Finite Group Databasebeta

← Group #13142272

Character table — Group #13142272

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11222222222333344444446666666666666666666666888888121212121212121212121212121212121212121224242424242424242424242424242424363636363636363636363636727272727272
order122344688121233666812242424243336666612121212121212121212242424248824242424666121212242424242424242424242424242424242424242424242424242424242424246688121224242424226666
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+i3211111111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321111111−1−i32−1+i321−1−i32−1+i32−1−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+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+i3211111111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321111111−1−i32−1+i321−1−i32−1+i32−1−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+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+i3211111111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1-1-1-1-11−1−i32−1+i321−1−i32−1+i32−1−i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-1-1-1-11+i321+i321+i321+i321+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+i3211111111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1-1-1-1-11−1−i32−1+i321−1−i32−1+i32−1−i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-1-1-1-11+i321+i321+i321+i321+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−i3211111111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321111111−1+i32−1−i321−1+i32−1−i32−1+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−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−i3211111111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321111111−1+i32−1−i321−1+i32−1−i32−1+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−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−i3211111111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1-1-1-1-11−1+i32−1−i321−1+i32−1−i32−1+i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-1-1-1-11−i321−i321−i321−i321−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−i3211111111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1-1-1-1-11−1+i32−1−i321−1+i32−1−i32−1+i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-1-1-1-11−i321−i321−i321−i321−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
χ131111111-1-11111111-11-1-1-1-1111111111111111111-1-1-1-11-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111-1-1-1111-1-1-11111-1-111-1-1-1-11-11-11-1
χ141111111-1-11111111-11-1-1-1-1111111111111111111-1-1-1-11-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111-1-1-1111-1-1-1-1-1-1-111-1-11111-11-11-11
χ151111111-1-11111111-11-1-1-1-1111111111111111111-1-1-1-1-11-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1111-1-1-11111111-1-111-1-1-1-1-11-11-11
χ161111111-1-11111111-11-1-1-1-1111111111111111111-1-1-1-1-11-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1111-1-1-1111-1-1-1-111-1-111111-11-11-1
χ171111111-1-111−1−i32−1+i32−1−i32−1+i321-11-1-1-1-11−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321+i321−i321−i321-111-1-11−1−i32−1+i321−1−i32−1+i321+i321−i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i3211-1-1−1−i32−1−i32−1−i321+i321+i321+i32−1+i32−1+i32−1+i321−i321−i321−i3211−1−i32−1+i32-1-1−1−i32−1+i321+i321+i321−i321−i321-1−1−i321+i32−1+i321−i32
χ181111111-1-111−1−i32−1+i32−1−i32−1+i321-11-1-1-1-11−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321+i321−i321−i321-111-1-11−1−i32−1+i321−1−i32−1+i321+i321−i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i3211-1-1−1−i32−1−i32−1−i321+i321+i321+i32−1+i32−1+i32−1+i321−i321−i321−i32-1-11+i321−i32111+i321−i32−1−i32−1−i32−1+i32−1+i32-111+i32−1−i321−i32−1+i32
χ191111111-1-111−1−i32−1+i32−1−i32−1+i321-11-1-1-1-11−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321+i321−i321−i32-11-1-1111−1−i32−1+i321−1−i32−1+i321+i321−i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32-1-1111+i321+i321+i32−1−i32−1−i32−1−i321−i321−i321−i32−1+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
χ201111111-1-111−1−i32−1+i32−1−i32−1+i321-11-1-1-1-11−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321+i321−i321−i32-11-1-1111−1−i32−1+i321−1−i32−1+i321+i321−i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32-1-1111+i321+i321+i32−1−i32−1−i32−1−i321−i321−i321−i32−1+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
χ211111111-1-111−1+i32−1−i32−1+i32−1−i321-11-1-1-1-11−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321−i321+i321+i321-111-1-11−1+i32−1−i321−1+i32−1−i321−i321+i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i3211-1-1−1+i32−1+i32−1+i321−i321−i321−i32−1−i32−1−i32−1−i321+i321+i321+i3211−1+i32−1−i32-1-1−1+i32−1−i321−i321−i321+i321+i321-1−1+i321−i32−1−i321+i32
χ221111111-1-111−1+i32−1−i32−1+i32−1−i321-11-1-1-1-11−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321−i321+i321+i321-111-1-11−1+i32−1−i321−1+i32−1−i321−i321+i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i3211-1-1−1+i32−1+i32−1+i321−i321−i321−i32−1−i32−1−i32−1−i321+i321+i321+i32-1-11−i321+i32111−i321+i32−1+i32−1+i32−1−i32−1−i32-111−i32−1+i321+i32−1−i32
χ231111111-1-111−1+i32−1−i32−1+i32−1−i321-11-1-1-1-11−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321−i321+i321+i32-11-1-1111−1+i32−1−i321−1+i32−1−i321−i321+i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32-1-1111−i321−i321−i32−1+i32−1+i32−1+i321+i321+i321+i32−1−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
χ241111111-1-111−1+i32−1−i32−1+i32−1−i321-11-1-1-1-11−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321−i321+i321+i32-11-1-1111−1+i32−1−i321−1+i32−1−i321−i321+i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32-1-1111−i321−i321−i32−1+i32−1+i32−1+i321+i321+i321+i32−1−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
χ252222222222222222222222-1-1-122-1-1-122-1-1-1-1-1-1222222222222-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-1-12-1-12-1-12-1-1000000000000000000
χ262222222222222222222222-1-1-122-1-1-122-1-1-1-1-1-1222222-2-2-2-2-2-2-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-11111-211-211-211-211000000000000000000
χ2722222222222−1−i3−1+i3−1−i3−1+i32222222-11+i321−i32−1−i3−1+i3-11+i321−i32−1−i3−1+i3-1-11+i321+i321−i321−i32−1−i3−1+i3−1−i3−1−i3−1+i3−1+i3222222-11+i321−i32-11+i321−i32−1−i3−1+i3-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32-1-1-1-1−1−i31+i321+i32−1−i31+i321+i32−1+i31−i321−i32−1+i31−i321−i32000000000000000000
χ2822222222222−1−i3−1+i3−1−i3−1+i32222222-11+i321−i32−1−i3−1+i3-11+i321−i32−1−i3−1+i3-1-11+i321+i321−i321−i32−1−i3−1+i3−1−i3−1−i3−1+i3−1+i3-2-2-2-2-2-2-11+i321−i32-11+i321−i32−1−i3−1+i3-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i3211111+i3−1−i32−1−i321+i3−1−i32−1−i321−i3−1+i32−1+i321−i3−1+i32−1+i32000000000000000000
χ2922222222222−1+i3−1−i3−1+i3−1−i32222222-11−i321+i32−1+i3−1−i3-11−i321+i32−1+i3−1−i3-1-11−i321−i321+i321+i32−1+i3−1−i3−1+i3−1+i3−1−i3−1−i3222222-11−i321+i32-11−i321+i32−1+i3−1−i3-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32-1-1-1-1−1+i31−i321−i32−1+i31−i321−i32−1−i31+i321+i32−1−i31+i321+i32000000000000000000
χ3022222222222−1+i3−1−i3−1+i3−1−i32222222-11−i321+i32−1+i3−1−i3-11−i321+i32−1+i3−1−i3-1-11−i321−i321+i321+i32−1+i3−1−i3−1+i3−1+i3−1−i3−1−i3-2-2-2-2-2-2-11−i321+i32-11−i321+i32−1+i3−1−i3-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i3211111−i3−1+i32−1+i321−i3−1+i32−1+i321+i3−1−i32−1−i321+i3−1−i32−1−i32000000000000000000
χ312222222-2-22222222-22-2-2-2-2-1-1-122-1-1-122-1-1-1-1-1-122-2-2-2-22-222-2-2-1-1-1-1-1-1-2-2111111111111-1-1112-1-1-2112-1-1-211000000000000000000
χ322222222-2-22222222-22-2-2-2-2-1-1-122-1-1-122-1-1-1-1-1-122-2-2-2-2-22-2-222-1-1-1-1-1-1-2-211111111111111-1-1-2112-1-1-2112-1-1000000000000000000
χ332222222-2-222−1−i3−1+i3−1−i3−1+i32-22-2-2-2-2-11+i321−i32−1−i3−1+i3-11+i321−i32−1−i3−1+i3-1-11+i321+i321−i321−i32−1−i3−1+i31+i31+i31−i31−i32-222-2-2-11+i321−i32-11+i321−i321+i31−i31111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-1-111−1−i31+i321+i321+i3−1−i32−1−i32−1+i31−i321−i321−i3−1+i32−1+i32000000000000000000
χ342222222-2-222−1−i3−1+i3−1−i3−1+i32-22-2-2-2-2-11+i321−i32−1−i3−1+i3-11+i321−i32−1−i3−1+i3-1-11+i321+i321−i321−i32−1−i3−1+i31+i31+i31−i31−i3-22-2-222-11+i321−i32-11+i321−i321+i31−i31111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i3211-1-11+i3−1−i32−1−i32−1−i31+i321+i321−i3−1+i32−1+i32−1+i31−i321−i32000000000000000000
χ352222222-2-222−1+i3−1−i3−1+i3−1−i32-22-2-2-2-2-11−i321+i32−1+i3−1−i3-11−i321+i32−1+i3−1−i3-1-11−i321−i321+i321+i32−1+i3−1−i31−i31−i31+i31+i32-222-2-2-11−i321+i32-11−i321+i321−i31+i31111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-1-111−1+i31−i321−i321−i3−1+i32−1+i32−1−i31+i321+i321+i3−1−i32−1−i32000000000000000000
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χ10312-120-6006−626263−63000000032−32−36360000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10412-120-6006−6262−6363000000032−3236−360000000000000000000000000000000000000000000000000000000000000000000000000000000000

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