Finite Group Databasebeta

← Group #14281931

Character table — Group #14281931

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111222222224444444444444444444555588888888888888888888888810101010101010101616161616161616161616162020202020202040404040404060606060606060606060606060606060
order1222223446664566101010121212121515303030303030444424661010121220202020303030306060606060606060444412121212101020203030303060606060412121212121244121212128888888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111-1-1-1-111-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111-1-1-1-111-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ61111111111111111111111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii
χ71111111111111111111111111111111-1-1-1-1-1-1-1-111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111iiii−i−i−i−i−i−i−i−iiiii
χ81111111111111111111111111111111-1-1-1-1-1-1-1-111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111−i−i−i−iiiiiiiii−i−i−i−i
χ91111-1-1111111-11-1-111111-1-11111111111111-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-11111-1-1-1-1-111-1-1-1-1-11-1-11111-1-111-1-111-1-111-1-1
χ101111-1-1111111-11-1-111111-1-11111111111111-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-11111-1-1-1-1-111-1-1-1-1-11-1-111-1-111-1-111-1-111-1-111
χ111111-1-1111111-11-1-111111-1-1111111111111-11-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-111-1-1-1-11111-111-1-1-1-11-111-1-111-1-111-1-1-1-111-1-111
χ121111-1-1111111-11-1-111111-1-1111111111111-11-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-111-1-1-1-11111-111-1-1-1-11-111-1-1-1-111-1-11111-1-111-1-1
χ131111-1-1111111-11-1-111111-1-111111111-1-1-1-11-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-111-1-11111-1-1-1-11-1-111111-111-1-1ii−i−i−i−iiiii−i−i−i−iii
χ141111-1-1111111-11-1-111111-1-111111111-1-1-1-11-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-111-1-11111-1-1-1-11-1-111111-111-1-1−i−iiiii−i−i−i−iiiii−i−i
χ151111-1-1111111-11-1-111111-1-111111111-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-111111-1-11111-11-1-111ii−i−i−i−iii−i−iiiii−i−i
χ161111-1-1111111-11-1-111111-1-111111111-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-111111-1-11111-11-1-111−i−iiiii−i−iii−i−i−i−iii
χ172222222-2-2222-2222222-2-2-2-222222222222200002200-2-2-2-22222-2-2-2-2-2-2-2-222-2-22222000000000000-2-2-2-2-2220000000000000000000000
χ182222222-2-2222-2222222-2-2-2-222222222-2-2-2-200002200-2-2-2-22222-2-2-2-2-2-2-2-2-2-222-2-2-2-200000000000022222-2-20000000000000000000000
χ19222222-122-1-1-122-1-1222-1-1-1-1-1-1-1-1-1-1-1-1222222-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-12-1-1-1-1-1-122-1-1-1-10000000000000000
χ20222222-122-1-1-122-1-1222-1-1-1-1-1-1-1-1-1-1-1-12222-2-21122112222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-2111111112-1-1-1-1-1-1-2-211110000000000000000
χ21222222-122-1-1-122-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211112222-1-1-1-1-1-1-1-1-2111111-2-211110000000000000000
χ22222222-122-1-1-122-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-21122112222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-21111-2-2-2-211111111-211111122-1-1-1-10000000000000000
χ23222222-1-2-2-1-1-1-22-1-12221111-1-1-1-1-1-1-1-1222200−i3i322−i3i3-2-2-2-2-1-1-1-11111111122-2-2-1-1-1-10000−i3−i3i3i3−i3−i3i3i3-21111-1-100−i3i3−i3i30000000000000000
χ24222222-1-2-2-1-1-1-22-1-12221111-1-1-1-1-1-1-1-1222200i3−i322i3−i3-2-2-2-2-1-1-1-11111111122-2-2-1-1-1-10000i3i3−i3−i3i3i3−i3−i3-21111-1-100i3−i3i3−i30000000000000000
χ25222222-1-2-2-1-1-1-22-1-12221111-1-1-1-1-1-1-1-1-2-2-2-200−i3i322−i3i3-2-2-2-2-1-1-1-111111111-2-22211110000−i3−i3i3i3−i3−i3i3i32-1-1-1-11100i3−i3i3−i30000000000000000
χ26222222-1-2-2-1-1-1-22-1-12221111-1-1-1-1-1-1-1-1-2-2-2-200i3−i322i3−i3-2-2-2-2-1-1-1-111111111-2-22211110000i3i3−i3−i3i3i3−i3−i32-1-1-1-11100−i3i3−i3i30000000000000000
χ272222-2-22-2-222222-2-2222-2-2222222222222220000-2-200-2-222-2-2-2-2-2-2-2-22222-2-2-2-222220000000000002-2-222-2-20000000000000000000000
χ282222-2-22-2-222222-2-2222-2-22222222222-2-2-2-20000-2-200-2-222-2-2-2-2-2-2-2-222222222-2-2-2-2000000000000-222-2-2220000000000000000000000
χ292222-2-2-122-1-1-1-2211222-1-111-1-1-1-1-1-1-1-122222-2-1-1-2-21122-2-21111-1-1-1-11111-2-222-1-1-1-122-2-2-1-1-1-11111-2-1-11111-2211-1-10000000000000000
χ302222-2-2-122-1-1-1-2211222-1-111-1-1-1-1-1-1-1-12222-2211-2-2-1-122-2-21111-1-1-1-11111-2-222-1-1-1-1-2-2221111-1-1-1-1-2-1-111112-2-1-1110000000000000000
χ312222-2-2-122-1-1-1-2211222-1-111-1-1-1-1-1-1-1-1-2-2-2-22-2-1-1-2-21122-2-21111-1-1-1-1111122-2-2111122-2-2-1-1-1-11111211-1-1-1-12-2-1-1110000000000000000
χ322222-2-2-122-1-1-1-2211222-1-111-1-1-1-1-1-1-1-1-2-2-2-2-2211-2-2-1-122-2-21111-1-1-1-1111122-2-21111-2-2221111-1-1-1-1211-1-1-1-1-2211-1-10000000000000000
χ332222-2-2-1-2-2-1-1-1221122211-1-1-1-1-1-1-1-1-1-1222200−i3i3-2-2i3−i3-2-22211111111-1-1-1-1-2-2-2-2-1-1-1-10000−i3−i3i3i3i3i3−i3−i3211-1-11100i3−i3−i3i30000000000000000
χ342222-2-2-1-2-2-1-1-1221122211-1-1-1-1-1-1-1-1-1-1222200i3−i3-2-2−i3i3-2-22211111111-1-1-1-1-2-2-2-2-1-1-1-10000i3i3−i3−i3−i3−i3i3i3211-1-11100−i3i3i3−i30000000000000000
χ352222-2-2-1-2-2-1-1-1221122211-1-1-1-1-1-1-1-1-1-1-2-2-2-200−i3i3-2-2i3−i3-2-22211111111-1-1-1-1222211110000−i3−i3i3i3i3i3−i3−i3-2-1-111-1-100−i3i3i3−i30000000000000000
χ362222-2-2-1-2-2-1-1-1221122211-1-1-1-1-1-1-1-1-1-1-2-2-2-200i3−i3-2-2−i3i3-2-22211111111-1-1-1-1222211110000i3i3−i3−i3−i3−i3i3i3-2-1-111-1-100i3−i3−i3i30000000000000000
χ3722-2-20022-22-2-20200-22-22-20022-2-222-2-22i−2i2i−2i000000002-200000022-2-20000002i−2i2i2i−2i−2i00000000000002i−2i0000000000002ζ7+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+2ζ10900000000
χ3822-2-20022-22-2-20200-22-22-20022-2-222-2-22i−2i2i−2i000000002-200000022-2-20000002i−2i2i2i−2i−2i00000000000002i−2i000000000000−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119002ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ10900000000
χ3922-2-20022-22-2-20200-22-22-20022-2-222-2-2−2i2i−2i2i000000002-200000022-2-2000000−2i2i−2i−2i2i2i0000000000000−2i2i000000000000−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109002ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ11900000000
χ4022-2-20022-22-2-20200-22-22-20022-2-222-2-2−2i2i−2i2i000000002-200000022-2-2000000−2i2i−2i−2i2i2i0000000000000−2i2i0000000000002ζ13+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+2ζ11900000000
χ4122-2-2002-222-2-20200-22-2-220022-2-222-2-22i−2i2i−2i00000000-22000000-2-222000000−2i2i2i2i−2i−2i0000000000000−2i2i00000000002ζ7+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+2ζ1090000000000
χ4222-2-2002-222-2-20200-22-2-220022-2-222-2-22i−2i2i−2i00000000-22000000-2-222000000−2i2i2i2i−2i−2i0000000000000−2i2i0000000000−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119002ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1090000000000
χ4322-2-2002-222-2-20200-22-2-220022-2-222-2-2−2i2i−2i2i00000000-22000000-2-2220000002i−2i−2i−2i2i2i00000000000002i−2i0000000000−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109002ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1190000000000
χ4422-2-2002-222-2-20200-22-2-220022-2-222-2-2−2i2i−2i2i00000000-22000000-2-2220000002i−2i−2i−2i2i2i00000000000002i−2i00000000002ζ13+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+2ζ1190000000000
χ452-22-22-2200-22-2022-2-2-22000022-2-2-2-2222i−2i−2i2i00002-200000022-2-2000000002i−2i002i−2i2i−2i000000000000000002i−2i000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i
χ462-22-22-2200-22-2022-2-2-22000022-2-2-2-2222i−2i−2i2i00002-200000022-2-2000000002i−2i002i−2i2i−2i000000000000000002i−2i00000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i
χ472-22-22-2200-22-2022-2-2-22000022-2-2-2-222−2i2i2i−2i00002-200000022-2-200000000−2i2i00−2i2i−2i2i00000000000000000−2i2i000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i
χ482-22-22-2200-22-2022-2-2-22000022-2-2-2-222−2i2i2i−2i00002-200000022-2-200000000−2i2i00−2i2i−2i2i00000000000000000−2i2i00000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i
χ492-22-2-22200-22-202-22-2-22000022-2-2-2-2222i−2i−2i2i0000-22000000-2-22200000000−2i2i002i−2i2i−2i00000000000000000−2i2i000000000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i
χ502-22-2-22200-22-202-22-2-22000022-2-2-2-2222i−2i−2i2i0000-22000000-2-22200000000−2i2i002i−2i2i−2i00000000000000000−2i2i00000000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i
χ512-22-2-22200-22-202-22-2-22000022-2-2-2-222−2i2i2i−2i0000-22000000-2-222000000002i−2i00−2i2i−2i2i000000000000000002i−2i000000000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i
χ522-22-2-22200-22-202-22-2-22000022-2-2-2-222−2i2i2i−2i0000-22000000-2-222000000002i−2i00−2i2i−2i2i000000000000000002i−2i00000000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i
χ534444444444444-144-1-1-14444-1-1-1-1-1-1-1-100004444-1-144-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000000000
χ544444444444444-144-1-1-14444-1-1-1-1-1-1-1-10000-4-4-4-4-1-1-4-4-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000011111111111100000000000000000000000000000
χ554444444-4-4444-4-144-1-1-1-4-4-4-4-1-1-1-1-1-1-1-100000000-1-1001111-1-1-1-11111111100000000−55−55−55−55−55−5500000000000000000000000000000
χ564444444-4-4444-4-144-1-1-1-4-4-4-4-1-1-1-1-1-1-1-100000000-1-1001111-1-1-1-111111111000000005−55−55−55−55−55−500000000000000000000000000000
χ57444444-244-2-2-24-1-2-2-1-1-1-2-2-2-21−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i152000044-2-2-1-1-2-2-1-1-1-11−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521−i1521+i1521+i15200000000-1-1-1-11−i1521+i1521+i1521−i1521−i1521+i1521+i1521−i15200000000000000000000000000000
χ58444444-244-2-2-24-1-2-2-1-1-1-2-2-2-21−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1520000-4-422-1-122-1-1-1-11−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521−i1521+i1521+i152000000001111−1+i152−1−i152−1−i152−1+i152−1+i152−1−i152−1−i152−1+i15200000000000000000000000000000
χ59444444-244-2-2-24-1-2-2-1-1-1-2-2-2-21+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i152000044-2-2-1-1-2-2-1-1-1-11+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521+i1521−i1521−i15200000000-1-1-1-11+i1521−i1521−i1521+i1521+i1521−i1521−i1521+i15200000000000000000000000000000
χ60444444-244-2-2-24-1-2-2-1-1-1-2-2-2-21+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1520000-4-422-1-122-1-1-1-11+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521+i1521−i1521−i152000000001111−1−i152−1+i152−1+i152−1−i152−1−i152−1+i152−1+i152−1−i15200000000000000000000000000000
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χ1018-88-8-88-4004-440-24-422-200001−i151+i15−1+i15−1−i15−1+i15−1−i151−i151+i15000000002-2000000−1+i15−1−i151−i151+i15000000000000000000000000000000000000000000000000000000000
χ1028-88-8-88-4004-440-24-422-200001+i151−i15−1−i15−1+i15−1−i15−1+i151+i151−i15000000002-2000000−1−i15−1+i151+i151−i15000000000000000000000000000000000000000000000000000000000
χ1038-8-8800800-8-880-200-2220000-2-2-2-2222200000000000000−2i52i500000000−2i52i52i5−2i50000000000000000000000000000000000000000000000000
χ1048-8-8800800-8-880-200-2220000-2-2-2-22222000000000000002i5−2i5000000002i5−2i5−2i52i50000000000000000000000000000000000000000000000000
χ1058-8-8800-40044-40-200-2220043−431−i151+i151−i151+i15−1+i15−1−i15−1+i15−1−i15000000000000002i5−2i5000000002ζ14−2ζ22+2ζ86−2ζ118−2ζ14+2ζ22−2ζ86+2ζ1182ζ38−2ζ46+2ζ62−2ζ94−2ζ38+2ζ46−2ζ62+2ζ940000000000000000000000000000000000000000000000000
χ1068-8-8800-40044-40-200-2220043−431+i151−i151+i151−i15−1−i15−1+i15−1−i15−1+i1500000000000000−2i52i5000000002ζ38−2ζ46+2ζ62−2ζ94−2ζ38+2ζ46−2ζ62+2ζ942ζ14−2ζ22+2ζ86−2ζ118−2ζ14+2ζ22−2ζ86+2ζ1180000000000000000000000000000000000000000000000000
χ1078-8-8800-40044-40-200-22200−43431−i151+i151−i151+i15−1+i15−1−i15−1+i15−1−i1500000000000000−2i52i500000000−2ζ14+2ζ22−2ζ86+2ζ1182ζ14−2ζ22+2ζ86−2ζ118−2ζ38+2ζ46−2ζ62+2ζ942ζ38−2ζ46+2ζ62−2ζ940000000000000000000000000000000000000000000000000
χ1088-8-8800-40044-40-200-22200−43431+i151−i151+i151−i15−1−i15−1+i15−1−i15−1+i15000000000000002i5−2i500000000−2ζ38+2ζ46−2ζ62+2ζ942ζ38−2ζ46+2ζ62−2ζ94−2ζ14+2ζ22−2ζ86+2ζ1182ζ14−2ζ22+2ζ86−2ζ1180000000000000000000000000000000000000000000000000

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