Finite Group Databasebeta

← Group #72227308

Character table — Group #72227308

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140
size111111112222222222226666666666666666666666666666666666666666666666666666666666666666666666666666666616161616161616161616161616161616323232323232323232323232323232323232323232323232
order1222444444448888888822222222224444444444444444444444444444448888888888888888888888888888888888888888336666661212121212121212121212121212121224242424242424242424242424242424
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111−1−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−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
χ31111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111−1+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+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
χ4111111111111-1-1-1-1-1-1-1-11111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ5111111111111-1-1-1-1-1-1-1-11111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−1−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+i321+i321+i321+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i321−i321−i32
χ6111111111111-1-1-1-1-1-1-1-11111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−1+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−i321−i321−i321−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i321+i321+i32
χ711111111-1-1-1-11111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ811111111-1-1-1-11111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−1−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+i321+i321+i321+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+i321−i321−i321−i321−i32
χ911111111-1-1-1-11111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−1+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−i321−i321−i321−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−i321+i321+i321+i321+i32
χ1011111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ1111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111−1−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+i321+i321+i321+i321+i321−i321−i321−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
χ1211111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111−1+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−i321−i321−i321−i321−i321+i321+i321+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
χ131111-1-1-1-111-1-1ii−i−iii−i−i111111-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1iiiiiiiiii−i−i−i−i−i−i−i−i−i−iiiiiiiiiii−i−i−i−i−i−i−i−i−i−i11111111-1-1-1-1-1-1-1-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i
χ141111-1-1-1-111-1-1ii−i−iii−i−i111111-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1iiiiiiiiii−i−i−i−i−i−i−i−i−i−iiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−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−i321+i321+i32−1+i32−1+i321−i321−i32ζ11ζ11−ζ11−ζ11ζ11ζ11−ζ11−ζ11ζ7ζ7−ζ7−ζ7ζ7ζ7−ζ7−ζ7
χ151111-1-1-1-111-1-1ii−i−iii−i−i111111-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1iiiiiiiiii−i−i−i−i−i−i−i−i−i−iiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−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+i321−i321−i32−1−i32−1−i321+i321+i32ζ7ζ7−ζ7−ζ7ζ7ζ7−ζ7−ζ7ζ11ζ11−ζ11−ζ11ζ11ζ11−ζ11−ζ11
χ161111-1-1-1-111-1-1−i−iii−i−iii111111-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−iiiiiiiiiii−i−i−i−i−i−i−i−i−i−iiiiiiiiiii11111111-1-1-1-1-1-1-1-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii
χ171111-1-1-1-111-1-1−i−iii−i−iii111111-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−iiiiiiiiiii−i−i−i−i−i−i−i−i−i−iiiiiiiiiii−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−i321+i321+i32−1+i32−1+i321−i321−i32−ζ11−ζ11ζ11ζ11−ζ11−ζ11ζ11ζ11−ζ7−ζ7ζ7ζ7−ζ7−ζ7ζ7ζ7
χ181111-1-1-1-111-1-1−i−iii−i−iii111111-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−iiiiiiiiiii−i−i−i−i−i−i−i−i−i−iiiiiiiiiii−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+i321−i321−i32−1−i32−1−i321+i321+i32−ζ7−ζ7ζ7ζ7−ζ7−ζ7ζ7ζ7−ζ11−ζ11ζ11ζ11−ζ11−ζ11ζ11ζ11
χ191111-1-1-1-1-1-111ii−i−i−i−iii111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111iiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiii11111111-1-1-1-1-1-1-1-1-1-111-1-111ii−i−i−i−iiiii−i−i−i−iii
χ201111-1-1-1-1-1-111ii−i−i−i−iii111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111iiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiii−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+i32−1−i32−1−i321−i321−i32−1+i32−1+i32ζ11ζ11−ζ11−ζ11−ζ11−ζ11ζ11ζ11ζ7ζ7−ζ7−ζ7−ζ7−ζ7ζ7ζ7
χ211111-1-1-1-1-1-111ii−i−i−i−iii111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111iiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiii−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−i32−1+i32−1+i321+i321+i32−1−i32−1−i32ζ7ζ7−ζ7−ζ7−ζ7−ζ7ζ7ζ7ζ11ζ11−ζ11−ζ11−ζ11−ζ11ζ11ζ11
χ221111-1-1-1-1-1-111−i−iiiii−i−i111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i11111111-1-1-1-1-1-1-1-1-1-111-1-111−i−iiiii−i−i−i−iiiii−i−i
χ231111-1-1-1-1-1-111−i−iiiii−i−i111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−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+i32−1−i32−1−i321−i321−i32−1+i32−1+i32−ζ11−ζ11ζ11ζ11ζ11ζ11−ζ11−ζ11−ζ7−ζ7ζ7ζ7ζ7ζ7−ζ7−ζ7
χ241111-1-1-1-1-1-111−i−iiiii−i−i111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−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−i32−1+i32−1+i321+i321+i32−1−i32−1−i32−ζ7−ζ7ζ7ζ7ζ7ζ7−ζ7−ζ7−ζ11−ζ11ζ11ζ11ζ11ζ11−ζ11−ζ11
χ2511-1-111-1-1i−ii−i1-11-1i−ii−i111-1-1-111-1-111-1-1111-1-1-1iiiii−i−i−i−i−iiiiii−i−i−i−i−i11111-1-1-1-1-111111-1-1-1-1-1iiiii−i−i−i−i−iiiiii−i−i−i−i−i111-1-11-1-111-1-111-1-1i−ii−ii−ii−i1-11-1i−ii−i1-11-1i−ii−i
χ2611-1-111-1-1i−ii−i1-11-1i−ii−i111-1-1-111-1-111-1-1111-1-1-1iiiii−i−i−i−i−iiiiii−i−i−i−i−i11111-1-1-1-1-111111-1-1-1-1-1iiiii−i−i−i−i−iiiiii−i−i−i−i−i−1−i32−1+i32−1−i321+i321+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32ζ11−ζ11ζ11−ζ11ζ7−ζ7ζ7−ζ7−1−i321+i32−1−i321+i32ζ11−ζ11ζ11−ζ11−1+i321−i32−1+i321−i32ζ7−ζ7ζ7−ζ7
χ2711-1-111-1-1i−ii−i1-11-1i−ii−i111-1-1-111-1-111-1-1111-1-1-1iiiii−i−i−i−i−iiiiii−i−i−i−i−i11111-1-1-1-1-111111-1-1-1-1-1iiiii−i−i−i−i−iiiiii−i−i−i−i−i−1+i32−1−i32−1+i321−i321−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32ζ7−ζ7ζ7−ζ7ζ11−ζ11ζ11−ζ11−1+i321−i32−1+i321−i32ζ7−ζ7ζ7−ζ7−1−i321+i32−1−i321+i32ζ11−ζ11ζ11−ζ11
χ2811-1-111-1-1i−ii−i-11-11−ii−ii111-1-1-111-1-111-1-1111-1-1-1iiiii−i−i−i−i−iiiiii−i−i−i−i−i-1-1-1-1-111111-1-1-1-1-111111−i−i−i−i−iiiiii−i−i−i−i−iiiiii111-1-11-1-111-1-111-1-1i−ii−ii−ii−i-11-11−ii−ii-11-11−ii−ii
χ2911-1-111-1-1i−ii−i-11-11−ii−ii111-1-1-111-1-111-1-1111-1-1-1iiiii−i−i−i−i−iiiiii−i−i−i−i−i-1-1-1-1-111111-1-1-1-1-111111−i−i−i−i−iiiiii−i−i−i−i−iiiiii−1−i32−1+i32−1−i321+i321+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32ζ11−ζ11ζ11−ζ11ζ7−ζ7ζ7−ζ71+i32−1−i321+i32−1−i32−ζ11ζ11−ζ11ζ111−i32−1+i321−i32−1+i32−ζ7ζ7−ζ7ζ7
χ3011-1-111-1-1i−ii−i-11-11−ii−ii111-1-1-111-1-111-1-1111-1-1-1iiiii−i−i−i−i−iiiiii−i−i−i−i−i-1-1-1-1-111111-1-1-1-1-111111−i−i−i−i−iiiiii−i−i−i−i−iiiiii−1+i32−1−i32−1+i321−i321−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32ζ7−ζ7ζ7−ζ7ζ11−ζ11ζ11−ζ111−i32−1+i321−i32−1+i32−ζ7ζ7−ζ7ζ71+i32−1−i321+i32−1−i32−ζ11ζ11−ζ11ζ11
χ3111-1-111-1-1−ii−ii1-11-1−ii−ii111-1-1-111-1-111-1-1111-1-1-1−i−i−i−i−iiiiii−i−i−i−i−iiiiii11111-1-1-1-1-111111-1-1-1-1-1−i−i−i−i−iiiiii−i−i−i−i−iiiiii111-1-11-1-111-1-111-1-1−ii−ii−ii−ii1-11-1−ii−ii1-11-1−ii−ii
χ3211-1-111-1-1−ii−ii1-11-1−ii−ii111-1-1-111-1-111-1-1111-1-1-1−i−i−i−i−iiiiii−i−i−i−i−iiiiii11111-1-1-1-1-111111-1-1-1-1-1−i−i−i−i−iiiiii−i−i−i−i−iiiiii−1−i32−1+i32−1−i321+i321+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−ζ11ζ11−ζ11ζ11−ζ7ζ7−ζ7ζ7−1−i321+i32−1−i321+i32−ζ11ζ11−ζ11ζ11−1+i321−i32−1+i321−i32−ζ7ζ7−ζ7ζ7
χ3311-1-111-1-1−ii−ii1-11-1−ii−ii111-1-1-111-1-111-1-1111-1-1-1−i−i−i−i−iiiiii−i−i−i−i−iiiiii11111-1-1-1-1-111111-1-1-1-1-1−i−i−i−i−iiiiii−i−i−i−i−iiiiii−1+i32−1−i32−1+i321−i321−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−ζ7ζ7−ζ7ζ7−ζ11ζ11−ζ11ζ11−1+i321−i32−1+i321−i32−ζ7ζ7−ζ7ζ7−1−i321+i32−1−i321+i32−ζ11ζ11−ζ11ζ11
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.