Finite Group Databasebeta

← Group #13047986

Character table — Group #13047986

Order 1296.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11222222222333344444444444446666666666666666666666661212121212121212121212121212121212121212121212121212121212121212121212545454545454108108108
order123469991818183366412121236363636363636363633366699999999121218181818181818181212121212121212121212363636363636363636363636363636363636363636363636882424242441212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1
χ3111111111111111-11-1-1111-1-1-1-1-1-1111111111111111111111111-1-1111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1
χ4111111111111111-11-1-1111-1-1-1-1-1-1111111111111111111111111-1-1111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111
χ511111111111−1−i32−1+i32−1−i32−1+i3211111111111111−1−i32−1+i321−1−i32−1+i3211−1−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+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i3211−1−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−i32−1+i32−1+i321−1−i32−1+i32
χ611111111111−1−i32−1+i32−1−i32−1+i3211111111111111−1−i32−1+i321−1−i32−1+i3211−1−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+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i3211−1−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+i321−i321−i32-11+i321−i32
χ711111111111−1−i32−1+i32−1−i32−1+i32-11-1-1111-1-1-1-1-1-11−1−i32−1+i321−1−i32−1+i3211−1−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+i321+i321−i321−1−i32−1+i32-1-11+i321+i321−i321−i3211−1−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−i32−1+i32−1+i32-11+i321−i32
χ811111111111−1−i32−1+i32−1−i32−1+i32-11-1-1111-1-1-1-1-1-11−1−i32−1+i321−1−i32−1+i3211−1−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+i321+i321−i321−1−i32−1+i32-1-11+i321+i321−i321−i3211−1−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+i321−i321−i321−1−i32−1+i32
χ911111111111−1+i32−1−i32−1+i32−1−i3211111111111111−1+i32−1−i321−1+i32−1−i3211−1+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−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i3211−1+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+i32−1−i32−1−i321−1+i32−1−i32
χ1011111111111−1+i32−1−i32−1+i32−1−i3211111111111111−1+i32−1−i321−1+i32−1−i3211−1+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−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i3211−1+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−i321+i321+i32-11−i321+i32
χ1111111111111−1+i32−1−i32−1+i32−1−i32-11-1-1111-1-1-1-1-1-11−1+i32−1−i321−1+i32−1−i3211−1+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−i321−i321+i321−1+i32−1−i32-1-11−i321−i321+i321+i3211−1+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+i32−1−i32−1−i32-11−i321+i32
χ1211111111111−1+i32−1−i32−1+i32−1−i32-11-1-1111-1-1-1-1-1-11−1+i32−1−i321−1+i32−1−i3211−1+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−i321−i321+i321−1+i32−1−i32-1-11−i321−i321+i321+i3211−1+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−i321+i321+i321−1+i32−1−i32
χ132222222222222222222222222222-1-1-1-1-1-1-1-12-1-12-1-122-1-12-1-12-1-122-1-1-1-1-1-1-1-1-1-1-12-1-12-1-1-1-1-1-122-1-1-1-122-1-1-1-1000000000
χ14222222222222222-22-2-2222-2-2-2-2-2-2-1-1-1-1-1-1-1-12-1-12-1-122-1-12-1-12-1-1-2-2-1-1-1111111-1-12-1-12-1-11111-2-21111-2-21111000000000
χ1522222222222−1−i3−1+i3−1−i3−1+i32222222222222-11+i321−i32-11+i321−i32-1-1−1−i31+i321+i32−1+i31−i321−i32−1−i3−1+i3-1-1−1−i31+i321+i32−1+i31−i321−i32−1−i3−1+i3-11+i321−i32-1-11+i321+i321−i321−i32-1-1−1−i31+i321+i32−1+i31−i321−i32-1-1-1-1−1−i3−1−i31+i321+i321+i321+i32−1+i3−1+i31−i321−i321−i321−i32000000000
χ1622222222222−1−i3−1+i3−1−i3−1+i3-22-2-2222-2-2-2-2-2-2-11+i321−i32-11+i321−i32-1-1−1−i31+i321+i32−1+i31−i321−i32−1−i3−1+i3-1-1−1−i31+i321+i32−1+i31−i321−i321+i31−i3-11+i321−i3211−1−i32−1−i32−1+i32−1+i32-1-1−1−i31+i321+i32−1+i31−i321−i3211111+i31+i3−1−i32−1−i32−1−i32−1−i321−i31−i3−1+i32−1+i32−1+i32−1+i32000000000
χ1722222222222−1+i3−1−i3−1+i3−1−i32222222222222-11−i321+i32-11−i321+i32-1-1−1+i31−i321−i32−1−i31+i321+i32−1+i3−1−i3-1-1−1+i31−i321−i32−1−i31+i321+i32−1+i3−1−i3-11−i321+i32-1-11−i321−i321+i321+i32-1-1−1+i31−i321−i32−1−i31+i321+i32-1-1-1-1−1+i3−1+i31−i321−i321−i321−i32−1−i3−1−i31+i321+i321+i321+i32000000000
χ1822222222222−1+i3−1−i3−1+i3−1−i3-22-2-2222-2-2-2-2-2-2-11−i321+i32-11−i321+i32-1-1−1+i31−i321−i32−1−i31+i321+i32−1+i3−1−i3-1-1−1+i31−i321−i32−1−i31+i321+i321−i31+i3-11−i321+i3211−1+i32−1+i32−1−i32−1−i32-1-1−1+i31−i321−i32−1−i31+i321+i3211111−i31−i3−1+i32−1+i32−1+i32−1+i321+i31+i3−1−i32−1−i32−1−i32−1−i32000000000
χ1922222-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000
χ2022222-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-1-12-1-12-1222-1-12-1-12-122-1-1-1-1-1-1-1-1-12-1-12-1-12-122-1-1-1-122-1-1-1-122-1-1000000000
χ2122222-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-1-12-1-1222-12-1-12-1-1222-1-1-1-1-1-1-1-1-1-12-1-12-1-12-1-122-1-1-1-122-1-1-1-122000000000
χ2222222-1-1-1-1-1-12222-22-2-2-1-1-1111111222222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2222-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111000000000
χ2322222-1-1-1-1-1-12222-22-2-2-1-1-1111111-1-1-1-1-1-12-1-12-1-12-1222-1-12-1-12-1-2-2-1-1-11111112-1-12-1-12-1-2-21111-2-21111-2-211000000000
χ2422222-1-1-1-1-1-12222-22-2-2-1-1-1111111-1-1-1-1-1-1-12-1-12-1-1222-12-1-12-1-12-2-2-1-1-1111111-12-1-12-1-1211-2-21111-2-21111-2-2000000000
χ2522222-1-1-1-1-1-1−1−i3−1+i3−1−i3−1+i32222-1-1-1-1-1-1-1-1-12−1−i3−1+i32−1−i3−1+i3-1-11+i321+i321+i321−i321−i321−i32−1−i3−1+i3-1-11+i321+i321+i321−i321−i321−i32−1−i3−1+i32−1−i3−1+i322−1−i3−1−i3−1+i3−1+i3-1-11+i321+i321+i321−i321−i321−i32-1-1-1-11+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i32000000000
χ2622222-1-1-1-1-1-1−1−i3−1+i3−1−i3−1+i32222-1-1-1-1-1-1-1-1-1-11+i321−i32-11+i321−i322-11+i32−1−i31+i321−i32−1+i31−i32−1−i3−1+i32-11+i32−1−i31+i321−i32−1+i31−i32−1−i3−1+i3-11+i321−i32-1-11+i321+i321−i321−i322-11+i32−1−i31+i321−i32−1+i31−i3222-1-11+i321+i32−1−i3−1−i31+i321+i321−i321−i32−1+i3−1+i31−i321−i32000000000
χ2722222-1-1-1-1-1-1−1−i3−1+i3−1−i3−1+i32222-1-1-1-1-1-1-1-1-1-11+i321−i32-11+i321−i32-121+i321+i32−1−i31−i321−i32−1+i3−1−i3−1+i3-121+i321+i32−1−i31−i321−i32−1+i3−1−i3−1+i3-11+i321−i32-1-11+i321+i321−i321−i32-121+i321+i32−1−i31−i321−i32−1+i3-1-1221+i321+i321+i321+i32−1−i3−1−i31−i321−i321−i321−i32−1+i3−1+i3000000000
χ2822222-1-1-1-1-1-1−1−i3−1+i3−1−i3−1+i3-22-2-2-1-1-11111112−1−i3−1+i32−1−i3−1+i3-1-11+i321+i321+i321−i321−i321−i32−1−i3−1+i3-1-11+i321+i321+i321−i321−i321−i321+i31−i32−1−i3−1+i3-2-21+i31+i31−i31−i3-1-11+i321+i321+i321−i321−i321−i321111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32000000000
χ2922222-1-1-1-1-1-1−1−i3−1+i3−1−i3−1+i3-22-2-2-1-1-1111111-11+i321−i32-11+i321−i322-11+i32−1−i31+i321−i32−1+i31−i32−1−i3−1+i32-11+i32−1−i31+i321−i32−1+i31−i321+i31−i3-11+i321−i3211−1−i32−1−i32−1+i32−1+i322-11+i32−1−i31+i321−i32−1+i31−i32-2-211−1−i32−1−i321+i31+i3−1−i32−1−i32−1+i32−1+i321−i31−i3−1+i32−1+i32000000000
χ3022222-1-1-1-1-1-1−1−i3−1+i3−1−i3−1+i3-22-2-2-1-1-1111111-11+i321−i32-11+i321−i32-121+i321+i32−1−i31−i321−i32−1+i3−1−i3−1+i3-121+i321+i32−1−i31−i321−i32−1+i31+i31−i3-11+i321−i3211−1−i32−1−i32−1+i32−1+i32-121+i321+i32−1−i31−i321−i32−1+i311-2-2−1−i32−1−i32−1−i32−1−i321+i31+i3−1+i32−1+i32−1+i32−1+i321−i31−i3000000000
χ3122222-1-1-1-1-1-1−1+i3−1−i3−1+i3−1−i32222-1-1-1-1-1-1-1-1-12−1+i3−1−i32−1+i3−1−i3-1-11−i321−i321−i321+i321+i321+i32−1+i3−1−i3-1-11−i321−i321−i321+i321+i321+i32−1+i3−1−i32−1+i3−1−i322−1+i3−1+i3−1−i3−1−i3-1-11−i321−i321−i321+i321+i321+i32-1-1-1-11−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i32000000000
χ3222222-1-1-1-1-1-1−1+i3−1−i3−1+i3−1−i32222-1-1-1-1-1-1-1-1-1-11−i321+i32-11−i321+i322-11−i32−1+i31−i321+i32−1−i31+i32−1+i3−1−i32-11−i32−1+i31−i321+i32−1−i31+i32−1+i3−1−i3-11−i321+i32-1-11−i321−i321+i321+i322-11−i32−1+i31−i321+i32−1−i31+i3222-1-11−i321−i32−1+i3−1+i31−i321−i321+i321+i32−1−i3−1−i31+i321+i32000000000
χ3322222-1-1-1-1-1-1−1+i3−1−i3−1+i3−1−i32222-1-1-1-1-1-1-1-1-1-11−i321+i32-11−i321+i32-121−i321−i32−1+i31+i321+i32−1−i3−1+i3−1−i3-121−i321−i32−1+i31+i321+i32−1−i3−1+i3−1−i3-11−i321+i32-1-11−i321−i321+i321+i32-121−i321−i32−1+i31+i321+i32−1−i3-1-1221−i321−i321−i321−i32−1+i3−1+i31+i321+i321+i321+i32−1−i3−1−i3000000000
χ3422222-1-1-1-1-1-1−1+i3−1−i3−1+i3−1−i3-22-2-2-1-1-11111112−1+i3−1−i32−1+i3−1−i3-1-11−i321−i321−i321+i321+i321+i32−1+i3−1−i3-1-11−i321−i321−i321+i321+i321+i321−i31+i32−1+i3−1−i3-2-21−i31−i31+i31+i3-1-11−i321−i321−i321+i321+i321+i321111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32000000000
χ3522222-1-1-1-1-1-1−1+i3−1−i3−1+i3−1−i3-22-2-2-1-1-1111111-11−i321+i32-11−i321+i322-11−i32−1+i31−i321+i32−1−i31+i32−1+i3−1−i32-11−i32−1+i31−i321+i32−1−i31+i321−i31+i3-11−i321+i3211−1+i32−1+i32−1−i32−1−i322-11−i32−1+i31−i321+i32−1−i31+i32-2-211−1+i32−1+i321−i31−i3−1+i32−1+i32−1−i32−1−i321+i31+i3−1−i32−1−i32000000000
χ3622222-1-1-1-1-1-1−1+i3−1−i3−1+i3−1−i3-22-2-2-1-1-1111111-11−i321+i32-11−i321+i32-121−i321−i32−1+i31+i321+i32−1−i3−1+i3−1−i3-121−i321−i32−1+i31+i321+i32−1−i31−i31+i3-11−i321+i3211−1+i32−1+i32−1−i32−1−i32-121−i321−i32−1+i31+i321+i32−1−i311-2-2−1+i32−1+i32−1+i32−1+i321−i31−i3−1−i32−1−i32−1−i32−1−i321+i31+i3000000000
χ37222-2222222222220-200-2-2-200000022222222222222-2-22222222200-2-2-2000000-2-2-2-2-2-2-2-20000000000000000000000000
χ38222-2222222222220-200-2-2-2000000-1-1-1-1-1-1-1-12-1-12-1-1-2-2-1-12-1-12-1-100111−i3i3−i3i3−i3i311-211-211−i3i3−i3i300−i3i3−i3i300−i3i3−i3i3000000000
χ39222-2222222222220-200-2-2-2000000-1-1-1-1-1-1-1-12-1-12-1-1-2-2-1-12-1-12-1-100111i3−i3i3−i3i3−i311-211-211i3−i3i3−i300i3−i3i3−i300i3−i3i3−i3000000000
χ40222-22222222−1−i3−1+i3−1−i3−1+i30-200-2-2-20000002−1−i3−1+i32−1−i3−1+i322−1−i3−1−i3−1−i3−1+i3−1+i3−1+i31+i31−i322−1−i3−1−i3−1−i3−1+i3−1+i3−1+i300-21+i31−i3000000-2-21+i31+i31+i31−i31−i31−i30000000000000000000000000
χ41222-22222222−1−i3−1+i3−1−i3−1+i30-200-2-2-2000000-11+i321−i32-11+i321−i32-1-1−1−i31+i321+i32−1+i31−i321−i321+i31−i3-1-1−1−i31+i321+i32−1+i31−i321−i32001−1−i32−1+i32−i3i3−3+i323−i323+i32−3−i32111+i3−1−i32−1−i321−i3−1+i32−1+i32−i3i3−i3i300−3+i323−i32−3+i323−i32003+i32−3−i323+i32−3−i32000000000
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χ9066-3-6-33ζ4−3ζ44+3ζ52−3ζ4−3ζ683ζ44−3ζ52+3ζ683ζ4−3ζ44+3ζ52−3ζ4−3ζ683ζ44−3ζ52+3ζ68000003−3i33i3−3ζ4+3ζ44−3ζ523ζ4+3ζ68−3ζ44+3ζ52−3ζ683ζ4+3ζ44+3ζ52−3ζ4+3ζ68−3ζ44−3ζ52−3ζ68−3ζ4−3ζ44−3ζ523ζ4−3ζ683ζ44+3ζ52+3ζ6800000000000000000000000000000000000000000000000000000000000000000000
χ9166-3-6-33ζ4−3ζ44+3ζ52−3ζ4−3ζ683ζ44−3ζ52+3ζ683ζ4−3ζ44+3ζ52−3ζ4−3ζ683ζ44−3ζ52+3ζ680000033i3−3i3−3ζ4+3ζ44−3ζ523ζ4+3ζ68−3ζ44+3ζ52−3ζ68−3ζ4−3ζ44−3ζ523ζ4−3ζ683ζ44+3ζ52+3ζ683ζ4+3ζ44+3ζ52−3ζ4+3ζ68−3ζ44−3ζ52−3ζ6800000000000000000000000000000000000000000000000000000000000000000000
χ9266-3-6-3−3ζ4−3ζ683ζ44−3ζ52+3ζ683ζ4−3ζ44+3ζ52−3ζ4−3ζ683ζ44−3ζ52+3ζ683ζ4−3ζ44+3ζ52000003−3i33i33ζ4+3ζ68−3ζ44+3ζ52−3ζ68−3ζ4+3ζ44−3ζ52−3ζ4+3ζ68−3ζ44−3ζ52−3ζ683ζ4+3ζ44+3ζ523ζ4−3ζ683ζ44+3ζ52+3ζ68−3ζ4−3ζ44−3ζ5200000000000000000000000000000000000000000000000000000000000000000000
χ9366-3-6-3−3ζ4−3ζ683ζ44−3ζ52+3ζ683ζ4−3ζ44+3ζ52−3ζ4−3ζ683ζ44−3ζ52+3ζ683ζ4−3ζ44+3ζ520000033i3−3i33ζ4+3ζ68−3ζ44+3ζ52−3ζ68−3ζ4+3ζ44−3ζ523ζ4−3ζ683ζ44+3ζ52+3ζ68−3ζ4−3ζ44−3ζ52−3ζ4+3ζ68−3ζ44−3ζ52−3ζ683ζ4+3ζ44+3ζ5200000000000000000000000000000000000000000000000000000000000000000000
χ9412-12-6066ζ44−6ζ52+6ζ686ζ4−6ζ44+6ζ52−6ζ4−6ζ68−6ζ44+6ζ52−6ζ68−6ζ4+6ζ44−6ζ526ζ4+6ζ680000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9512-12-6066ζ4−6ζ44+6ζ52−6ζ4−6ζ686ζ44−6ζ52+6ζ68−6ζ4+6ζ44−6ζ526ζ4+6ζ68−6ζ44+6ζ52−6ζ680000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9612-12-606−6ζ4−6ζ686ζ44−6ζ52+6ζ686ζ4−6ζ44+6ζ526ζ4+6ζ68−6ζ44+6ζ52−6ζ68−6ζ4+6ζ44−6ζ520000000000000000000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 72 (ζ72 = 1); i = ζ18.