Finite Group Databasebeta

← Group #10630833

Character table — Group #10630833

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93
size111111111111222222444444444444444444888888888888888888888888888888161616161616161616161616161616161616161616161616161616
order122233666666226666224444666612121212121212122244444444666612121212121212121212121212121212444448888121212121212121212122424242424242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11-1-11111-1-1-1-111-1-1-1-111111111
χ511111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-1
χ611111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111
χ811111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-11111-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ91111−1−i32−1+i32−1−i32−1+i32−1−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+i321111111111−1−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+i32111111111−1−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
χ101111−1−i32−1+i32−1−i32−1+i32−1−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+i321111111111−1−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+i32-1-11-1-1-1-1-1-11+i321−i321+i321−i32−1−i32−1+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+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+i32-1-1-1-1-1-1-1-1111+i321+i321−i321−i321+i321+i321−i321−i321+i321+i321−i321−i321+i321+i321−i321−i32−1−i32−1+i32−1−i32−1+i3211111-1-1-1-1−1−i32−1+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
χ121111−1−i32−1+i32−1−i32−1+i32−1−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+i32-1-1-1-1-1-1-1-1111+i321+i321−i321−i321+i321+i321−i321−i321+i321+i321−i321−i321+i321+i321−i321−i32−1−i32−1+i32−1−i32−1+i32-1-11-1-111111+i321−i321+i321−i32−1−i32−1+i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32
χ131111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211−1−i32−1+i32−1−i32−1+i3211-1-1-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i3211-1-1-1-11111−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i3211-1-1-111-1-1−1−i32−1+i32−1−i32−1+i321+i321−i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32
χ141111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211−1−i32−1+i32−1−i32−1+i3211-1-1-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i3211-1-1-1-11111−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-1-111-1-1111+i321−i321+i321−i321+i321−i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−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+i3211−1−i32−1+i32−1−i32−1+i3211-1-1-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32-1-11111-1-1111+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32−1−i32−1+i32−1−i32−1+i3211-1-1-1-1-111−1−i32−1+i32−1−i32−1+i321+i321−i321+i321+i321−i321−i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32
χ161111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211−1−i32−1+i32−1−i32−1+i3211-1-1-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32-1-11111-1-1111+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32−1−i32−1+i32−1−i32−1+i32-1-1-11111-1-11+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−i32
χ171111−1+i32−1−i32−1+i32−1−i32−1+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−i321111111111−1+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−i32111111111−1+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
χ181111−1+i32−1−i32−1+i32−1−i32−1+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−i321111111111−1+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−i32-1-11-1-1-1-1-1-11−i321+i321−i321+i32−1+i32−1−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−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−i32-1-1-1-1-1-1-1-1111−i321−i321+i321+i321−i321−i321+i321+i321−i321−i321+i321+i321−i321−i321+i321+i32−1+i32−1−i32−1+i32−1−i3211111-1-1-1-1−1+i32−1−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
χ201111−1+i32−1−i32−1+i32−1−i32−1+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−i32-1-1-1-1-1-1-1-1111−i321−i321+i321+i321−i321−i321+i321+i321−i321−i321+i321+i321−i321−i321+i321+i32−1+i32−1−i32−1+i32−1−i32-1-11-1-111111−i321+i321−i321+i32−1+i32−1−i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32
χ211111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211−1+i32−1−i32−1+i32−1−i3211-1-1-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i3211-1-1-1-11111−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i3211-1-1-111-1-1−1+i32−1−i32−1+i32−1−i321−i321+i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32
χ221111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211−1+i32−1−i32−1+i32−1−i3211-1-1-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i3211-1-1-1-11111−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-1-111-1-1111−i321+i321−i321+i321−i321+i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+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−i3211−1+i32−1−i32−1+i32−1−i3211-1-1-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32-1-11111-1-1111−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32−1+i32−1−i32−1+i32−1−i3211-1-1-1-1-111−1+i32−1−i32−1+i32−1−i321−i321+i321−i321−i321+i321+i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32
χ241111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211−1+i32−1−i32−1+i32−1−i3211-1-1-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32-1-11111-1-1111−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32−1+i32−1−i32−1+i32−1−i32-1-1-11111-1-11−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+i32
χ2522222222222222222222222222222222222200000000-2-20000000000000000-2-2-2-200-20000000000-2-2000000000000
χ2622222222222222222222-2-2-2-22222-2-2-2-2-2-2-2-200000000-2-20000000000000000-2-2-2-2002000000000022000000000000
χ27222222222222222222-2-20000-2-2-2-2000000000022-2-2002-200002222-2-2-2-2000022-2-2000000000000000000000000000
χ28222222222222222222-2-20000-2-2-2-20000000000-2-222002-20000-2-2-2-22222000022-2-2000000000000000000000000000
χ29222222222222222222-2-20000-2-2-2-200000000220000-2-2-22222200000000-2-2-2-2-2-222000000000000000000000000000
χ30222222222222222222-2-20000-2-2-2-200000000-2-2000022-22-2-2-2-2000000002222-2-222000000000000000000000000000
χ312222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i322−1−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+i300000000-2-200000000000000001+i31−i31+i31−i300-200000000001+i31−i3000000000000
χ322222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i322−1−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−i300000000-2-200000000000000001+i31−i31+i31−i30020000000000−1−i3−1+i3000000000000
χ332222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i322−1−i3−1+i3−1−i3−1+i3-2-200001+i31−i31+i31−i3000000000022-2-2002-20000−1−i3−1−i3−1+i3−1+i31+i31+i31−i31−i30000−1−i3−1+i31+i31−i3000000000000000000000000000
χ342222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i322−1−i3−1+i3−1−i3−1+i3-2-200001+i31−i31+i31−i30000000000-2-222002-200001+i31+i31−i31−i3−1−i3−1−i3−1+i3−1+i30000−1−i3−1+i31+i31−i3000000000000000000000000000
χ352222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i322−1−i3−1+i3−1−i3−1+i3-2-200001+i31−i31+i31−i300000000220000-2-2-22−1−i3−1−i3−1+i3−1+i3000000001+i31+i31−i31−i31+i31−i3−1−i3−1+i3000000000000000000000000000
χ362222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i322−1−i3−1+i3−1−i3−1+i3-2-200001+i31−i31+i31−i300000000-2-2000022-221+i31+i31−i31−i300000000−1−i3−1−i3−1+i3−1+i31+i31−i3−1−i3−1+i3000000000000000000000000000
χ372222−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i322−1+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−i300000000-2-200000000000000001−i31+i31−i31+i300-200000000001−i31+i3000000000000
χ382222−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i322−1+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+i300000000-2-200000000000000001−i31+i31−i31+i30020000000000−1+i3−1−i3000000000000
χ392222−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i322−1+i3−1−i3−1+i3−1−i3-2-200001−i31+i31−i31+i3000000000022-2-2002-20000−1+i3−1+i3−1−i3−1−i31−i31−i31+i31+i30000−1+i3−1−i31−i31+i3000000000000000000000000000
χ402222−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i322−1+i3−1−i3−1+i3−1−i3-2-200001−i31+i31−i31+i30000000000-2-222002-200001−i31−i31+i31+i3−1+i3−1+i3−1−i3−1−i30000−1+i3−1−i31−i31+i3000000000000000000000000000
χ412222−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i322−1+i3−1−i3−1+i3−1−i3-2-200001−i31+i31−i31+i300000000220000-2-2-22−1+i3−1+i3−1−i3−1−i3000000001−i31−i31+i31+i31−i31+i3−1+i3−1−i3000000000000000000000000000
χ422222−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i322−1+i3−1−i3−1+i3−1−i3-2-200001−i31+i31−i31+i300000000-2-2000022-221−i31−i31+i31+i300000000−1+i3−1+i3−1−i3−1−i31−i31+i3−1+i3−1−i3000000000000000000000000000
χ4322-2-22222-2-2-2-2-22-2-222-222i2i−2i−2i-2-2222i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000000−i2i22−20000000000−i2i2−i2i22−22−2
χ4422-2-22222-2-2-2-2-22-2-222-222i2i−2i−2i-2-2222i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000000i2−i2−220000000000i2−i2i2−i2−22−22
χ4522-2-22222-2-2-2-2-22-2-222-22−2i−2i2i2i-2-222−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000000−i2i2−220000000000−i2i2−i2i2−22−22
χ4622-2-22222-2-2-2-2-22-2-222-22−2i−2i2i2i-2-222−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000000i2−i22−20000000000i2−i2i2−i22−22−2
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.