Finite Group Databasebeta

← Group #10628826

Character table — Group #10628826

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111111111111222222222222222222444444444444888888888888888888888888888888888888161616161616161616161616161616161616161616161616
order12223366666622444466661212121212121212444412121212121212128888888888882424242424242424242424242424242424242424242424242224444466666612121212121212121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1
χ5111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ7111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-11111-1-1-1-11111-1-1-1-1
χ8111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-11111-1-1-1-11111
χ91111−1−i32−1+i32−1−i32−1−i32−1−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+i321111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32111111111111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i3211111111−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32
χ101111−1−i32−1+i32−1−i32−1−i32−1−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+i321111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32111111111111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-1-1-1-1-1-1-1-11+i321+i321−i321−i321+i321−i321+i321−i321+i321+i321−i321−i321+i321+i321−i321−i32
χ111111−1−i32−1+i32−1−i32−1−i32−1−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+i321111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321111-1-1-1-1-1-1-1-1−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i321+i321+i321+i321+i321−i321−i321−i321−i3211-1-1-1-111−1−i32−1−i32−1+i32−1+i321+i321−i321+i321−i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32
χ121111−1−i32−1+i32−1−i32−1−i32−1−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+i321111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321111-1-1-1-1-1-1-1-1−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i321+i321+i321+i321+i321−i321−i321−i321−i32-1-11111-1-11+i321+i321−i321−i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32
χ131111−1−i32−1+i32−1−i32−1−i32−1−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+i321111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1-1-11111-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i321111-1-1-1-1−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i321+i321+i321−i321−i32
χ141111−1−i32−1+i32−1−i32−1−i32−1−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+i321111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1-1-11111-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32-1-1-1-111111+i321+i321−i321−i321+i321−i321+i321−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32
χ151111−1−i32−1+i32−1−i32−1−i32−1−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+i321111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1-1-1-1-1-1-111111+i321+i321+i321+i321−i321−i321−i321−i321+i321+i321+i321+i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i3211-1-111-1-1−1−i32−1−i32−1+i32−1+i321+i321−i321+i321−i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32
χ161111−1−i32−1+i32−1−i32−1−i32−1−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+i321111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1-1-1-1-1-1-111111+i321+i321+i321+i321−i321−i321−i321−i321+i321+i321+i321+i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-1-111-1-1111+i321+i321−i321−i32−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32
χ171111−1+i32−1−i32−1+i32−1+i32−1+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−i321111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32111111111111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i3211111111−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32
χ181111−1+i32−1−i32−1+i32−1+i32−1+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−i321111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32111111111111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-1-1-1-1-1-1-1-11−i321−i321+i321+i321−i321+i321−i321+i321−i321−i321+i321+i321−i321−i321+i321+i32
χ191111−1+i32−1−i32−1+i32−1+i32−1+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−i321111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321111-1-1-1-1-1-1-1-1−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i321−i321−i321−i321−i321+i321+i321+i321+i3211-1-1-1-111−1+i32−1+i32−1−i32−1−i321−i321+i321−i321+i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32
χ201111−1+i32−1−i32−1+i32−1+i32−1+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−i321111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321111-1-1-1-1-1-1-1-1−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i321−i321−i321−i321−i321+i321+i321+i321+i32-1-11111-1-11−i321−i321+i321+i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32
χ211111−1+i32−1−i32−1+i32−1+i32−1+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−i321111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1-1-11111-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i321111-1-1-1-1−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i321−i321−i321+i321+i32
χ221111−1+i32−1−i32−1+i32−1+i32−1+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−i321111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1-1-11111-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32-1-1-1-111111−i321−i321+i321+i321−i321+i321−i321+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32
χ231111−1+i32−1−i32−1+i32−1+i32−1+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−i321111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1-1-1-1-1-1-111111−i321−i321−i321−i321+i321+i321+i321+i321−i321−i321−i321−i321+i321+i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i3211-1-111-1-1−1+i32−1+i32−1−i32−1−i321−i321+i321−i321+i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32
χ241111−1+i32−1−i32−1+i32−1+i32−1+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−i321111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1-1-1-1-1-1-111111−i321−i321−i321−i321+i321+i321+i321+i321−i321−i321−i321−i321+i321+i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-1-111-1-1111−i321−i321+i321+i32−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32
χ25222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-20000000022-2-222-2-20000000000000000000000000000000000000000
χ26222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-22200000000-2-222-2-2220000000000000000000000000000000000000000
χ2722222222222222-2-2-2-22222-2-2-2-2-2-2-2-22-22-22-22-22-22-20000000022-2-2000000000000000022-2-222-2-2000000000000000000000000
χ2822222222222222-2-2-2-22222-2-2-2-2-2-2-2-22-22-22-22-22-22-200000000-2-2220000000000000000-2-222-2-222000000000000000000000000
χ2922222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-22-22-22-22-22-22000022-2-200000000000022-2-222-2-200000000000000000000000000000000
χ3022222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-22-22-22-22-22-220000-2-222000000000000-2-222-2-22200000000000000000000000000000000
χ31222222222222-2-222-2-2-2-2-2-22222-2-2-2-222-2-22222-2-2-2-20000000000000000000000000000000000000000002i−2i0000000000002i−2i2i−2i
χ32222222222222-2-222-2-2-2-2-2-22222-2-2-2-222-2-22222-2-2-2-2000000000000000000000000000000000000000000−2i2i000000000000−2i2i−2i2i
χ33222222222222-2-222-2-2-2-2-2-22222-2-2-2-2-2-222-2-2-2-222220000000000000000000000000000000000002-20000002-22-2000000000000
χ34222222222222-2-222-2-2-2-2-2-22222-2-2-2-2-2-222-2-2-2-22222000000000000000000000000000000000000-22000000-22-22000000000000
χ35222222222222-2-2-2-222-2-2-2-2-2-2-2-222222-2-222-22-2-22-22000000000000000000000000000000000000002-20000000022-2-200000000
χ36222222222222-2-2-2-222-2-2-2-2-2-2-2-222222-2-222-22-2-22-2200000000000000000000000000000000000000-2200000000-2-22200000000
χ37222222222222-2-2-2-222-2-2-2-2-2-2-2-22222-222-2-22-222-22-200000000000000000000000000000000000000002-200000000002-22-20000
χ38222222222222-2-2-2-222-2-2-2-2-2-2-2-22222-222-2-22-222-22-20000000000000000000000000000000000000000-220000000000-22-220000
χ392222−1−i3−1+i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3222222−1−i3−1+i3−1−i3−1+i3−1−i3−1−i3−1+i3−1+i3−1−i3−1−i3−1+i3−1+i3-2-2-2-21+i31+i31−i31−i31+i31+i31−i31−i322-2-200000000−1−i3−1−i31+i31+i3−1+i3−1+i31−i31−i30000000000000000000000000000000000000000
χ402222−1−i3−1+i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3222222−1−i3−1+i3−1−i3−1+i3−1−i3−1−i3−1+i3−1+i3−1−i3−1−i3−1+i3−1+i3-2-2-2-21+i31+i31−i31−i31+i31+i31−i31−i3-2-222000000001+i31+i3−1−i3−1−i31−i31−i3−1+i3−1+i30000000000000000000000000000000000000000
χ412222−1−i3−1+i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i322-2-2-2-2−1−i3−1+i3−1−i3−1+i31+i31+i31−i31−i31+i31+i31−i31−i32-22-2−1−i31+i3−1+i31−i3−1−i31+i3−1+i31−i30000000022-2-20000000000000000−1−i3−1−i31+i31+i3−1+i3−1+i31−i31−i3000000000000000000000000
χ422222−1−i3−1+i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i322-2-2-2-2−1−i3−1+i3−1−i3−1+i31+i31+i31−i31−i31+i31+i31−i31−i32-22-2−1−i31+i3−1+i31−i3−1−i31+i3−1+i31−i300000000-2-22200000000000000001+i31+i3−1−i3−1−i31−i31−i3−1+i3−1+i3000000000000000000000000
χ432222−1−i3−1+i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i322-2-2-2-2−1−i3−1+i3−1−i3−1+i31+i31+i31−i31−i31+i31+i31−i31−i3-22-221+i3−1−i31−i3−1+i31+i3−1−i31−i3−1+i3000022-2-2000000000000−1−i3−1−i31+i31+i3−1+i3−1+i31−i31−i300000000000000000000000000000000
χ442222−1−i3−1+i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i322-2-2-2-2−1−i3−1+i3−1−i3−1+i31+i31+i31−i31−i31+i31+i31−i31−i3-22-221+i3−1−i31−i3−1+i31+i3−1−i31−i3−1+i30000-2-2220000000000001+i31+i3−1−i3−1−i31−i31−i3−1+i3−1+i300000000000000000000000000000000
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χ9022-2-2−1+i3−1−i3−1+i31−i31−i3−1−i31+i31+i32-2-22-22−1+i3−1−i31−i31+i31−i3−1+i31+i3−1−i31−i3−1+i31+i3−1−i3000000000000−2i2i00−222−2−i2i2i2−i2−2ζ142ζ1400−2ζ222ζ2200−ζ5+ζ23ζ5−ζ23ζ5−ζ23−ζ5+ζ23ζ7−ζ13−ζ7+ζ13−ζ7+ζ13ζ7−ζ13ζ5+ζ23−ζ5−ζ23−ζ5−ζ23ζ5+ζ23ζ7+ζ13−ζ7−ζ13−ζ7−ζ13ζ7+ζ13000000000000000000000000
χ9144-4-4444-4-44-4-4-444-4-44-4-4444-44-4-44-44000000000000000000000000000000000000000000000000000000000000000000000000
χ9244-4-4444-4-44-4-4-44-444-4-4-444-44-444-44-4000000000000000000000000000000000000000000000000000000000000000000000000
χ9344-4-4−2−2i3−2+2i3−2−2i32+2i32+2i3−2+2i32−2i32−2i3-444-4-442+2i32−2i3−2−2i3−2+2i3−2−2i32+2i3−2+2i32−2i32+2i3−2−2i32−2i3−2+2i3000000000000000000000000000000000000000000000000000000000000000000000000
χ9444-4-4−2−2i3−2+2i3−2−2i32+2i32+2i3−2+2i32−2i32−2i3-44-444-42+2i32−2i3−2−2i3−2+2i32+2i3−2−2i32−2i3−2+2i3−2−2i32+2i3−2+2i32−2i3000000000000000000000000000000000000000000000000000000000000000000000000
χ9544-4-4−2+2i3−2−2i3−2+2i32−2i32−2i3−2−2i32+2i32+2i3-444-4-442−2i32+2i3−2+2i3−2−2i3−2+2i32−2i3−2−2i32+2i32−2i3−2+2i32+2i3−2−2i3000000000000000000000000000000000000000000000000000000000000000000000000
χ9644-4-4−2+2i3−2−2i3−2+2i32−2i32−2i3−2−2i32+2i32+2i3-44-444-42−2i32+2i3−2+2i3−2−2i32−2i3−2+2i32+2i3−2−2i3−2+2i32−2i3−2−2i32+2i3000000000000000000000000000000000000000000000000000000000000000000000000
χ978-88-888-88-8-88-8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ988-88-8−4−4i3−4+4i34+4i3−4−4i34+4i34−4i3−4+4i34−4i3000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ998-88-8−4+4i3−4−4i34−4i3−4+4i34−4i34+4i3−4−4i34+4i3000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1008-8-8888-8-88-8-88000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1018-8-88−4−4i3−4+4i34+4i34+4i3−4−4i34−4i34−4i3−4+4i3000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1028-8-88−4+4i3−4−4i34−4i34−4i3−4+4i34+4i34+4i3−4−4i3000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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