Finite Group Databasebeta

← Group #10632026

Character table — Group #10632026

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93
size111111111111222222444444444444444444888888888888888888888888888888161616161616161616161616161616161616161616161616161616
order1222336666662266662222446666666612121212222244444466666666121212121212121212121212444444488121212121212121212121212121224242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-11111-1-11111-1-1-1-111111111-1-1-1-1-11-111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11111-1-111-1-1-1-1-1-111111111
χ5111111111111111111111111111111111111-1-1111111-1-1-1-1-1-1111111111111-1-1-1-1-1-11-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1
χ6111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-111-1-1-1-1111111-1-1-1-11111
χ7111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-11111-1-111-1-1-1-111111111-1-1-1-1
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+i321111-1-1-1-111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32111-1-1-1-1-1-1−1−i32−1+i32−1−i32−1+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+i3211-1-11111-1-1−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32-11-111-1-1-1-11+i321−i32−1−i32−1+i321+i321−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+i3211-1-1-1-1-1-1-1-1−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i321+i321+i321−i321−i321+i321+i321−i321−i321+i321+i321−i321−i32-11-1-1-111111+i321−i32−1−i32−1+i321+i321−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+i32111111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-1111111-1-11+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32-1-11-1-111-1-11+i321−i321+i321−i32−1−i32−1+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+i32111111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-111-1-1-1-1-1-11+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i321+i321+i321−i321−i321+i321+i321−i321−i32-1-1111-1-1111+i321−i321+i321−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
χ151111−1−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+i32-1-1-1-11111111+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−i32−1−i32−1+i32−1+i321-1-1-1-1-1-111−1−i32−1+i321+i321−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+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+i321-1-11111-1-1−1−i32−1+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−i321111-1-1-1-111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32111-1-1-1-1-1-1−1+i32−1−i32−1+i32−1−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−i3211-1-11111-1-1−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32-11-111-1-1-1-11−i321+i32−1+i32−1−i321−i321+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−i3211-1-1-1-1-1-1-1-1−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i321−i321−i321+i321+i321−i321−i321+i321+i321−i321−i321+i321+i32-11-1-1-111111−i321+i32−1+i32−1−i321−i321+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−i32111111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-1111111-1-11−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32-1-11-1-111-1-11−i321+i321−i321+i32−1+i32−1−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−i32111111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-111-1-1-1-1-1-11−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i321−i321−i321+i321+i321−i321−i321+i321+i32-1-1111-1-1111−i321+i321−i321+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
χ231111−1+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−i32-1-1-1-11111111−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+i32−1+i32−1−i32−1−i321-1-1-1-1-1-111−1+i32−1−i321−i321+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−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−i321-1-11111-1-1−1+i32−1−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
χ252222222222222222222-22-2-2-22-22-22-22-2-2-2-2-200220000000000222200000000000000-20000000000-2-2000000000000
χ262222222222222222222-22-2-2-22-22-22-22-2-2-2-2-200-2-20000000000-2-2-2-2000000000000002000000000022000000000000
χ27222222222222222222-22-22-2-2-22-22-22-22-2-2-2-22200000000222200000000000000000-2000000000-2-200000000000000
χ28222222222222222222-22-22-2-2-22-22-22-22-2-2-2-2-2-200000000-2-2-2-20000000000000000020000000002200000000000000
χ29222222222222222222-2-2-2-222-2-2-2-2-2-2-2-22222000000002200000000000000002222-200000000-2-20000000000000000
χ30222222222222222222-2-2-2-222-2-2-2-2-2-2-2-2222200000000-2-20000000000000000-2-2-2-2200000000220000000000000000
χ312222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i322−1−i3−1+i3−1−i3−1+i32-22-2-2-2−1−i31+i3−1+i31−i3−1−i31+i3−1+i31−i31+i31−i31+i31−i300220000000000−1−i3−1−i3−1+i3−1+i300000000000000-200000000001+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+i32-22-2-2-2−1−i31+i3−1+i31−i3−1−i31+i3−1+i31−i31+i31−i31+i31−i300-2-200000000001+i31+i31−i31−i30000000000000020000000000−1−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+i3-22-22-2-21+i3−1−i31−i3−1+i31+i3−1−i31−i3−1+i31+i31−i31+i31−i32200000000−1−i3−1−i3−1+i3−1+i300000000000000000-20000000001+i31−i300000000000000
χ342222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i322−1−i3−1+i3−1−i3−1+i3-22-22-2-21+i3−1−i31−i3−1+i31+i3−1−i31−i3−1+i31+i31−i31+i31−i3-2-2000000001+i31+i31−i31−i3000000000000000002000000000−1−i3−1+i300000000000000
χ352222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i322−1−i3−1+i3−1−i3−1+i3-2-2-2-2221+i31+i31−i31−i31+i31+i31−i31−i3−1−i3−1+i3−1−i3−1+i300000000220000000000000000−1−i3−1−i3−1+i3−1+i3-2000000001+i31−i30000000000000000
χ362222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i322−1−i3−1+i3−1−i3−1+i3-2-2-2-2221+i31+i31−i31−i31+i31+i31−i31−i3−1−i3−1+i3−1−i3−1+i300000000-2-200000000000000001+i31+i31−i31−i3200000000−1−i3−1+i30000000000000000
χ372222−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i322−1+i3−1−i3−1+i3−1−i32-22-2-2-2−1+i31−i3−1−i31+i3−1+i31−i3−1−i31+i31−i31+i31−i31+i300220000000000−1+i3−1+i3−1−i3−1−i300000000000000-200000000001−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−i32-22-2-2-2−1+i31−i3−1−i31+i3−1+i31−i3−1−i31+i31−i31+i31−i31+i300-2-200000000001−i31−i31+i31+i30000000000000020000000000−1+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−i3-22-22-2-21−i3−1+i31+i3−1−i31−i3−1+i31+i3−1−i31−i31+i31−i31+i32200000000−1+i3−1+i3−1−i3−1−i300000000000000000-20000000001−i31+i300000000000000
χ402222−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i322−1+i3−1−i3−1+i3−1−i3-22-22-2-21−i3−1+i31+i3−1−i31−i3−1+i31+i3−1−i31−i31+i31−i31+i3-2-2000000001−i31−i31+i31+i3000000000000000002000000000−1+i3−1−i300000000000000
χ412222−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i322−1+i3−1−i3−1+i3−1−i3-2-2-2-2221−i31−i31+i31+i31−i31−i31+i31+i3−1+i3−1−i3−1+i3−1−i300000000220000000000000000−1+i3−1+i3−1−i3−1−i3-2000000001−i31+i30000000000000000
χ422222−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i322−1+i3−1−i3−1+i3−1−i3-2-2-2-2221−i31−i31+i31+i31−i31−i31+i31+i3−1+i3−1−i3−1+i3−1−i300000000-2-200000000000000001−i31−i31+i31+i3200000000−1+i3−1−i30000000000000000
χ4322-2-22222-2-2-2-2-22-2-22222-2-2-222222-2-2-2-2-2-22200002i−2i2i−2i00000000002i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000
χ4422-2-22222-2-2-2-2-22-2-22222-2-2-222222-2-2-2-2-2-2220000−2i2i−2i2i0000000000−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000
χ4522-2-22222-2-2-2-2-22-2-2222-2-222-22-22-2-22-2222-2-2000000000000000000000000000000000002i−2i0000000000002i−2i2i−2i0000
χ4622-2-22222-2-2-2-2-22-2-2222-2-222-22-22-2-22-2222-2-200000000000000000000000000000000000−2i2i000000000000−2i2i−2i2i0000
χ4722-2-22222-2-2-2-2-22-2-222-222-22-2-22-222-22-222-2-20000000000000000000000000000000002i−2i00000000002i−2i2i−2i00000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.