Finite Group Databasebeta

← Group #13146901

Character table — Group #13146901

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89
size11112222222222333333336666666666121212121212121212121212121212242424242424242424242424242424242424242424242424363636363636363636363636727272727272
order122222366666663366666644666612121212412121212121212121212121212129991818181818181818181818181818181818181818188888242424242424242424661212
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+i3211111−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i321−1−i32−1+i321111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−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+i3211111−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i321−1−i32−1+i321111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−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−i3211111−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i321−1+i32−1−i321111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+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−i3211111−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i321−1+i32−1−i321111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+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
χ71111-1-1111-1-1-1-111111111111-1-1-1-11111-111-1-111-1-1-111-1-1-1111111-1-1-1-1111-1-1-1-1111-1-1-1-111-1-111-1-111-1-11-111-1-1
χ81111-1-1111-1-1-1-111111111111-1-1-1-11111-111-1-111-1-1-111-1-1-1111111-1-1-1-1111-1-1-1-1111-1-1-1-1-1-111-1-111-1-111-11-1-111
χ91111-1-1111-1-1-1-11−1−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+i32-111-1-1−1−i32−1−i321+i321+i321+i32−1+i32−1+i321−i321−i321−i321−1−i32−1+i32111-1-1-1-1−1−i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i32−1+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
χ101111-1-1111-1-1-1-11−1−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+i32-111-1-1−1−i32−1−i321+i321+i321+i32−1+i32−1+i321−i321−i321−i321−1−i32−1+i32111-1-1-1-1−1−i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i32−1+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
χ111111-1-1111-1-1-1-11−1+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−i32-111-1-1−1+i32−1+i321−i321−i321−i32−1−i32−1−i321+i321+i321+i321−1+i32−1−i32111-1-1-1-1−1+i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i32−1−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
χ121111-1-1111-1-1-1-11−1+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−i32-111-1-1−1+i32−1+i321−i321−i321−i32−1−i32−1−i321+i321+i321+i321−1+i32−1−i32111-1-1-1-1−1+i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i32−1−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+i322222−1−i3−1−i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3−1+i3−1+i3-11+i321−i32-1-1-1-1-1-1-11+i321+i321+i321+i321+i321+i321+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−i322222−1+i3−1+i3−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3−1−i3−1−i3-11−i321+i32-1-1-1-1-1-1-11−i321−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i321+i32000000000000000000
χ162222-2-2222-2-2-2-222222222222-2-2-2-22222-222-2-222-2-2-222-2-2-2-1-1-1-1-1-11111-1-1-11111-1-1-11111000000000000000000
χ172222-2-2222-2-2-2-22−1−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+i3-222-2-2−1−i3−1−i31+i31+i31+i3−1+i3−1+i31−i31−i31−i3-11+i321−i32-1-1-111111+i321+i321+i32−1−i32−1−i32−1−i32−1−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32000000000000000000
χ182222-2-2222-2-2-2-22−1+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−i3-222-2-2−1+i3−1+i31−i31−i31−i3−1−i3−1−i31+i31+i31+i3-11−i321+i32-1-1-111111−i321−i321−i32−1+i32−1+i32−1+i32−1+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32000000000000000000
χ192-22-2002-2-20000222-2-22-22-22-200002-22-202-2002-20002-20002222-2-200002-2-200002-2-20000000000000000000000
χ202-22-2002-2-20000222-2-22-22-22-200002-22-202-2002-20002-2000-1-1-1-111−i3−i3i3i3-111−i3−i3i3i3-111−i3−i3i3i3000000000000000000
χ212-22-2002-2-20000222-2-22-22-22-200002-22-202-2002-20002-2000-1-1-1-111i3i3−i3−i3-111i3i3−i3−i3-111i3i3−i3−i3000000000000000000
χ222-22-2002-2-200002−1−i3−1+i31+i31−i3−1−i31+i3−1+i31−i32-20000−1−i31+i3−1+i31−i302-200−1−i31+i3000−1+i31−i30002−1−i3−1+i32-2-20000−1−i31+i31+i30000−1+i31−i31−i30000000000000000000000
χ232-22-2002-2-200002−1−i3−1+i31+i31−i3−1−i31+i3−1+i31−i32-20000−1−i31+i3−1+i31−i302-200−1−i31+i3000−1+i31−i3000-11+i321−i32-111−i3−i3i3i31+i32−1−i32−1−i32−3+i32−3+i323−i323−i321−i32−1+i32−1+i323+i323+i32−3−i32−3−i32000000000000000000
χ242-22-2002-2-200002−1−i3−1+i31+i31−i3−1−i31+i3−1+i31−i32-20000−1−i31+i3−1+i31−i302-200−1−i31+i3000−1+i31−i3000-11+i321−i32-111i3i3−i3−i31+i32−1−i32−1−i323−i323−i32−3+i32−3+i321−i32−1+i32−1+i32−3−i32−3−i323+i323+i32000000000000000000
χ252-22-2002-2-200002−1+i3−1−i31−i31+i3−1+i31−i3−1−i31+i32-20000−1+i31−i3−1−i31+i302-200−1+i31−i3000−1−i31+i30002−1+i3−1−i32-2-20000−1+i31−i31−i30000−1−i31+i31+i30000000000000000000000
χ262-22-2002-2-200002−1+i3−1−i31−i31+i3−1+i31−i3−1−i31+i32-20000−1+i31−i3−1−i31+i302-200−1+i31−i3000−1−i31+i3000-11−i321+i32-111−i3−i3i3i31−i32−1+i32−1+i323+i323+i32−3−i32−3−i321+i32−1−i32−1−i32−3+i32−3+i323−i323−i32000000000000000000
χ272-22-2002-2-200002−1+i3−1−i31−i31+i3−1+i31−i3−1−i31+i32-20000−1+i31−i3−1−i31+i302-200−1+i31−i3000−1−i31+i3000-11−i321+i32-111i3i3−i3−i31−i32−1+i32−1+i32−3−i32−3−i323+i323+i321+i32−1−i32−1−i323−i323−i32−3+i32−3+i32000000000000000000
χ282-2-222-222-222-2-2-222-2-2-22-22002-22-20000000000000000000-1-1-111-11-11-111-11-11-111-11-11-1−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000
χ292-2-222-222-222-2-2-222-2-2-22-22002-22-20000000000000000000-1-1-111-11-11-111-11-11-111-11-11-1i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000
χ302-2-222-222-222-2-2-2−1−i3−1+i31+i31−i31+i3−1−i31−i3−1+i300−1−i31+i3−1+i31−i30000000000000000000-11+i321−i3211-11-11-1−1−i32−1−i321+i32−1−i321+i32−1−i321+i32−1+i32−1+i321−i32−1+i321−i32−1+i321−i32−i2i2−i2i2ζ7+ζ13−ζ7−ζ13ζ7+ζ13−ζ7−ζ13ζ5+ζ23−ζ5−ζ23ζ5+ζ23−ζ5−ζ23000000
χ312-2-222-222-222-2-2-2−1−i3−1+i31+i31−i31+i3−1−i31−i3−1+i300−1−i31+i3−1+i31−i30000000000000000000-11+i321−i3211-11-11-1−1−i32−1−i321+i32−1−i321+i32−1−i321+i32−1+i32−1+i321−i32−1+i321−i32−1+i321−i32i2−i2i2−i2−ζ7−ζ13ζ7+ζ13−ζ7−ζ13ζ7+ζ13−ζ5−ζ23ζ5+ζ23−ζ5−ζ23ζ5+ζ23000000
χ322-2-222-222-222-2-2-2−1+i3−1−i31−i31+i31−i3−1+i31+i3−1−i300−1+i31−i3−1−i31+i30000000000000000000-11−i321+i3211-11-11-1−1+i32−1+i321−i32−1+i321−i32−1+i321−i32−1−i32−1−i321+i32−1−i321+i32−1−i321+i32−i2i2−i2i2ζ5+ζ23−ζ5−ζ23ζ5+ζ23−ζ5−ζ23ζ7+ζ13−ζ7−ζ13ζ7+ζ13−ζ7−ζ13000000
χ332-2-222-222-222-2-2-2−1+i3−1−i31−i31+i31−i3−1+i31+i3−1−i300−1+i31−i3−1−i31+i30000000000000000000-11−i321+i3211-11-11-1−1+i32−1+i321−i32−1+i321−i32−1+i321−i32−1−i32−1−i321+i32−1−i321+i32−1−i321+i32i2−i2i2−i2−ζ5−ζ23ζ5+ζ23−ζ5−ζ23ζ5+ζ23−ζ7−ζ13ζ7+ζ13−ζ7−ζ13ζ7+ζ13000000
χ342-2-22-2222-2-2-222-222-2-2-22-2200-22-220000000000000000000-1-1-111-1-11-1111-1-11-1111-1-11-11−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2000000
χ352-2-22-2222-2-2-222-222-2-2-22-2200-22-220000000000000000000-1-1-111-1-11-1111-1-11-1111-1-11-11i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2000000
χ362-2-22-2222-2-2-222-2−1−i3−1+i31+i31−i31+i3−1−i31−i3−1+i3001+i3−1−i31−i3−1+i30000000000000000000-11+i321−i3211-1-11-11−1−i32−1−i321+i321+i32−1−i321+i32−1−i32−1+i32−1+i321−i321−i32−1+i321−i32−1+i32−i2i2i2−i2ζ7+ζ13−ζ7−ζ13−ζ7−ζ13ζ7+ζ13ζ5+ζ23−ζ5−ζ23−ζ5−ζ23ζ5+ζ23000000
χ372-2-22-2222-2-2-222-2−1−i3−1+i31+i31−i31+i3−1−i31−i3−1+i3001+i3−1−i31−i3−1+i30000000000000000000-11+i321−i3211-1-11-11−1−i32−1−i321+i321+i32−1−i321+i32−1−i32−1+i32−1+i321−i321−i32−1+i321−i32−1+i32i2−i2−i2i2−ζ7−ζ13ζ7+ζ13ζ7+ζ13−ζ7−ζ13−ζ5−ζ23ζ5+ζ23ζ5+ζ23−ζ5−ζ23000000
χ382-2-22-2222-2-2-222-2−1+i3−1−i31−i31+i31−i3−1+i31+i3−1−i3001−i3−1+i31+i3−1−i30000000000000000000-11−i321+i3211-1-11-11−1+i32−1+i321−i321−i32−1+i321−i32−1+i32−1−i32−1−i321+i321+i32−1−i321+i32−1−i32−i2i2i2−i2ζ5+ζ23−ζ5−ζ23−ζ5−ζ23ζ5+ζ23ζ7+ζ13−ζ7−ζ13−ζ7−ζ13ζ7+ζ13000000
χ392-2-22-2222-2-2-222-2−1+i3−1−i31−i31+i31−i3−1+i31+i3−1−i3001−i3−1+i31+i3−1−i30000000000000000000-11−i321+i3211-1-11-11−1+i32−1+i321−i321−i32−1+i321−i32−1+i32−1−i32−1−i321+i321+i32−1−i321+i32−1−i32i2−i2−i2i2−ζ5−ζ23ζ5+ζ23ζ5+ζ23−ζ5−ζ23−ζ7−ζ13ζ7+ζ13ζ7+ζ13−ζ7−ζ13000000
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−i32-1-1-1-1-11+i321+i321+i321+i321+i321−i321−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−i32-1-1-1-1-11+i321+i321+i321+i321+i321−i321−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+i32-1-1-1-1-11−i321−i321−i321−i321−i321+i321+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+i32-1-1-1-1-11−i321−i321−i321−i321−i321+i321+i321+i321+i321+i32000000000000000000000000-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i3211−1+i32−1−i32−1+i32−1−i32
χ463333-3-3333-3-3-3-3333333333-1-1-3-3-3-3-1-1-1-11-1-111-1-1111-1-111100000000000000000000000011-1-111-1-111-1-1-11-1-111
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.