Finite Group Databasebeta

← Group #13146921

Character table — Group #13146921

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89
size11112222222222333333336666666666121212121212121212121212121212242424242424242424242424242424242424242424242424363636363636363636363636727272727272
order122234466612121212336666664412121212121212122666666661212121212129991818181818181818183636363636363636363636368888242424242424242424661212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i3211−1−i32−1+i32−1−i32−1+i32
χ411111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32-1-11+i321−i321+i321−i32
χ511111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i3211−1+i32−1−i32−1+i32−1−i32
χ611111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32-1-11−i321+i321−i321+i32
χ711111-1-1111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-11-111-1-1
χ811111-1-1111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-11-1-111
χ911111-1-1111-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32111+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32-1-1-11+i321+i321+i321−i321−i321−i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i3211-1-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321-1−1−i32−1+i321+i321−i32
χ1011111-1-1111-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32111+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32-1-1-11+i321+i321+i321−i321−i321−i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32-1-1111+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32-111+i321−i32−1−i32−1+i32
χ1111111-1-1111-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32111−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32-1-1-11−i321−i321−i321+i321+i321+i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i3211-1-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321-1−1+i32−1−i321−i321+i32
χ1211111-1-1111-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32111−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32-1-1-11−i321−i321−i321+i321+i321+i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32-1-1111−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32-111−i321+i32−1+i32−1−i32
χ1322222222222222222222222222222222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000
χ1422222222222222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i322−1−i3−1−i3−1+i3−1+i3−1−i3−1−i3−1+i3−1+i3222−1−i3−1−i3−1−i3−1+i3−1+i3−1+i322−1−i3−1−i3−1+i3−1+i3-11+i321−i32-1-11+i321+i321−i321−i32-11+i321−i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32000000000000000000
χ1522222222222222−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i322−1+i3−1+i3−1−i3−1−i3−1+i3−1+i3−1−i3−1−i3222−1+i3−1+i3−1+i3−1−i3−1−i3−1−i322−1+i3−1+i3−1−i3−1−i3-11−i321+i32-1-11−i321−i321+i321+i32-11−i321+i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32000000000000000000
χ1622222-2-2222-2-2-2-22222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2222222-1-1-1-1-1-1-1-1-1-1-1-1111111111111000000000000000000
χ1722222-2-2222-2-2-2-2−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3221+i31+i31−i31−i3−1−i3−1−i3−1+i3−1+i3-2-2-21+i31+i31+i31−i31−i31−i322−1−i3−1−i3−1+i3−1+i3-11+i321−i32-1-11+i321+i321−i321−i32-11+i321−i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32000000000000000000
χ1822222-2-2222-2-2-2-2−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3221−i31−i31+i31+i3−1+i3−1+i3−1−i3−1−i3-2-2-21−i31−i31−i31+i31+i31+i322−1+i3−1+i3−1−i3−1−i3-11−i321+i32-1-11−i321−i321+i321+i32-11−i321+i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32000000000000000000
χ1922-2-222i−2i2-2-22i2i−2i−2i2222-2-2-2-2002i−2i2i−2i0000000000000000000-1-1-11-11-11-1111ii−i−iii−i−iii−i−i−i2i22−2−i2i22−2−i2i22−2000000
χ2022-2-222i−2i2-2-22i2i−2i−2i2222-2-2-2-2002i−2i2i−2i0000000000000000000-1-1-11-11-11-1111ii−i−iii−i−iii−i−ii2−i2−22i2−i2−22i2−i2−22000000
χ2122-2-222i−2i2-2-22i2i−2i−2i−1−i3−1+i3−1−i3−1+i31+i31−i31+i31−i3002ζ22−2ζ222ζ14−2ζ140000000000000000000-11+i321−i321-1−1−i321+i32−1+i321−i321−1−i32−1+i32ii−i−iζ22ζ22−ζ22−ζ22ζ14ζ14−ζ14−ζ14−i2i22−2ζ7+ζ13−ζ7−ζ13−ζ7+ζ13ζ7−ζ13ζ5+ζ23−ζ5−ζ23ζ5−ζ23−ζ5+ζ23000000
χ2222-2-222i−2i2-2-22i2i−2i−2i−1−i3−1+i3−1−i3−1+i31+i31−i31+i31−i3002ζ22−2ζ222ζ14−2ζ140000000000000000000-11+i321−i321-1−1−i321+i32−1+i321−i321−1−i32−1+i32ii−i−iζ22ζ22−ζ22−ζ22ζ14ζ14−ζ14−ζ14i2−i2−22−ζ7−ζ13ζ7+ζ13ζ7−ζ13−ζ7+ζ13−ζ5−ζ23ζ5+ζ23−ζ5+ζ23ζ5−ζ23000000
χ2322-2-222i−2i2-2-22i2i−2i−2i−1+i3−1−i3−1+i3−1−i31−i31+i31−i31+i3002ζ14−2ζ142ζ22−2ζ220000000000000000000-11−i321+i321-1−1+i321−i32−1−i321+i321−1+i32−1−i32ii−i−iζ14ζ14−ζ14−ζ14ζ22ζ22−ζ22−ζ22−i2i22−2ζ5+ζ23−ζ5−ζ23ζ5−ζ23−ζ5+ζ23ζ7+ζ13−ζ7−ζ13−ζ7+ζ13ζ7−ζ13000000
χ2422-2-222i−2i2-2-22i2i−2i−2i−1+i3−1−i3−1+i3−1−i31−i31+i31−i31+i3002ζ14−2ζ142ζ22−2ζ220000000000000000000-11−i321+i321-1−1+i321−i32−1−i321+i321−1+i32−1−i32ii−i−iζ14ζ14−ζ14−ζ14ζ22ζ22−ζ22−ζ22i2−i2−22−ζ5−ζ23ζ5+ζ23−ζ5+ζ23ζ5−ζ23−ζ7−ζ13ζ7+ζ13ζ7−ζ13−ζ7+ζ13000000
χ2522-2-22−2i2i2-2-2−2i−2i2i2i2222-2-2-2-200−2i2i−2i2i0000000000000000000-1-1-11-11-11-1111−i−iii−i−iii−i−iii−i2i2−22−i2i2−22−i2i2−22000000
χ2622-2-22−2i2i2-2-2−2i−2i2i2i2222-2-2-2-200−2i2i−2i2i0000000000000000000-1-1-11-11-11-1111−i−iii−i−iii−i−iiii2−i22−2i2−i22−2i2−i22−2000000
χ2722-2-22−2i2i2-2-2−2i−2i2i2i−1−i3−1+i3−1−i3−1+i31+i31−i31+i31−i300−2ζ222ζ22−2ζ142ζ140000000000000000000-11+i321−i321-1−1−i321+i32−1+i321−i321−1−i32−1+i32−i−iii−ζ22−ζ22ζ22ζ22−ζ14−ζ14ζ14ζ14−i2i2−22ζ7+ζ13−ζ7−ζ13ζ7−ζ13−ζ7+ζ13ζ5+ζ23−ζ5−ζ23−ζ5+ζ23ζ5−ζ23000000
χ2822-2-22−2i2i2-2-2−2i−2i2i2i−1−i3−1+i3−1−i3−1+i31+i31−i31+i31−i300−2ζ222ζ22−2ζ142ζ140000000000000000000-11+i321−i321-1−1−i321+i32−1+i321−i321−1−i32−1+i32−i−iii−ζ22−ζ22ζ22ζ22−ζ14−ζ14ζ14ζ14i2−i22−2−ζ7−ζ13ζ7+ζ13−ζ7+ζ13ζ7−ζ13−ζ5−ζ23ζ5+ζ23ζ5−ζ23−ζ5+ζ23000000
χ2922-2-22−2i2i2-2-2−2i−2i2i2i−1+i3−1−i3−1+i3−1−i31−i31+i31−i31+i300−2ζ142ζ14−2ζ222ζ220000000000000000000-11−i321+i321-1−1+i321−i32−1−i321+i321−1+i32−1−i32−i−iii−ζ14−ζ14ζ14ζ14−ζ22−ζ22ζ22ζ22−i2i2−22ζ5+ζ23−ζ5−ζ23−ζ5+ζ23ζ5−ζ23ζ7+ζ13−ζ7−ζ13ζ7−ζ13−ζ7+ζ13000000
χ3022-2-22−2i2i2-2-2−2i−2i2i2i−1+i3−1−i3−1+i3−1−i31−i31+i31−i31+i300−2ζ142ζ14−2ζ222ζ220000000000000000000-11−i321+i321-1−1+i321−i32−1−i321+i321−1+i32−1−i32−i−iii−ζ14−ζ14ζ14ζ14−ζ22−ζ22ζ22ζ22i2−i22−2−ζ5−ζ23ζ5+ζ23ζ5−ζ23−ζ5+ζ23−ζ7−ζ13ζ7+ζ13−ζ7+ζ13ζ7−ζ13000000
χ312-22-2200-2-22000022-2-222-2-22-200002-22-20000000002-22-22-2222-2-2-2-2-2-2222000000000000000000000000000000
χ322-22-2200-2-22000022-2-222-2-22-200002-22-20000000002-22-22-2-1-1-1111111-1-1-1−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3000000000000000000
χ332-22-2200-2-22000022-2-222-2-22-200002-22-20000000002-22-22-2-1-1-1111111-1-1-1i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3000000000000000000
χ342-22-2200-2-220000−1−i3−1+i31+i31−i3−1−i3−1+i31+i31−i32-20000−1−i31+i3−1+i31−i30000000002-2−1−i31+i3−1+i31−i32−1−i3−1+i3-2-21+i31+i31−i31−i32−1−i3−1+i3000000000000000000000000000000
χ352-22-2200-2-220000−1−i3−1+i31+i31−i3−1−i3−1+i31+i31−i32-20000−1−i31+i3−1+i31−i30000000002-2−1−i31+i3−1+i31−i3-11+i321−i3211−1−i32−1−i32−1+i32−1+i32-11+i321−i32−i3i3−i3i3−3+i323−i32−3+i323−i323+i32−3−i323+i32−3−i32000000000000000000
χ362-22-2200-2-220000−1−i3−1+i31+i31−i3−1−i3−1+i31+i31−i32-20000−1−i31+i3−1+i31−i30000000002-2−1−i31+i3−1+i31−i3-11+i321−i3211−1−i32−1−i32−1+i32−1+i32-11+i321−i32i3−i3i3−i33−i32−3+i323−i32−3+i32−3−i323+i32−3−i323+i32000000000000000000
χ372-22-2200-2-220000−1+i3−1−i31−i31+i3−1+i3−1−i31−i31+i32-20000−1+i31−i3−1−i31+i30000000002-2−1+i31−i3−1−i31+i32−1+i3−1−i3-2-21−i31−i31+i31+i32−1+i3−1−i3000000000000000000000000000000
χ382-22-2200-2-220000−1+i3−1−i31−i31+i3−1+i3−1−i31−i31+i32-20000−1+i31−i3−1−i31+i30000000002-2−1+i31−i3−1−i31+i3-11−i321+i3211−1+i32−1+i32−1−i32−1−i32-11−i321+i32−i3i3−i3i33+i32−3−i323+i32−3−i32−3+i323−i32−3+i323−i32000000000000000000
χ392-22-2200-2-220000−1+i3−1−i31−i31+i3−1+i3−1−i31−i31+i32-20000−1+i31−i3−1−i31+i30000000002-2−1+i31−i3−1−i31+i3-11−i321+i3211−1+i32−1+i32−1−i32−1−i32-11−i321+i32i3−i3i3−i3−3−i323+i32−3−i323+i323−i32−3+i323−i32−3+i32000000000000000000
χ403333333333333333333333-1-13333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000111111111111-1-1-1-1-1-1
χ413333333333333333333333-1-13333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000-1-1-1-1-1-1-1-1-1-1-1-1111111
χ4233333333333333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-1-1−3−3i32−3−3i32−3+3i32−3+3i321+i321+i321−i321−i32-1-1-11+i321+i321+i321−i321−i321−i32-1-11+i321+i321−i321−i320000000000000000000000001111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-1-11+i321−i321+i321−i32
χ4333333333333333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-1-1−3−3i32−3−3i32−3+3i32−3+3i321+i321+i321−i321−i32-1-1-11+i321+i321+i321−i321−i321−i32-1-11+i321+i321−i321−i32000000000000000000000000-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i3211−1−i32−1+i32−1−i32−1+i32
χ4433333333333333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32-1-1−3+3i32−3+3i32−3−3i32−3−3i321−i321−i321+i321+i32-1-1-11−i321−i321−i321+i321+i321+i32-1-11−i321−i321+i321+i320000000000000000000000001111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-1-11−i321+i321−i321+i32
χ4533333333333333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32-1-1−3+3i32−3+3i32−3−3i32−3−3i321−i321−i321+i321+i32-1-1-11−i321−i321−i321+i321+i321+i32-1-11−i321−i321+i321+i32000000000000000000000000-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i3211−1+i32−1−i32−1+i32−1−i32
χ4633333-3-3333-3-3-3-333333333-1-1-3-3-3-3-1-1-1-1111111111-1-1-1-1-1-100000000000000000000000011-1-111-1-111-1-1-11-1-111
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.