888888101010101010101012202020202020202020202020202424242430303030303060606011112222444444455556688888888881010101010101010122020202020202020202020202024242424303030303030606060
order122236662566101010444444101015303030303030308888121212124488121224242424242424242020202044888828822226666210661010104444441010303030303030303088881212121244881212242424242424242420202020448888288
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-11-1-11111111111111111111111111111111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-11-1-1
χ31111111111111111111-1-1111111111111111111-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111-1-1111111111111111111-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111-1-11111111111-1-1-1-11111-11-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1111111111111111111111-1-11111111111-1-1-1-11111-11-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111
χ5111111111111111-1-1-1-1111111111111ii−i−i-1-1-1-11-1i−i-1-1iiii−i−i−i−i1111-1-1ii−i−i-1i−i111111111111111-1-1-1-1111111111111ii−i−i-1-1-1-11-1i−i-1-1iiii−i−i−i−i1111-1-1ii−i−i-1i−i
χ6111111111111111-1-1-1-1111111111111−i−iii-1-1-1-11-1−ii-1-1−i−i−i−iiiii1111-1-1−i−iii-1−ii111111111111111-1-1-1-1111111111111−i−iii-1-1-1-11-1−ii-1-1−i−i−i−iiiii1111-1-1−i−iii-1−ii
χ7111111111111111-1-1-1-1-1-11111111111ii−i−i-1-1-1-1-1-1i−i-1-1iiii−i−i−i−i-1-1-1-111−i−iii1−ii111111111111111-1-1-1-1-1-11111111111ii−i−i-1-1-1-1-1-1i−i-1-1iiii−i−i−i−i-1-1-1-111−i−iii1−ii
χ8111111111111111-1-1-1-1-1-11111111111−i−iii-1-1-1-1-1-1−ii-1-1−i−i−i−iiiii-1-1-1-111ii−i−i1i−i111111111111111-1-1-1-1-1-11111111111−i−iii-1-1-1-1-1-1−ii-1-1−i−i−i−iiiii-1-1-1-111ii−i−i1i−i
χ911111111-11-1-1111111111-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-111-1-111-1-1111111-1-1-111111111-11-1-1111111111-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-111-1-111-1-1111111-1-1-1
χ1011111111-11-1-1111111111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-11111-1-111-1-1-1-1-11111111111-11-1-1111111111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-11111-1-111-1-1-1-1-111
χ1111111111-11-1-11111111-1-1-1-11111-1-1-1-1111111111-1-1-1-1-111-1-111-1-1-1-111-1-1-1-1-1-111111111111-11-1-11111111-1-1-1-11111-1-1-1-1111111111-1-1-1-1-111-1-111-1-1-1-111-1-1-1-1-1-1111
χ1211111111-11-1-11111111-1-1-1-11111-1-1-1-1-1-1-1-111111-111-1-1-1-111-1-111-1-111-1-111111-1-111111111-11-1-11111111-1-1-1-11111-1-1-1-1-1-1-1-111111-111-1-1-1-111-1-111-1-111-1-111111-1-1
χ1311111111-11-1-1111-1-1-1-111-1-11111-1-1-1-1ii−i−i-1-1-1-1-11−ii11ii−i−i−i−iii11-1-1-1-1ii−i−i1−ii11111111-11-1-1111-1-1-1-111-1-11111-1-1-1-1ii−i−i-1-1-1-1-11−ii11ii−i−i−i−iii11-1-1-1-1ii−i−i1−ii
χ1411111111-11-1-1111-1-1-1-111-1-11111-1-1-1-1−i−iii-1-1-1-1-11i−i11−i−iiiii−i−i11-1-1-1-1−i−iii1i−i11111111-11-1-1111-1-1-1-111-1-11111-1-1-1-1−i−iii-1-1-1-1-11i−i11−i−iiiii−i−i11-1-1-1-1−i−iii1i−i
χ1511111111-11-1-1111-1-1-1-1-1-1-1-11111-1-1-1-1ii−i−i-1-1-1-111−ii11ii−i−i−i−iii-1-11111−i−iii-1i−i11111111-11-1-1111-1-1-1-1-1-1-1-11111-1-1-1-1ii−i−i-1-1-1-111−ii11ii−i−i−i−iii-1-11111−i−iii-1i−i
χ1611111111-11-1-1111-1-1-1-1-1-1-1-11111-1-1-1-1−i−iii-1-1-1-111i−i11−i−iiiii−i−i-1-11111ii−i−i-1−ii11111111-11-1-1111-1-1-1-1-1-1-1-11111-1-1-1-1−i−iii-1-1-1-111i−i11−i−iiiii−i−i-1-11111ii−i−i-1−ii
χ172222-1-1-1-122-1-122222220022-1-1-1-1-1-1-1-12222-1-1-1-10222-1-1-1-1-1-1-1-1-1-100000000000002222-1-1-1-122-1-122222220022-1-1-1-1-1-1-1-12222-1-1-1-10222-1-1-1-1-1-1-1-1-1-10000000000000
χ182222-1-1-1-122-1-122222220022-1-1-1-1-1-1-1-1-2-2-2-2-1-1-1-102-2-2-1-11111111100000000000002222-1-1-1-122-1-122222220022-1-1-1-1-1-1-1-1-2-2-2-2-1-1-1-102-2-2-1-1111111110000000000000
χ192222-1-1-1-122-1-1222-2-2-2-20022-1-1-1-1-1-1-1-12i2i−2i−2i11110-22i−2i11−i−i−i−iiiii00000000000002222-1-1-1-122-1-1222-2-2-2-20022-1-1-1-1-1-1-1-12i2i−2i−2i11110-22i−2i11−i−i−i−iiiii0000000000000
χ202222-1-1-1-122-1-1222-2-2-2-20022-1-1-1-1-1-1-1-1−2i−2i2i2i11110-2−2i2i11iiii−i−i−i−i00000000000002222-1-1-1-122-1-1222-2-2-2-20022-1-1-1-1-1-1-1-1−2i−2i2i2i11110-2−2i2i11iiii−i−i−i−i0000000000000
χ212222-1-1-1-1-2211222222200-2-2-1-1-1-111112222-1-1-1-10-2-2-211-1-111-1-11100000000000002222-1-1-1-1-2211222222200-2-2-1-1-1-111112222-1-1-1-10-2-2-211-1-111-1-1110000000000000
χ222222-1-1-1-1-2211222222200-2-2-1-1-1-11111-2-2-2-2-1-1-1-10-2221111-1-111-1-100000000000002222-1-1-1-1-2211222222200-2-2-1-1-1-11111-2-2-2-2-1-1-1-10-2221111-1-111-1-10000000000000
χ232222-1-1-1-1-2211222-2-2-2-200-2-2-1-1-1-111112i2i−2i−2i111102−2i2i-1-1−i−iiiii−i−i00000000000002222-1-1-1-1-2211222-2-2-2-200-2-2-1-1-1-111112i2i−2i−2i111102−2i2i-1-1−i−iiiii−i−i0000000000000
χ242222-1-1-1-1-2211222-2-2-2-200-2-2-1-1-1-11111−2i−2i2i2i1111022i−2i-1-1ii−i−i−i−iii00000000000002222-1-1-1-1-2211222-2-2-2-200-2-2-1-1-1-11111−2i−2i2i2i1111022i−2i-1-1ii−i−i−i−iii0000000000000
χ2522-2-222-2-20200-22-22i−2i2i−2i000022-2-2000000002i−2i2i−2i000000000000000000002ζ7+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+2ζ10900022-2-222-2-20200-22-22i−2i2i−2i000022-2-2000000002i−2i2i−2i000000000000000000002ζ7+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+2ζ109000
χ2622-2-222-2-20200-22-22i−2i2i−2i000022-2-2000000002i−2i2i−2i00000000000000000000−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ1192ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ10900022-2-222-2-20200-22-22i−2i2i−2i000022-2-2000000002i−2i2i−2i00000000000000000000−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ1192ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ109000
χ2722-2-222-2-20200-22-2−2i2i−2i2i000022-2-200000000−2i2i−2i2i00000000000000000000−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ1092ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ11900022-2-222-2-20200-22-2−2i2i−2i2i000022-2-200000000−2i2i−2i2i00000000000000000000−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ1092ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ119000
χ2822-2-222-2-20200-22-2−2i2i−2i2i000022-2-200000000−2i2i−2i2i000000000000000000002ζ13+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+2ζ11900022-2-222-2-20200-22-2−2i2i−2i2i000022-2-200000000−2i2i−2i2i000000000000000000002ζ13+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+2ζ119000
χ292-22-22-2-220200-2-2222-2-200002-22-200002i−2i2i−2i22-2-20000002i−2i002i−2i0000000000000002-22-22-2-220200-2-2222-2-200002-22-200002i−2i2i−2i22-2-20000002i−2i002i−2i000000000000000
χ302-22-22-2-220200-2-2222-2-200002-22-20000−2i2i−2i2i22-2-2000000−2i2i00−2i2i0000000000000002-22-22-2-220200-2-2222-2-200002-22-20000−2i2i−2i2i22-2-2000000−2i2i00−2i2i000000000000000
χ312-22-22-2-220200-2-22-2-22200002-22-200002-2-22-2-2220000002-200-220000000000000002-22-22-2-220200-2-22-2-22200002-22-200002-2-22-2-2220000002-200-22000000000000000
χ322-22-22-2-220200-2-22-2-22200002-22-20000-222-2-2-222000000-22002-20000000000000002-22-22-2-220200-2-22-2-22200002-22-20000-222-2-2-222000000-22002-2000000000000000
χ332-22-2-111-102−i3i3-2-2222-2-20000-11-11−i3−i3i3i32i−2i2i−2i-1-1110000−i3i3−ii3−3−ii3−300000000000002-22-2-111-102−i3i3-2-2222-2-20000-11-11−i3−i3i3i32i−2i2i−2i-1-1110000−i3i3−ii3−3−ii3−30000000000000
χ342-22-2-111-102−i3i3-2-2222-2-20000-11-11−i3−i3i3i3−2i2i−2i2i-1-1110000−i3i3i−i−33i−i−3300000000000002-22-2-111-102−i3i3-2-2222-2-20000-11-11−i3−i3i3i3−2i2i−2i2i-1-1110000−i3i3i−i−33i−i−330000000000000
χ352-22-2-111-102−i3i3-2-22-2-2220000-11-11−i3−i3i3i32-2-2211-1-10000i3−i3-11−i3i31-1i3−i300000000000002-22-2-111-102−i3i3-2-22-2-2220000-11-11−i3−i3i3i32-2-2211-1-10000i3−i3-11−i3i31-1i3−i30000000000000
χ362-22-2-111-102−i3i3-2-22-2-2220000-11-11−i3−i3i3i3-222-211-1-10000i3−i31-1i3−i3-11−i3i300000000000002-22-2-111-102−i3i3-2-22-2-2220000-11-11−i3−i3i3i3-222-211-1-10000i3−i31-1i3−i3-11−i3i30000000000000
χ372-22-2-111-102i3−i3-2-2222-2-20000-11-11i3i3−i3−i32i−2i2i−2i-1-1110000i3−i3−ii−33−ii−3300000000000002-22-2-111-102i3−i3-2-2222-2-20000-11-11i3i3−i3−i32i−2i2i−2i-1-1110000i3−i3−ii−33−ii−330000000000000
χ382-22-2-111-102i3−i3-2-2222-2-20000-11-11i3i3−i3−i3−2i2i−2i2i-1-1110000i3−i3i−i3−3i−i3−300000000000002-22-2-111-102i3−i3-2-2222-2-20000-11-11i3i3−i3−i3−2i2i−2i2i-1-1110000i3−i3i−i3−3i−i3−30000000000000
χ392-22-2-111-102i3−i3-2-22-2-2220000-11-11i3i3−i3−i32-2-2211-1-10000−i3i3-11i3−i31-1−i3i300000000000002-22-2-111-102i3−i3-2-22-2-2220000-11-11i3i3−i3−i32-2-2211-1-10000−i3i3-11i3−i31-1−i3i30000000000000
χ402-22-2-111-102i3−i3-2-22-2-2220000-11-11i3i3−i3−i3-222-211-1-10000−i3i31-1−i3i3-11i3−i300000000000002-22-2-111-102i3−i3-2-22-2-2220000-11-11i3i3−i3−i3-222-211-1-10000−i3i31-1−i3i3-11i3−i30000000000000
χ412-2-222-22-202002-2-22i−2i−2i2i2i−2i002-2-22000000002i−2i−2i2i000000000000002i−2i002-200000002-2-222-22-202002-2-22i−2i−2i2i2i−2i002-2-22000000002i−2i−2i2i000000000000002i−2i002-20000000
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χ46444444444-144-1-1-10000-4-4-1-1-1-1-1-1-1-1-1-100000000-400000000000001111000000000444444444-144-1-1-10000-4-4-1-1-1-1-1-1-1-1-1-100000000-400000000000001111000000000
χ4744444444-4-1-4-4-1-1-100004411-1-1-1-1111100000000-40000000000000-1-11100000000044444444-4-1-4-4-1-1-100004411-1-1-1-1111100000000-40000000000000-1-111000000000
χ4844444444-4-1-4-4-1-1-10000-4-411-1-1-1-11111000000004000000000000011-1-100000000044444444-4-1-4-4-1-1-10000-4-411-1-1-1-11111000000004000000000000011-1-1000000000
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χ1238888-4-4-4-48-2-4-4-2-2-2000000-2-21111111100000000000000000000000000000000000-8-8-8-84444-824422200000022-1-1-1-1-1-1-1-100000000000000000000000000000000000
χ1248888-4-4-4-4-8-244-2-2-2000000221111-1-1-1-100000000000000000000000000000000000-8-8-8-8444482-4-4222000000-2-2-1-1-1-1111100000000000000000000000000000000000
χ12588-8-888-8-80-2002-2200000000-2-222000000000000000000000000000000000000000-8-888-8-8880200-22-20000000022-2-2000000000000000000000000000000000000000
χ12688-8-8-4-4440-2002-220000000011-1-1−i15i15i15−i1500000000000000000000000000000000000-8-88844-4-40200-22-200000000-1-111i15−i15−i15i1500000000000000000000000000000000000
χ12788-8-8-4-4440-2002-220000000011-1-1i15−i15−i15i1500000000000000000000000000000000000-8-88844-4-40200-22-200000000-1-111−i15i15i15−i1500000000000000000000000000000000000
χ1288-88-88-8-880-20022-200000000-22-22000000000000000000000000000000000000000-88-88-888-80200-2-22000000002-22-2000000000000000000000000000000000000000
χ1298-88-8-444-40-2−4i34i322-2000000001-11-1i3i3−i3−i300000000000000000000000000000000000-88-884-4-44024i3−4i3-2-2200000000-11-11−i3−i3i3i300000000000000000000000000000000000
χ1308-88-8-444-40-24i3−4i322-2000000001-11-1−i3−i3i3i300000000000000000000000000000000000-88-884-4-4402−4i34i3-2-2200000000-11-11i3i3−i3−i300000000000000000000000000000000000
χ1318-8-88-44-440-200-222000000−25251-1-115−55−500000000000000000000000000000000000-888-84-44-402002-2-200000025−25-111-1−55−5500000000000000000000000000000000000
χ1328-8-88-44-440-200-22200000025−251-1-11−55−5500000000000000000000000000000000000-888-84-44-402002-2-2000000−2525-111-15−55−500000000000000000000000000000000000

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