Finite Group Databasebeta

← Group #13143502

Character table — Group #13143502

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1122222333344444666666666666888888881212121212121212121212121224242424242424242424242424242424242424242424363636363636363636363636363636363636727272
order122344633662461212333666661212121246812121224246666612121212121212126661212121212121212121212242424242424242422244466666612121212121282424
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-11-11-1-1-1-11111111111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1
χ41111111111111111111111111111-11-11-1-1-1-11111111111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111
χ511111111111-1-11111111111111111-1-1-111-1-1-1-1111-1-1111111-1-1-111-1-1-1111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1
χ611111111111-1-11111111111111111-1-1-111-1-1-1-1111-1-1111111-1-1-111-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111
χ711111111111-1-1111111111111111-1-11-1-1-111-1-1111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1111
χ811111111111-1-1111111111111111-1-11-1-1-111-1-1111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-111111111-1-1-1
χ91111111−1−i32−1+i32−1−i32−1+i32111111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211111111−1−i32−1+i321−1−i32−1+i32−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32111111−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32
χ101111111−1−i32−1+i32−1−i32−1+i32111111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211111111−1−i32−1+i321−1−i32−1+i32−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32-1-1-1-1-1-11+i321+i321−i321−i321+i321−i321+i321−i321+i321+i321−i321−i32-11+i321−i32
χ111111111−1−i32−1+i32−1−i32−1+i32111111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-11-11-1-1-1-1−1−i32−1+i321−1−i32−1+i32−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321+i321−i321−1−i32−1+i32-1-11+i321+i321−i321−i321+i321−i32-1-11+i321+i321−i321−i321111-1-1−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32-11+i321−i32
χ121111111−1−i32−1+i32−1−i32−1+i32111111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-11-11-1-1-1-1−1−i32−1+i321−1−i32−1+i32−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321+i321−i321−1−i32−1+i32-1-11+i321+i321−i321−i321+i321−i32-1-11+i321+i321−i321−i32-1-1-1-1111+i321+i321−i321−i321+i321−i321+i321−i32−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32
χ131111111−1−i32−1+i32−1−i32−1+i32-1-11111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321-1-1-111-1-11+i321−i321−1−i32−1+i321+i321−i321−1−i32−1+i321−1−i32−1+i32-11+i321−i32−1−i32−1+i32-11+i321−i3211−1−i32−1−i32−1+i32−1+i321+i321−i32-1-11+i321+i321−i321−i3211-1-111−1−i32−1−i32−1+i32−1+i321+i321−i321+i321−i32−1−i32−1−i32−1+i32−1+i32-11+i321−i32
χ141111111−1−i32−1+i32−1−i32−1+i32-1-11111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321-1-1-111-1-11+i321−i321−1−i32−1+i321+i321−i321−1−i32−1+i321−1−i32−1+i32-11+i321−i32−1−i32−1+i32-11+i321−i3211−1−i32−1−i32−1+i32−1+i321+i321−i32-1-11+i321+i321−i321−i32-1-111-1-11+i321+i321−i321−i32−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i321−1−i32−1+i32
χ151111111−1−i32−1+i32−1−i32−1+i32-1-11111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-11-1-1-1111+i321−i321−1−i32−1+i321+i321−i321−1−i32−1+i321−1−i32−1+i32-11+i321−i321+i321−i32-11+i321−i32-1-11+i321+i321−i321−i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i3211-1-1-1-1−1−i32−1−i32−1+i32−1+i321+i321−i321+i321−i321+i321+i321−i321−i321−1−i32−1+i32
χ161111111−1−i32−1+i32−1−i32−1+i32-1-11111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-11-1-1-1111+i321−i321−1−i32−1+i321+i321−i321−1−i32−1+i321−1−i32−1+i32-11+i321−i321+i321−i32-11+i321−i32-1-11+i321+i321−i321−i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32-1-111111+i321+i321−i321−i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-11+i321−i32
χ171111111−1+i32−1−i32−1+i32−1−i32111111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211111111−1+i32−1−i321−1+i32−1−i32−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32111111−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32
χ181111111−1+i32−1−i32−1+i32−1−i32111111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211111111−1+i32−1−i321−1+i32−1−i32−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32-1-1-1-1-1-11−i321−i321+i321+i321−i321+i321−i321+i321−i321−i321+i321+i32-11−i321+i32
χ191111111−1+i32−1−i32−1+i32−1−i32111111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-11-11-1-1-1-1−1+i32−1−i321−1+i32−1−i32−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−i321+i321−1+i32−1−i32-1-11−i321−i321+i321+i321−i321+i32-1-11−i321−i321+i321+i321111-1-1−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32-11−i321+i32
χ201111111−1+i32−1−i32−1+i32−1−i32111111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-11-11-1-1-1-1−1+i32−1−i321−1+i32−1−i32−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−i321+i321−1+i32−1−i32-1-11−i321−i321+i321+i321−i321+i32-1-11−i321−i321+i321+i32-1-1-1-1111−i321−i321+i321+i321−i321+i321−i321+i32−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32
χ211111111−1+i32−1−i32−1+i32−1−i32-1-11111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321-1-1-111-1-11−i321+i321−1+i32−1−i321−i321+i321−1+i32−1−i321−1+i32−1−i32-11−i321+i32−1+i32−1−i32-11−i321+i3211−1+i32−1+i32−1−i32−1−i321−i321+i32-1-11−i321−i321+i321+i3211-1-111−1+i32−1+i32−1−i32−1−i321−i321+i321−i321+i32−1+i32−1+i32−1−i32−1−i32-11−i321+i32
χ221111111−1+i32−1−i32−1+i32−1−i32-1-11111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321-1-1-111-1-11−i321+i321−1+i32−1−i321−i321+i321−1+i32−1−i321−1+i32−1−i32-11−i321+i32−1+i32−1−i32-11−i321+i3211−1+i32−1+i32−1−i32−1−i321−i321+i32-1-11−i321−i321+i321+i32-1-111-1-11−i321−i321+i321+i32−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i321−1+i32−1−i32
χ231111111−1+i32−1−i32−1+i32−1−i32-1-11111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-11-1-1-1111−i321+i321−1+i32−1−i321−i321+i321−1+i32−1−i321−1+i32−1−i32-11−i321+i321−i321+i32-11−i321+i32-1-11−i321−i321+i321+i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i3211-1-1-1-1−1+i32−1+i32−1−i32−1−i321−i321+i321−i321+i321−i321−i321+i321+i321−1+i32−1−i32
χ241111111−1+i32−1−i32−1+i32−1−i32-1-11111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-11-1-1-1111−i321+i321−1+i32−1−i321−i321+i321−1+i32−1−i321−1+i32−1−i32-11−i321+i321−i321+i32-11−i321+i32-1-11−i321−i321+i321+i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32-1-111111−i321−i321+i321+i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-11−i321+i32
χ252222222222222222-1-1-122-1-1-122222222222222-1-1-122-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1000000000000000000000
χ262222222222222222-1-1-122-1-1-12222-22-22-2-2-2-222-1-1-122-1-1-1-1-1-1-1-1-1-2-2-1-1-1111111-2-2111111000000000000000000000
χ2722222222222-2-2222-1-1-122-1-1-122222-2-2-222-2-2-2-2-1-1-1-2-2-1-1-1-1-1-111122111-1-1-1-1-1-1-2-2111111000000000000000000000
χ2822222222222-2-2222-1-1-122-1-1-12222-2-22-2-2-222-2-2-1-1-1-2-2-1-1-1-1-1-1111-2-211111111122-1-1-1-1-1-1000000000000000000000
χ292222222−1−i3−1+i3−1−i3−1+i322222-11+i321−i32−1−i3−1+i3-11+i321−i32−1−i3−1+i3−1−i3−1+i322222222−1−i3−1+i3-11+i321−i32−1−i3−1+i3-11+i321−i32-11+i321−i32-11+i321−i32−1−i3−1+i3-11+i321−i32-1-11+i321+i321−i321−i32−1−i3−1+i3-1-11+i321+i321−i321−i32000000000000000000000
χ302222222−1−i3−1+i3−1−i3−1+i322222-11+i321−i32−1−i3−1+i3-11+i321−i32−1−i3−1+i3−1−i3−1+i3-22-22-2-2-2-2−1−i3−1+i3-11+i321−i32−1−i3−1+i3-11+i321−i32-11+i321−i32-11+i321−i321+i31−i3-11+i321−i3211−1−i32−1−i32−1+i32−1+i321+i31−i311−1−i32−1−i32−1+i32−1+i32000000000000000000000
χ312222222−1−i3−1+i3−1−i3−1+i3-2-2222-11+i321−i32−1−i3−1+i3-11+i321−i32−1−i3−1+i3−1−i3−1+i32-2-2-222-2-21+i31−i3-11+i321−i321+i31−i3-11+i321−i32-11+i321−i321−1−i32−1+i32−1−i3−1+i31−1−i32−1+i32-1-11+i321+i321−i321−i321+i31−i311−1−i32−1−i32−1+i32−1+i32000000000000000000000
χ322222222−1−i3−1+i3−1−i3−1+i3-2-2222-11+i321−i32−1−i3−1+i3-11+i321−i32−1−i3−1+i3−1−i3−1+i3-2-22-2-2-2221+i31−i3-11+i321−i321+i31−i3-11+i321−i32-11+i321−i321−1−i32−1+i321+i31−i31−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i3−1+i3-1-11+i321+i321−i321−i32000000000000000000000
χ332222222−1+i3−1−i3−1+i3−1−i322222-11−i321+i32−1+i3−1−i3-11−i321+i32−1+i3−1−i3−1+i3−1−i322222222−1+i3−1−i3-11−i321+i32−1+i3−1−i3-11−i321+i32-11−i321+i32-11−i321+i32−1+i3−1−i3-11−i321+i32-1-11−i321−i321+i321+i32−1+i3−1−i3-1-11−i321−i321+i321+i32000000000000000000000
χ342222222−1+i3−1−i3−1+i3−1−i322222-11−i321+i32−1+i3−1−i3-11−i321+i32−1+i3−1−i3−1+i3−1−i3-22-22-2-2-2-2−1+i3−1−i3-11−i321+i32−1+i3−1−i3-11−i321+i32-11−i321+i32-11−i321+i321−i31+i3-11−i321+i3211−1+i32−1+i32−1−i32−1−i321−i31+i311−1+i32−1+i32−1−i32−1−i32000000000000000000000
χ352222222−1+i3−1−i3−1+i3−1−i3-2-2222-11−i321+i32−1+i3−1−i3-11−i321+i32−1+i3−1−i3−1+i3−1−i32-2-2-222-2-21−i31+i3-11−i321+i321−i31+i3-11−i321+i32-11−i321+i321−1+i32−1−i32−1+i3−1−i31−1+i32−1−i32-1-11−i321−i321+i321+i321−i31+i311−1+i32−1+i32−1−i32−1−i32000000000000000000000
χ362222222−1+i3−1−i3−1+i3−1−i3-2-2222-11−i321+i32−1+i3−1−i3-11−i321+i32−1+i3−1−i3−1+i3−1−i3-2-22-2-2-2221−i31+i3-11−i321+i321−i31+i3-11−i321+i32-11−i321+i321−1+i32−1−i321−i31+i31−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i3−1−i3-1-11−i321−i321+i321+i32000000000000000000000
χ372222-2-222222002-2-222222222-2-2-2-2000000000022200-2-2-2-2-2-200000000000000000000002-200002-22-200000000000
χ382222-2-222222002-2-222222222-2-2-2-2000000000022200-2-2-2-2-2-20000000000000000000000-220000-22-2200000000000
χ392222-2-22−1−i3−1+i3−1−i3−1+i3002-2-22−1−i3−1+i3−1−i3−1+i32−1−i3−1+i31+i31−i31+i31−i300000000002−1−i3−1+i300-21+i31−i3-21+i31−i300000000000000000000002-20000−1−i31+i3−1+i31−i300000000000
χ402222-2-22−1−i3−1+i3−1−i3−1+i3002-2-22−1−i3−1+i3−1−i3−1+i32−1−i3−1+i31+i31−i31+i31−i300000000002−1−i3−1+i300-21+i31−i3-21+i31−i30000000000000000000000-2200001+i3−1−i31−i3−1+i300000000000
χ412222-2-22−1+i3−1−i3−1+i3−1−i3002-2-22−1+i3−1−i3−1+i3−1−i32−1+i3−1−i31−i31+i31−i31+i300000000002−1+i3−1−i300-21−i31+i3-21−i31+i300000000000000000000002-20000−1+i31−i3−1−i31+i300000000000
χ422222-2-22−1+i3−1−i3−1+i3−1−i3002-2-22−1+i3−1−i3−1+i3−1−i32−1+i3−1−i31−i31+i31−i31+i300000000002−1+i3−1−i300-21−i31+i3-21−i31+i30000000000000000000000-2200001−i3−1+i31+i3−1−i300000000000
χ4322-222-2222222-2-2-22222-2-222222-2-2020-2000022-2-2-2-2-2-2-2-222222200-2-2-200000000000000000000000000000000000
χ4422-222-2222222-2-2-22-1-1-1-2-2-1-1-122-2-2020-2000022111-2-2111-1-1-1-1-1-100111−i3i3−i3i3−i3i300−i3i3−i3i3−i3i3000000000000000000000
χ4522-222-2222222-2-2-22-1-1-1-2-2-1-1-122-2-2020-2000022111-2-2111-1-1-1-1-1-100111i3−i3i3−i3i3−i300i3−i3i3−i3i3−i3000000000000000000000
χ4622-222-222222-22-2-22222-2-222222-2-20-2020000-2-2-2-2-222-2-2-2222-2-2-20022200000000000000000000000000000000000
χ4722-222-222222-22-2-22-1-1-1-2-2-1-1-122-2-20-2020000-2-211122111-1-1-111100-1-1-1−i3i3−i3i3−i3i300i3−i3i3−i3i3−i3000000000000000000000
χ4822-222-222222-22-2-22-1-1-1-2-2-1-1-122-2-20-2020000-2-211122111-1-1-111100-1-1-1i3−i3i3−i3i3−i300−i3i3−i3i3−i3i3000000000000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.