Finite Group Databasebeta

← Group #13141653

Character table — Group #13141653

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1122222333344444666666666666888888881212121212121212121212121224242424242424242424242424242424242424242424363636363636363636363636363636363636727272
order1222236336624666333666666666446121212121266666666666121266612121212121212121212121212121212121212222244666666661212121241212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-111-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1
χ41111111111111111111111111111-1-111-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111
χ511111111111-1-11111111111111111-1-1-111-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-11-1111-111-1-1111111-1-1-1-1-1
χ611111111111-1-11111111111111111-1-1-111-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-11-1-1-11-1-111-1-1-1-1-1-111111
χ711111111111-1-1111111111111111-11-1-1-1-111-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111111-1-1-11-111-1-1-1-1-1-111-1-1111
χ811111111111-1-1111111111111111-11-1-1-1-111-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1111-11-1-1111111-1-111-1-1-1
χ91111111−1−i32−1+i32−1−i32−1+i32111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32−1−i32−1+i3211111111−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211−1−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−i32−1+i32−1+i321−1−i32−1+i32−1−i32−1+i3211111111−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211−1−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−i32−1+i32−1+i321−1−i32−1+i32−1−i32−1+i32-1-111-1-1-1-1−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321+i321−i321+i321−i32-1-11+i321+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
χ121111111−1−i32−1+i32−1−i32−1+i32111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32−1−i32−1+i32-1-111-1-1-1-1−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321+i321−i321+i321−i32-1-11+i321+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
χ131111111−1−i32−1+i32−1−i32−1+i32-1-11111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32−1−i32−1+i321-1-1-111-1-11+i321−i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321+i321−i32-11+i321−i32-11+i321−i32−1−i32−1+i321+i321−i3211−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i321-1111-1−1−i32−1+i321+i321−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321−i32-11+i321−i32
χ141111111−1−i32−1+i32−1−i32−1+i32-1-11111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32−1−i32−1+i321-1-1-111-1-11+i321−i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321+i321−i32-11+i321−i32-11+i321−i32−1−i32−1+i321+i321−i3211−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i32-11-1-1-111+i321−i32−1−i32−1+i321+i321+i321−i321−i321+i321−i32−1−i32−1+i321−1−i32−1+i32
χ151111111−1−i32−1+i32−1−i32−1+i32-1-11111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32−1−i32−1+i32-11-1-1-1-1111+i321−i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321+i321−i32-11+i321−i32-11+i321−i321+i321−i32−1−i32−1+i32-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i321-1-1-11-1−1−i32−1+i321+i321−i321+i321+i321−i321−i32−1−i32−1+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−i32−1+i32−1+i321−1−i32−1+i32−1−i32−1+i32-11-1-1-1-1111+i321−i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321+i321−i32-11+i321−i32-11+i321−i321+i321−i32−1−i32−1+i32-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i32-1111-111+i321−i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321−i32−1−i32−1+i32-11+i321−i32
χ171111111−1+i32−1−i32−1+i32−1−i32111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32−1+i32−1−i3211111111−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211−1+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+i32−1−i32−1−i321−1+i32−1−i32−1+i32−1−i3211111111−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211−1+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+i32−1−i32−1−i321−1+i32−1−i32−1+i32−1−i32-1-111-1-1-1-1−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−i321+i321−i321+i32-1-11−i321−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
χ201111111−1+i32−1−i32−1+i32−1−i32111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32−1+i32−1−i32-1-111-1-1-1-1−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−i321+i321−i321+i32-1-11−i321−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
χ211111111−1+i32−1−i32−1+i32−1−i32-1-11111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32−1+i32−1−i321-1-1-111-1-11−i321+i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−i321+i32-11−i321+i32-11−i321+i32−1+i32−1−i321−i321+i3211−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i321-1111-1−1+i32−1−i321−i321+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321+i32-11−i321+i32
χ221111111−1+i32−1−i32−1+i32−1−i32-1-11111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32−1+i32−1−i321-1-1-111-1-11−i321+i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−i321+i32-11−i321+i32-11−i321+i32−1+i32−1−i321−i321+i3211−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i32-11-1-1-111−i321+i32−1+i32−1−i321−i321−i321+i321+i321−i321+i32−1+i32−1−i321−1+i32−1−i32
χ231111111−1+i32−1−i32−1+i32−1−i32-1-11111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32−1+i32−1−i32-11-1-1-1-1111−i321+i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−i321+i32-11−i321+i32-11−i321+i321−i321+i32−1+i32−1−i32-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i321-1-1-11-1−1+i32−1−i321−i321+i321−i321−i321+i321+i32−1+i32−1−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+i32−1−i32−1−i321−1+i32−1−i32−1+i32−1−i32-11-1-1-1-1111−i321+i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−i321+i32-11−i321+i32-11−i321+i321−i321+i32−1+i32−1−i32-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i32-1111-111−i321+i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321+i32−1+i32−1−i32-11−i321+i32
χ252222222222222222-1-1-12222-1-1-1222222222222-1-1-1-1-1-1-1-1-122-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000
χ262222222222222222-1-1-12222-1-1-122-2-222-2-2-2-222-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-2-2-2-2111111111111000000000000000000000
χ2722222222222-2-2222-1-1-12222-1-1-1222-2-2-222-2-2-2-2-1-1-1-1-1-1-1-1-1-2-211111122-2-2-1-1-1-1-1-1111111000000000000000000000
χ2822222222222-2-2222-1-1-12222-1-1-122-22-2-2-2-222-2-2-1-1-1-1-1-1-1-1-1-2-2111111-2-222111111-1-1-1-1-1-1000000000000000000000
χ292222222−1−i3−1+i3−1−i3−1+i322222-11+i321−i32−1−i3−1−i3−1+i3−1+i3-11+i321−i32−1−i3−1+i322222222−1−i3−1+i3-11+i321−i32-1-11+i321+i321−i321−i32−1−i3−1+i3-11+i321−i32-11+i321−i32−1−i3−1+i3−1−i3−1+i3-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i32000000000000000000000
χ302222222−1−i3−1+i3−1−i3−1+i322222-11+i321−i32−1−i3−1−i3−1+i3−1+i3-11+i321−i32−1−i3−1+i3-2-222-2-2-2-2−1−i3−1+i3-11+i321−i32-1-11+i321+i321−i321−i32−1−i3−1+i3-11+i321−i32-11+i321−i321+i31−i31+i31−i311−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i32000000000000000000000
χ312222222−1−i3−1+i3−1−i3−1+i3-2-2222-11+i321−i32−1−i3−1−i3−1+i3−1+i3-11+i321−i32−1−i3−1+i32-2-2-222-2-21+i31−i3-11+i321−i32-1-11+i321+i321−i321−i321+i31−i31−1−i32−1+i321−1−i32−1+i32−1−i3−1+i31+i31−i3-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i32000000000000000000000
χ322222222−1−i3−1+i3−1−i3−1+i3-2-2222-11+i321−i32−1−i3−1−i3−1+i3−1+i3-11+i321−i32−1−i3−1+i3-22-2-2-2-2221+i31−i3-11+i321−i32-1-11+i321+i321−i321−i321+i31−i31−1−i32−1+i321−1−i32−1+i321+i31−i3−1−i3−1+i311−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i32000000000000000000000
χ332222222−1+i3−1−i3−1+i3−1−i322222-11−i321+i32−1+i3−1+i3−1−i3−1−i3-11−i321+i32−1+i3−1−i322222222−1+i3−1−i3-11−i321+i32-1-11−i321−i321+i321+i32−1+i3−1−i3-11−i321+i32-11−i321+i32−1+i3−1−i3−1+i3−1−i3-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i32000000000000000000000
χ342222222−1+i3−1−i3−1+i3−1−i322222-11−i321+i32−1+i3−1+i3−1−i3−1−i3-11−i321+i32−1+i3−1−i3-2-222-2-2-2-2−1+i3−1−i3-11−i321+i32-1-11−i321−i321+i321+i32−1+i3−1−i3-11−i321+i32-11−i321+i321−i31+i31−i31+i311−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i32000000000000000000000
χ352222222−1+i3−1−i3−1+i3−1−i3-2-2222-11−i321+i32−1+i3−1+i3−1−i3−1−i3-11−i321+i32−1+i3−1−i32-2-2-222-2-21−i31+i3-11−i321+i32-1-11−i321−i321+i321+i321−i31+i31−1+i32−1−i321−1+i32−1−i32−1+i3−1−i31−i31+i3-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i32000000000000000000000
χ362222222−1+i3−1−i3−1+i3−1−i3-2-2222-11−i321+i32−1+i3−1+i3−1−i3−1−i3-11−i321+i32−1+i3−1−i3-22-2-2-2-2221−i31+i3-11−i321+i32-1-11−i321−i321+i321+i321−i31+i31−1+i32−1−i321−1+i32−1−i321−i31+i3−1+i3−1−i311−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i32000000000000000000000
χ37222-2-222222200-22-22222-22-2222-2-20000000000-2-2-22-22-22-20000000000000000000000002000-2022000000-2-200000
χ38222-2-222222200-22-22222-22-2222-2-20000000000-2-2-22-22-22-2000000000000000000000000-200020-2-20000002200000
χ39222-2-222−1−i3−1+i3−1−i3−1+i300-22-22−1−i3−1+i3−1−i31+i3−1+i31−i32−1−i3−1+i31+i31−i30000000000-21+i31−i32-2−1−i31+i3−1+i31−i30000000000000000000000002000-20−1−i3−1+i30000001+i31−i300000
χ40222-2-222−1−i3−1+i3−1−i3−1+i300-22-22−1−i3−1+i3−1−i31+i3−1+i31−i32−1−i3−1+i31+i31−i30000000000-21+i31−i32-2−1−i31+i3−1+i31−i3000000000000000000000000-2000201+i31−i3000000−1−i3−1+i300000
χ41222-2-222−1+i3−1−i3−1+i3−1−i300-22-22−1+i3−1−i3−1+i31−i3−1−i31+i32−1+i3−1−i31−i31+i30000000000-21−i31+i32-2−1+i31−i3−1−i31+i30000000000000000000000002000-20−1+i3−1−i30000001−i31+i300000
χ42222-2-222−1+i3−1−i3−1+i3−1−i300-22-22−1+i3−1−i3−1+i31−i3−1−i31+i32−1+i3−1−i31−i31+i30000000000-21−i31+i32-2−1+i31−i3−1−i31+i3000000000000000000000000-2000201−i31+i3000000−1+i3−1−i300000
χ4322-22-222222200-2-22222-22-22222-2-20000000000-2-2-2-22-22-2200000000000000000000000002000-20022000000-2-2000
χ4422-22-222222200-2-22222-22-22222-2-20000000000-2-2-2-22-22-220000000000000000000000000-2000200-2-200000022000
χ4522-22-222−1−i3−1+i3−1−i3−1+i300-2-222−1−i3−1+i31+i3−1−i31−i3−1+i32−1−i3−1+i31+i31−i30000000000-21+i31−i3-221+i3−1−i31−i3−1+i300000000000000000000000002000-200−1−i3−1+i30000001+i31−i3000
χ4622-22-222−1−i3−1+i3−1−i3−1+i300-2-222−1−i3−1+i31+i3−1−i31−i3−1+i32−1−i3−1+i31+i31−i30000000000-21+i31−i3-221+i3−1−i31−i3−1+i30000000000000000000000000-20002001+i31−i3000000−1−i3−1+i3000
χ4722-22-222−1+i3−1−i3−1+i3−1−i300-2-222−1+i3−1−i31−i3−1+i31+i3−1−i32−1+i3−1−i31−i31+i30000000000-21−i31+i3-221−i3−1+i31+i3−1−i300000000000000000000000002000-200−1+i3−1−i30000001−i31+i3000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.