Finite Group Databasebeta

← Group #13164397

Character table — Group #13164397

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116
size11112222222222333333333333333333336666666666666666666666666666666666242424242424242424242424242424242424242424242424363636363636363636363636363636363636363636363636
order124423466612121212223344666666121212121212121224666666666666666612121212121212121212121212121212333666666666121212121212121212121212224444446666121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111−1−i32−1+i3211−1−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+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+i32−1+i32−1+i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i321111−1−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
χ41111111111111111−1−i32−1+i3211−1−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+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+i32−1+i32−1+i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-1-1-1-1-1-1-1-11+i321+i321−i321−i321+i321+i321+i321+i321−i321−i321−i321−i321+i321+i321−i321−i32
χ51111111111111111−1+i32−1−i3211−1+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−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−i32−1−i32−1−i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i321111−1+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
χ61111111111111111−1+i32−1−i3211−1+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−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−i32−1−i32−1−i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-1-1-1-1-1-1-1-11−i321−i321+i321+i321−i321−i321−i321−i321+i321+i321+i321+i321−i321−i321+i321+i32
χ71111-11-1-1-1111-1-111111111111111111111-1-111-1-111-1-1-1-111-1-1-1-111-1-111-1-1-1-111-1-1-1-1111-1-1-1-1-1-111111-1-111-1-111-1-11-11-111-1-11-11-111-1-111-1-11-11-1
χ81111-11-1-1-1111-1-111111111111111111111-1-111-1-111-1-1-1-111-1-1-1-111-1-111-1-1-1-111-1-1-1-1111-1-1-1-1-1-111111-1-111-1-111-1-1-11-11-1-111-11-11-1-111-1-111-11-11
χ91111-11-1-1-1111-1-111−1−i32−1+i3211−1−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+i32-1-111-1-1−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i321−i321−i321−i321−i3211-1-1−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i321−i321−i321−i321−i321−1−i32−1+i32-1-11+i321+i321−i321−i321−1−i32−1+i3211-1-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321-11-111-1-1−1−i321+i32−1+i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−1−i321+i32−1+i321−i32
χ101111-11-1-1-1111-1-111−1−i32−1+i3211−1−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+i32-1-111-1-1−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i321−i321−i321−i321−i3211-1-1−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i321−i321−i321−i321−i321−1−i32−1+i32-1-11+i321+i321−i321−i321−1−i32−1+i3211-1-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32-11-11-1-1111+i32−1−i321−i32−1+i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321+i32−1−i321−i32−1+i32
χ111111-11-1-1-1111-1-111−1+i32−1−i3211−1+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−i32-1-111-1-1−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i321+i321+i321+i321+i3211-1-1−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i321+i321+i321+i321+i321−1+i32−1−i32-1-11−i321−i321+i321+i321−1+i32−1−i3211-1-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321-11-111-1-1−1+i321−i32−1−i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−1+i321−i32−1−i321+i32
χ121111-11-1-1-1111-1-111−1+i32−1−i3211−1+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−i32-1-111-1-1−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i321+i321+i321+i321+i3211-1-1−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i321+i321+i321+i321+i321−1+i32−1−i32-1-11−i321−i321+i321+i321−1+i32−1−i3211-1-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32-11-11-1-1111−i32−1+i321+i32−1−i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321−i32−1+i321+i32−1−i32
χ1311-1-111-1111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-11-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-111-11-11-11-11-11-11-11-1-11-11
χ1411-1-111-1111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-11-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-11-11-11-11-11-11-111-11-1
χ1511-1-111-1111-1-1-1-111−1−i32−1+i32-1-1−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i321-11111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32-1-1-1-11+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i321-1-111-11-1−1−i321+i32−1+i321−i32−1−i321+i32−1−i321+i32−1+i321−i32−1+i321−i321+i32−1−i321−i32−1+i32
χ1611-1-111-1111-1-1-1-111−1−i32−1+i32-1-1−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i321-11111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32-1-1-1-11+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32-111-1-11-111+i32−1−i321−i32−1+i321+i32−1−i321+i32−1−i321−i32−1+i321−i32−1+i32−1−i321+i32−1+i321−i32
χ1711-1-111-1111-1-1-1-111−1+i32−1−i32-1-1−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i321-11111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32-1-1-1-11−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i321-1-111-11-1−1+i321−i32−1−i321+i32−1+i321−i32−1+i321−i32−1−i321+i32−1−i321+i321−i32−1+i321+i32−1−i32
χ1811-1-111-1111-1-1-1-111−1+i32−1−i32-1-1−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i321-11111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32-1-1-1-11−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32-111-1-11-111−i32−1+i321+i32−1−i321−i32−1+i321−i32−1+i321+i32−1−i321+i32−1−i32−1+i321−i32−1−i321+i32
χ1911-1-1-111-1-11-1-1111111-1-1111111-1-1-1-1-1-1-1-1-1111-1-111-1-1-1-111-1-1-1-1-1-111-1-11111-1-11111111-1-1-1-1-1-1111-1-111-1-111-1-11111-1-11-1-1111111-1-111-1-11-1-1-1-1
χ2011-1-1-111-1-11-1-1111111-1-1111111-1-1-1-1-1-1-1-1-1111-1-111-1-1-1-111-1-1-1-1-1-111-1-11111-1-11111111-1-1-1-1-1-1111-1-111-1-111-1-111-1-111-111-1-1-1-1-1-111-1-111-11111
χ2111-1-1-111-1-11-1-11111−1−i32−1+i32-1-1−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32-1111-1-1−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i321−i321−i321−i321−i32-1-1111+i321+i32−1−i32−1−i32−1−i32−1−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−1−i32−1+i32-1-11+i321+i321−i321−i321−1−i32−1+i32-1-1111+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i3211-1-11-1-11−1−i32−1−i32−1+i32−1+i32−1−i321+i321+i32−1−i32−1+i321−i321−i32−1+i321+i321+i321−i321−i32
χ2211-1-1-111-1-11-1-11111−1−i32−1+i32-1-1−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32-1111-1-1−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i321−i321−i321−i321−i32-1-1111+i321+i32−1−i32−1−i32−1−i32−1−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−1−i32−1+i32-1-11+i321+i321−i321−i321−1−i32−1+i32-1-1111+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32-1-111-111-11+i321+i321−i321−i321+i32−1−i32−1−i321+i321−i32−1+i32−1+i321−i32−1−i32−1−i32−1+i32−1+i32
χ2311-1-1-111-1-11-1-11111−1+i32−1−i32-1-1−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32-1111-1-1−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i321+i321+i321+i321+i32-1-1111−i321−i32−1+i32−1+i32−1+i32−1+i321+i321+i32−1−i32−1−i32−1−i32−1−i321−1+i32−1−i32-1-11−i321−i321+i321+i321−1+i32−1−i32-1-1111−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i3211-1-11-1-11−1+i32−1+i32−1−i32−1−i32−1+i321−i321−i32−1+i32−1−i321+i321+i32−1−i321−i321−i321+i321+i32
χ2411-1-1-111-1-11-1-11111−1+i32−1−i32-1-1−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32-1111-1-1−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i321+i321+i321+i321+i32-1-1111−i321−i32−1+i32−1+i32−1+i32−1+i321+i321+i32−1−i32−1−i32−1−i32−1−i321−1+i32−1−i32-1-11−i321−i321+i321+i321−1+i32−1−i32-1-1111−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32-1-111-111-11−i321−i321+i321+i321−i32−1+i32−1+i321−i321+i32−1−i32−1−i321+i32−1+i32−1+i32−1−i32−1−i32
χ2522222222222222222222222222222222222222222222222222222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000
χ262222222222222222−1−i3−1+i322−1−i3−1−i3−1+i3−1+i3−1−i3−1+i3−1−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+i32222−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3-11+i321−i32-1-11+i321+i321−i321−i32-11+i321−i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32000000000000000000000000
χ272222222222222222−1+i3−1−i322−1+i3−1+i3−1−i3−1−i3−1+i3−1−i3−1+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−i32222−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3-11−i321+i32-1-11−i321−i321+i321+i32-11−i321+i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32000000000000000000000000
χ282222-22-2-2-2222-2-222222222222222222222-2-222-2-222-2-2-2-222-2-2-2-222-2-222-2-2-2-222-2-2-2-2-1-1-1111111-1-1-1-1-111-1-111-1-111000000000000000000000000
χ292222-22-2-2-2222-2-222−1−i3−1+i322−1−i3−1−i3−1+i3−1+i3−1−i3−1+i3−1−i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3−1+i3-2-222-2-2−1−i3−1−i31+i31+i31+i31+i3−1+i3−1+i31−i31−i31−i31−i322-2-2−1−i3−1−i31+i31+i31+i31+i3−1+i3−1+i31−i31−i31−i31−i3-11+i321−i3211−1−i32−1−i32−1+i32−1+i32-11+i321−i32-1-1111+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32000000000000000000000000
χ302222-22-2-2-2222-2-222−1+i3−1−i322−1+i3−1+i3−1−i3−1−i3−1+i3−1−i3−1+i3−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3−1−i3-2-222-2-2−1+i3−1+i31−i31−i31−i31−i3−1−i3−1−i31+i31+i31+i31+i322-2-2−1+i3−1+i31−i31−i31−i31−i3−1−i3−1−i31+i31+i31+i31+i3-11−i321+i3211−1+i32−1+i32−1−i32−1−i32-11−i321+i32-1-1111−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32000000000000000000000000
χ3122-2-222-2222-2-2-2-22222-2-2222222-2-2-2-2-2-2-2-22-22222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1111111111111000000000000000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.