Finite Group Databasebeta

← Group #13143327

Character table — Group #13143327

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11222222222333344444446666666666666666666666888888121212121212121212121212121212121212121224242424242424242424242424242424363636363636363636363636727272727272
order1223446668833668121224242424669991212121218181818181818181824242424226666242436363636363672727272727272727272727266661818181818181818181818182466881212242424248824242424
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111−1−i32−1+i32−1−i32−1+i321111111−1−i32−1+i321−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32111111−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−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+i3211−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i32
χ611111111111−1−i32−1+i32−1−i32−1+i321111111−1−i32−1+i321−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32111111−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-1-11+i321−i32-1-11+i321−i321+i321+i321−i321−i32-1-11+i321+i321−i321−i32
χ711111111111−1−i32−1+i32−1−i32−1+i321111111−1−i32−1+i321−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1-1-1-1-1−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321+i321+i321−i321−i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i3211−1−i32−1+i3211−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i32
χ811111111111−1−i32−1+i32−1−i32−1+i321111111−1−i32−1+i321−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1-1-1-1-1−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321+i321+i321−i321−i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32-1-11+i321−i32-1-11+i321−i321+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i32
χ911111111111−1+i32−1−i32−1+i32−1−i321111111−1+i32−1−i321−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32111111−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+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−i3211−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i32
χ1011111111111−1+i32−1−i32−1+i32−1−i321111111−1+i32−1−i321−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32111111−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-1-11−i321+i32-1-11−i321+i321−i321−i321+i321+i32-1-11−i321−i321+i321+i32
χ1111111111111−1+i32−1−i32−1+i32−1−i321111111−1+i32−1−i321−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1-1-1-1-1−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321−i321−i321+i321+i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i3211−1+i32−1−i3211−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i32
χ1211111111111−1+i32−1−i32−1+i32−1−i321111111−1+i32−1−i321−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1-1-1-1-1−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321−i321−i321+i321+i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32-1-11−i321+i32-1-11−i321+i321−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i32
χ13111111111-1-11111-111-1-1-1-1111111111111111111-1-1-1-11-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-111-1-111-1-11111-1-111-1-1-1-11-11-11-1
χ14111111111-1-11111-111-1-1-1-1111111111111111111-1-1-1-11-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-111-1-111-1-1-1-1-1-111-1-11111-11-11-11
χ15111111111-1-11111-111-1-1-1-1111111111111111111-1-1-1-1-11-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-111-1-1111111-1-111-1-1-1-1-11-11-11
χ16111111111-1-11111-111-1-1-1-1111111111111111111-1-1-1-1-11-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-111-1-111-1-1-1-111-1-111111-11-11-1
χ17111111111-1-1−1−i32−1+i32−1−i32−1+i32-111-1-1-1-1−1−i32−1+i321−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i321+i321+i321−i321−i321-111-1-11+i321−i321−1−i32−1+i321−1−i32−1+i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32−1−i321+i32−1+i321−i3211-1-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i3211−1−i32−1+i32-1-1−1−i32−1+i321+i321+i321−i321−i321-1−1−i321+i32−1+i321−i32
χ18111111111-1-1−1−i32−1+i32−1−i32−1+i32-111-1-1-1-1−1−i32−1+i321−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i321+i321+i321−i321−i321-111-1-11+i321−i321−1−i32−1+i321−1−i32−1+i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32−1−i321+i32−1+i321−i3211-1-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32-1-11+i321−i32111+i321−i32−1−i32−1−i32−1+i32−1+i32-111+i32−1−i321−i32−1+i32
χ19111111111-1-1−1−i32−1+i32−1−i32−1+i32-111-1-1-1-1−1−i32−1+i321−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i321+i321+i321−i321−i32-11-1-1111+i321−i321−1−i32−1+i321−1−i32−1+i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i321+i32−1−i321−i32−1+i32-1-1111+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i3211−1−i32−1+i32-1-1−1−i32−1+i321+i321+i321−i321−i32-111+i32−1−i321−i32−1+i32
χ20111111111-1-1−1−i32−1+i32−1−i32−1+i32-111-1-1-1-1−1−i32−1+i321−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i321+i321+i321−i321−i32-11-1-1111+i321−i321−1−i32−1+i321−1−i32−1+i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i321+i32−1−i321−i32−1+i32-1-1111+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32-1-11+i321−i32111+i321−i32−1−i32−1−i32−1+i32−1+i321-1−1−i321+i32−1+i321−i32
χ21111111111-1-1−1+i32−1−i32−1+i32−1−i32-111-1-1-1-1−1+i32−1−i321−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i321−i321−i321+i321+i321-111-1-11−i321+i321−1+i32−1−i321−1+i32−1−i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32−1+i321−i32−1−i321+i3211-1-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i3211−1+i32−1−i32-1-1−1+i32−1−i321−i321−i321+i321+i321-1−1+i321−i32−1−i321+i32
χ22111111111-1-1−1+i32−1−i32−1+i32−1−i32-111-1-1-1-1−1+i32−1−i321−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i321−i321−i321+i321+i321-111-1-11−i321+i321−1+i32−1−i321−1+i32−1−i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32−1+i321−i32−1−i321+i3211-1-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32-1-11−i321+i32111−i321+i32−1+i32−1+i32−1−i32−1−i32-111−i32−1+i321+i32−1−i32
χ23111111111-1-1−1+i32−1−i32−1+i32−1−i32-111-1-1-1-1−1+i32−1−i321−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i321−i321−i321+i321+i32-11-1-1111−i321+i321−1+i32−1−i321−1+i32−1−i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i321−i32−1+i321+i32−1−i32-1-1111−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i3211−1+i32−1−i32-1-1−1+i32−1−i321−i321−i321+i321+i32-111−i32−1+i321+i32−1−i32
χ24111111111-1-1−1+i32−1−i32−1+i32−1−i32-111-1-1-1-1−1+i32−1−i321−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i321−i321−i321+i321+i32-11-1-1111−i321+i321−1+i32−1−i321−1+i32−1−i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i321−i32−1+i321+i32−1−i32-1-1111−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32-1-11−i321+i32111−i321+i32−1+i32−1+i32−1−i32−1−i321-1−1+i321−i32−1−i321+i32
χ25222222222222222222222222-1-1-12222-1-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000
χ26222222222222222222222222-1-1-12222-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111111111000000000000000000
χ2722222222222−1−i3−1+i3−1−i3−1+i32222222−1−i3−1+i3-11+i321−i32−1−i3−1+i3−1−i3−1+i3-1-11+i321+i321−i321−i32-11+i321−i32−1−i3−1−i3−1+i3−1+i3222222−1−i3−1+i3-11+i321−i32-11+i321−i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32−1−i3−1−i3−1+i3−1+i3-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32000000000000000000
χ2822222222222−1−i3−1+i3−1−i3−1+i32222222−1−i3−1+i3-11+i321−i32−1−i3−1+i3−1−i3−1+i3-1-11+i321+i321−i321−i32-11+i321−i32−1−i3−1−i3−1+i3−1+i3-2-2-2-2-2-2−1−i3−1+i3-11+i321−i32-11+i321−i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i321+i31+i31−i31−i31111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32000000000000000000
χ2922222222222−1+i3−1−i3−1+i3−1−i32222222−1+i3−1−i3-11−i321+i32−1+i3−1−i3−1+i3−1−i3-1-11−i321−i321+i321+i32-11−i321+i32−1+i3−1+i3−1−i3−1−i3222222−1+i3−1−i3-11−i321+i32-11−i321+i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32−1+i3−1+i3−1−i3−1−i3-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32000000000000000000
χ3022222222222−1+i3−1−i3−1+i3−1−i32222222−1+i3−1−i3-11−i321+i32−1+i3−1−i3−1+i3−1−i3-1-11−i321−i321+i321+i32-11−i321+i32−1+i3−1+i3−1−i3−1−i3-2-2-2-2-2-2−1+i3−1−i3-11−i321+i32-11−i321+i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i321−i31−i31+i31+i31111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32000000000000000000
χ31222222222-2-22222-222-2-2-2-222-1-1-12222-1-1-1-1-1-1-1-1-1-2-2-2-22-222-2-2-2-2-1-1-1-1-1-11111111111112-22-2-1-111-1-111-1-111000000000000000000
χ32222222222-2-22222-222-2-2-2-222-1-1-12222-1-1-1-1-1-1-1-1-1-2-2-2-2-22-2-222-2-2-1-1-1-1-1-1111111111111-22-2211-1-111-1-111-1-1000000000000000000
χ33222222222-2-2−1−i3−1+i3−1−i3−1+i3-222-2-2-2-2−1−i3−1+i3-11+i321−i32−1−i3−1+i3−1−i3−1+i3-1-11+i321+i321−i321−i32-11+i321−i321+i31+i31−i31−i32-222-2-21+i31−i3-11+i321−i32-11+i321−i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i31+i3−1+i31−i3-1-1111+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32000000000000000000
χ34222222222-2-2−1−i3−1+i3−1−i3−1+i3-222-2-2-2-2−1−i3−1+i3-11+i321−i32−1−i3−1+i3−1−i3−1+i3-1-11+i321+i321−i321−i32-11+i321−i321+i31+i31−i31−i3-22-2-2221+i31−i3-11+i321−i32-11+i321−i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321+i3−1−i31−i3−1+i311-1-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32000000000000000000
χ35222222222-2-2−1+i3−1−i3−1+i3−1−i3-222-2-2-2-2−1+i3−1−i3-11−i321+i32−1+i3−1−i3−1+i3−1−i3-1-11−i321−i321+i321+i32-11−i321+i321−i31−i31+i31+i32-222-2-21−i31+i3-11−i321+i32-11−i321+i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i31−i3−1−i31+i3-1-1111−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32000000000000000000
χ36222222222-2-2−1+i3−1−i3−1+i3−1−i3-222-2-2-2-2−1+i3−1−i3-11−i321+i32−1+i3−1−i3−1+i3−1−i3-1-11−i321−i321+i321+i32-11−i321+i321−i31−i31+i31+i3-22-2-2221−i31+i3-11−i321+i32-11−i321+i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321−i3−1+i31+i3−1−i311-1-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32000000000000000000
χ372222-2-22220022220-2-2000022222-2-2-2-2222222222000000000000-2-2-2-2-2-2000000000000000000000000000000002i−2i002i−2i2i−2i000000
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χ10212-120-600−6i36i36−6262000000032−32−3i63i60000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10312-120-6006i3−6i3662−620000000−3232−3i63i60000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10412-120-6006i3−6i36−6262000000032−323i6−3i60000000000000000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.