Finite Group Databasebeta

← Group #13141990

Character table — Group #13141990

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size112222222333344444444446666666666666666668888812121212121212121212121212121212121212121212121212122424242424242424242424242424363636363636363636363636727272727272
order1223446121233662444612121212126699912121212181818363636363636681224246612121212121218181836363636363636363636363636363618181824243636367272727272722224666666121226682424
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111-1-111-1-1-1-11111111111111111111-11-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1111-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ4111111111111111-1-111-1-1-1-11111111111111111111-11-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111-1-111111111111111111111111111-1-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1111-1-1-1
χ61111111111111-1-111111111111111111111111111-1-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1111
χ71111111111111-1-1-1-111-1-1-1-1111111111111111111-11-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111111111-1-11111-1-1-1-1-1-1-1111
χ81111111111111-1-1-1-111-1-1-1-1111111111111111111-11-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1111111-1-111-1-1-1-11111111-1-1-1
χ9111111111−1−i32−1+i32−1−i32−1+i321111111111−1−i32−1+i321−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i3211111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321−1−i32−1+i321−1−i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321−1−i32−1+i32−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321111−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32
χ10111111111−1−i32−1+i32−1−i32−1+i321111111111−1−i32−1+i321−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i3211111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321−1−i32−1+i321−1−i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321−1−i32−1+i32−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32-1-1-1-11+i321+i321−i321−i321+i321−i321+i321−i32-11+i321−i32-11+i321−i32
χ11111111111−1−i32−1+i32−1−i32−1+i3211-1-111-1-1-1-1−1−i32−1+i321−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321-11-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i321−1−i32−1+i321−1−i32−1+i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i321−1−i32−1+i321+i321−i321−1−i32−1+i32-1-11+i321+i321−i321−i321111−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i32-11+i321−i32-11+i321−i32
χ12111111111−1−i32−1+i32−1−i32−1+i3211-1-111-1-1-1-1−1−i32−1+i321−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321-11-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i321−1−i32−1+i321−1−i32−1+i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i321−1−i32−1+i321+i321−i321−1−i32−1+i32-1-11+i321+i321−i321−i32-1-1-1-11+i321+i321−i321−i321+i321−i321+i321−i321−1−i32−1+i321−1−i32−1+i32
χ13111111111−1−i32−1+i32−1−i32−1+i32-1-111111111−1−i32−1+i321−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32-1-1-1-1-11+i321−i321+i321−i32−1−i32−1−i32−1+i32−1+i321−1−i32−1+i321−1−i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-11+i321−i321+i321−i32-11+i321−i32-1-11+i321+i321−i321−i3211-1-1−1−i32−1−i32−1+i32−1+i321+i321−i321+i321−i321−1−i32−1+i32-11+i321−i32
χ14111111111−1−i32−1+i32−1−i32−1+i32-1-111111111−1−i32−1+i321−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32-1-1-1-1-11+i321−i321+i321−i32−1−i32−1−i32−1+i32−1+i321−1−i32−1+i321−1−i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-11+i321−i321+i321−i32-11+i321−i32-1-11+i321+i321−i321−i32-1-1111+i321+i321−i321−i32−1−i32−1+i32−1−i32−1+i32-11+i321−i321−1−i32−1+i32
χ15111111111−1−i32−1+i32−1−i32−1+i32-1-1-1-111-1-1-1-1−1−i32−1+i321−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32-11-1111+i321−i321+i321−i321+i321+i321−i321−i321−1−i32−1+i321−1−i32−1+i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32-11+i321−i32−1−i32−1+i32-11+i321−i3211−1−i32−1−i32−1+i32−1+i3211-1-1−1−i32−1−i32−1+i32−1+i321+i321−i321+i321−i32-11+i321−i321−1−i32−1+i32
χ16111111111−1−i32−1+i32−1−i32−1+i32-1-1-1-111-1-1-1-1−1−i32−1+i321−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32-11-1111+i321−i321+i321−i321+i321+i321−i321−i321−1−i32−1+i321−1−i32−1+i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32-11+i321−i32−1−i32−1+i32-11+i321−i3211−1−i32−1−i32−1+i32−1+i32-1-1111+i321+i321−i321−i32−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32-11+i321−i32
χ17111111111−1+i32−1−i32−1+i32−1−i321111111111−1+i32−1−i321−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i3211111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−1+i32−1−i321−1+i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321−1+i32−1−i32−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321111−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32
χ18111111111−1+i32−1−i32−1+i32−1−i321111111111−1+i32−1−i321−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i3211111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−1+i32−1−i321−1+i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321−1+i32−1−i32−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32-1-1-1-11−i321−i321+i321+i321−i321+i321−i321+i32-11−i321+i32-11−i321+i32
χ19111111111−1+i32−1−i32−1+i32−1−i3211-1-111-1-1-1-1−1+i32−1−i321−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321-11-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i321−1+i32−1−i321−1+i32−1−i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i321−1+i32−1−i321−i321+i321−1+i32−1−i32-1-11−i321−i321+i321+i321111−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i32-11−i321+i32-11−i321+i32
χ20111111111−1+i32−1−i32−1+i32−1−i3211-1-111-1-1-1-1−1+i32−1−i321−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321-11-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i321−1+i32−1−i321−1+i32−1−i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i321−1+i32−1−i321−i321+i321−1+i32−1−i32-1-11−i321−i321+i321+i32-1-1-1-11−i321−i321+i321+i321−i321+i321−i321+i321−1+i32−1−i321−1+i32−1−i32
χ21111111111−1+i32−1−i32−1+i32−1−i32-1-111111111−1+i32−1−i321−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32-1-1-1-1-11−i321+i321−i321+i32−1+i32−1+i32−1−i32−1−i321−1+i32−1−i321−1+i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-11−i321+i321−i321+i32-11−i321+i32-1-11−i321−i321+i321+i3211-1-1−1+i32−1+i32−1−i32−1−i321−i321+i321−i321+i321−1+i32−1−i32-11−i321+i32
χ22111111111−1+i32−1−i32−1+i32−1−i32-1-111111111−1+i32−1−i321−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32-1-1-1-1-11−i321+i321−i321+i32−1+i32−1+i32−1−i32−1−i321−1+i32−1−i321−1+i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-11−i321+i321−i321+i32-11−i321+i32-1-11−i321−i321+i321+i32-1-1111−i321−i321+i321+i32−1+i32−1−i32−1+i32−1−i32-11−i321+i321−1+i32−1−i32
χ23111111111−1+i32−1−i32−1+i32−1−i32-1-1-1-111-1-1-1-1−1+i32−1−i321−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32-11-1111−i321+i321−i321+i321−i321−i321+i321+i321−1+i32−1−i321−1+i32−1−i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32-11−i321+i32−1+i32−1−i32-11−i321+i3211−1+i32−1+i32−1−i32−1−i3211-1-1−1+i32−1+i32−1−i32−1−i321−i321+i321−i321+i32-11−i321+i321−1+i32−1−i32
χ24111111111−1+i32−1−i32−1+i32−1−i32-1-1-1-111-1-1-1-1−1+i32−1−i321−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32-11-1111−i321+i321−i321+i321−i321−i321+i321+i321−1+i32−1−i321−1+i32−1−i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32-11−i321+i32−1+i32−1−i32-11−i321+i3211−1+i32−1+i32−1−i32−1−i32-1-1111−i321−i321+i321+i32−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32-11−i321+i32
χ252222222222222222222222222-1-1-12222-1-1-1-1-1-1-1-1-12222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1000000000000000000
χ26222222222222222-2-222-2-2-2-222-1-1-12222-1-1-1-1-1-1-1-1-12-22-2-22222-2-2-2-2-1-1-1-1-1-1111111111111-1-1-1-2-2-1-1-1111111000000000000000000
χ272222222222222-2-22222222222-1-1-12222-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-2-2111111111000000000000000000
χ282222222222222-2-2-2-222-2-2-2-222-1-1-12222-1-1-1-1-1-1-1-1-1-22-222-2-2-2-2-2-2-2-2-1-1-1-1-1-111111111111111122111-1-1-1-1-1-1000000000000000000
χ29222222222−1−i3−1+i3−1−i3−1+i32222222222−1−i3−1+i3-11+i321−i32−1−i3−1+i3−1−i3−1+i3-11+i321−i32-1-11+i321+i321−i321−i3222222−1−i3−1+i3−1−i3−1+i3−1−i3−1−i3−1+i3−1+i3-11+i321−i32-11+i321−i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32-11+i321−i32−1−i3−1+i3-11+i321−i32-1-11+i321+i321−i321−i32000000000000000000
χ30222222222−1−i3−1+i3−1−i3−1+i322-2-222-2-2-2-2−1−i3−1+i3-11+i321−i32−1−i3−1+i3−1−i3−1+i3-11+i321−i32-1-11+i321+i321−i321−i322-22-2-2−1−i3−1+i3−1−i3−1+i31+i31+i31−i31−i3-11+i321−i32-11+i321−i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-11+i321−i321+i31−i3-11+i321−i3211−1−i32−1−i32−1+i32−1+i32000000000000000000
χ31222222222−1−i3−1+i3−1−i3−1+i3-2-222222222−1−i3−1+i3-11+i321−i32−1−i3−1+i3−1−i3−1+i3-11+i321−i32-1-11+i321+i321−i321−i32-2-2-2-2-21+i31−i31+i31−i3−1−i3−1−i3−1+i3−1+i3-11+i321−i32-11+i321−i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i321−1−i32−1+i321+i31−i31−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32000000000000000000
χ32222222222−1−i3−1+i3−1−i3−1+i3-2-2-2-222-2-2-2-2−1−i3−1+i3-11+i321−i32−1−i3−1+i3−1−i3−1+i3-11+i321−i32-1-11+i321+i321−i321−i32-22-2221+i31−i31+i31−i31+i31+i31−i31−i3-11+i321−i32-11+i321−i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321−1−i32−1+i32−1−i3−1+i31−1−i32−1+i32-1-11+i321+i321−i321−i32000000000000000000
χ33222222222−1+i3−1−i3−1+i3−1−i32222222222−1+i3−1−i3-11−i321+i32−1+i3−1−i3−1+i3−1−i3-11−i321+i32-1-11−i321−i321+i321+i3222222−1+i3−1−i3−1+i3−1−i3−1+i3−1+i3−1−i3−1−i3-11−i321+i32-11−i321+i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32-11−i321+i32−1+i3−1−i3-11−i321+i32-1-11−i321−i321+i321+i32000000000000000000
χ34222222222−1+i3−1−i3−1+i3−1−i322-2-222-2-2-2-2−1+i3−1−i3-11−i321+i32−1+i3−1−i3−1+i3−1−i3-11−i321+i32-1-11−i321−i321+i321+i322-22-2-2−1+i3−1−i3−1+i3−1−i31−i31−i31+i31+i3-11−i321+i32-11−i321+i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-11−i321+i321−i31+i3-11−i321+i3211−1+i32−1+i32−1−i32−1−i32000000000000000000
χ35222222222−1+i3−1−i3−1+i3−1−i3-2-222222222−1+i3−1−i3-11−i321+i32−1+i3−1−i3−1+i3−1−i3-11−i321+i32-1-11−i321−i321+i321+i32-2-2-2-2-21−i31+i31−i31+i3−1+i3−1+i3−1−i3−1−i3-11−i321+i32-11−i321+i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i321−1+i32−1−i321−i31+i31−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32000000000000000000
χ36222222222−1+i3−1−i3−1+i3−1−i3-2-2-2-222-2-2-2-2−1+i3−1−i3-11−i321+i32−1+i3−1−i3−1+i3−1−i3-11−i321+i32-1-11−i321−i321+i321+i32-22-2221−i31+i31−i31+i31−i31−i31+i31+i3-11−i321+i32-11−i321+i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321−1+i32−1−i32−1+i3−1−i31−1+i32−1−i32-1-11−i321−i321+i321+i32000000000000000000
χ372222-2-22-2-2222200002-2000022222-2-2-2-2222-2-2-2-2-2-20000000000000222-2-2-2000000000000000000000000002-2002-22-20000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.