Finite Group Databasebeta

← Group #13167639

Character table — Group #13167639

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144
size111188889999181818181818181818181818111188889999181818181818181818181818111188889999181818181818181818181818111188889999181818181818181818181818111188889999181818181818181818181818111188889999181818181818181818181818
order122236662222444444444444366636666666121212121212121212121212366636666666121212121212121212121212222266662222444444444444666666666666121212121212121212121212666666666666121212121212121212121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ3111111111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1
χ4111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111
χ511-1-111-1-111-1-111-1-1ii−i−iii−i−i11-1-111-1-111-1-111-1-1ii−i−iii−i−i11-1-111-1-111-1-111-1-1ii−i−iii−i−i11-1-111-1-111-1-111-1-1ii−i−iii−i−i11-1-111-1-111-1-111-1-1ii−i−iii−i−i11-1-111-1-111-1-111-1-1ii−i−iii−i−i
χ611-1-111-1-111-1-111-1-1−i−iii−i−iii11-1-111-1-111-1-111-1-1−i−iii−i−iii11-1-111-1-111-1-111-1-1−i−iii−i−iii11-1-111-1-111-1-111-1-1−i−iii−i−iii11-1-111-1-111-1-111-1-1−i−iii−i−iii11-1-111-1-111-1-111-1-1−i−iii−i−iii
χ711-1-111-1-111-1-1-1-111ii−i−i−i−iii11-1-111-1-111-1-1-1-111ii−i−i−i−iii11-1-111-1-111-1-1-1-111ii−i−i−i−iii11-1-111-1-111-1-1-1-111ii−i−i−i−iii11-1-111-1-111-1-1-1-111ii−i−i−i−iii11-1-111-1-111-1-1-1-111ii−i−i−i−iii
χ811-1-111-1-111-1-1-1-111−i−iiiii−i−i11-1-111-1-111-1-1-1-111−i−iiiii−i−i11-1-111-1-111-1-1-1-111−i−iiiii−i−i11-1-111-1-111-1-1-1-111−i−iiiii−i−i11-1-111-1-111-1-1-1-111−i−iiiii−i−i11-1-111-1-111-1-1-1-111−i−iiiii−i−i
χ91-11-11-11-11-11-1i−ii−i1-11-1i−ii−i1-11-11-11-11-11-1i−ii−i1-11-1i−ii−i1-11-11-11-11-11-1i−ii−i1-11-1i−ii−i1-11-11-11-11-11-1i−ii−i1-11-1i−ii−i1-11-11-11-11-11-1i−ii−i1-11-1i−ii−i1-11-11-11-11-11-1i−ii−i1-11-1i−ii−i
χ101-11-11-11-11-11-1i−ii−i-11-11−ii−ii1-11-11-11-11-11-1i−ii−i-11-11−ii−ii1-11-11-11-11-11-1i−ii−i-11-11−ii−ii1-11-11-11-11-11-1i−ii−i-11-11−ii−ii1-11-11-11-11-11-1i−ii−i-11-11−ii−ii1-11-11-11-11-11-1i−ii−i-11-11−ii−ii
χ111-11-11-11-11-11-1−ii−ii1-11-1−ii−ii1-11-11-11-11-11-1−ii−ii1-11-1−ii−ii1-11-11-11-11-11-1−ii−ii1-11-1−ii−ii1-11-11-11-11-11-1−ii−ii1-11-1−ii−ii1-11-11-11-11-11-1−ii−ii1-11-1−ii−ii1-11-11-11-11-11-1−ii−ii1-11-1−ii−ii
χ121-11-11-11-11-11-1−ii−ii-11-11i−ii−i1-11-11-11-11-11-1−ii−ii-11-11i−ii−i1-11-11-11-11-11-1−ii−ii-11-11i−ii−i1-11-11-11-11-11-1−ii−ii-11-11i−ii−i1-11-11-11-11-11-1−ii−ii-11-11i−ii−i1-11-11-11-11-11-1−ii−ii-11-11i−ii−i
χ131-1-111-1-111-1-11i−i−iii−i−ii-111-11-1-111-1-111-1-11i−i−iii−i−ii-111-11-1-111-1-111-1-11i−i−iii−i−ii-111-11-1-111-1-111-1-11i−i−iii−i−ii-111-11-1-111-1-111-1-11i−i−iii−i−ii-111-11-1-111-1-111-1-11i−i−iii−i−ii-111-1
χ141-1-111-1-111-1-11i−i−ii−iii−i1-1-111-1-111-1-111-1-11i−i−ii−iii−i1-1-111-1-111-1-111-1-11i−i−ii−iii−i1-1-111-1-111-1-111-1-11i−i−ii−iii−i1-1-111-1-111-1-111-1-11i−i−ii−iii−i1-1-111-1-111-1-111-1-11i−i−ii−iii−i1-1-11
χ151-1-111-1-111-1-11−iii−ii−i−ii1-1-111-1-111-1-111-1-11−iii−ii−i−ii1-1-111-1-111-1-111-1-11−iii−ii−i−ii1-1-111-1-111-1-111-1-11−iii−ii−i−ii1-1-111-1-111-1-111-1-11−iii−ii−i−ii1-1-111-1-111-1-111-1-11−iii−ii−i−ii1-1-11
χ161-1-111-1-111-1-11−iii−i−iii−i-111-11-1-111-1-111-1-11−iii−i−iii−i-111-11-1-111-1-111-1-11−iii−i−iii−i-111-11-1-111-1-111-1-11−iii−i−iii−i-111-11-1-111-1-111-1-11−iii−i−iii−i-111-11-1-111-1-111-1-11−iii−i−iii−i-111-1
χ1722222222-2-2-2-200000000000022222222-2-2-2-200000000000022222222-2-2-2-200000000000022222222-2-2-2-200000000000022222222-2-2-2-200000000000022222222-2-2-2-2000000000000
χ1822-2-222-2-2-2-22200000000000022-2-222-2-2-2-22200000000000022-2-222-2-2-2-22200000000000022-2-222-2-2-2-22200000000000022-2-222-2-2-2-22200000000000022-2-222-2-2-2-222000000000000
χ192-22-22-22-2-22-220000000000002-22-22-22-2-22-220000000000002-22-22-22-2-22-220000000000002-22-22-22-2-22-220000000000002-22-22-22-2-22-220000000000002-22-22-22-2-22-22000000000000
χ202-2-222-2-22-222-20000000000002-2-222-2-22-222-20000000000002-2-222-2-22-222-20000000000002-2-222-2-22-222-20000000000002-2-222-2-22-222-20000000000002-2-222-2-22-222-2000000000000
χ218888-1-1-1-100000000000000008888-1-1-1-100000000000000008888-1-1-1-100000000000000008888-1-1-1-100000000000000008888-1-1-1-100000000000000008888-1-1-1-10000000000000000
χ2288-8-8-1-111000000000000000088-8-8-1-111000000000000000088-8-8-1-111000000000000000088-8-8-1-111000000000000000088-8-8-1-111000000000000000088-8-8-1-1110000000000000000
χ238-88-8-11-1100000000000000008-88-8-11-1100000000000000008-88-8-11-1100000000000000008-88-8-11-1100000000000000008-88-8-11-1100000000000000008-88-8-11-110000000000000000
χ248-8-88-111-100000000000000008-8-88-111-100000000000000008-8-88-111-100000000000000008-8-88-111-100000000000000008-8-88-111-100000000000000008-8-88-111-10000000000000000
χ25111111111111111111111111−1+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−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32111111111111111111111111−1+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−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32
χ261111111111111111-1-1-1-1-1-1-1-1−1+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−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+i321111111111111111-1-1-1-1-1-1-1-1−1+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−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
χ27111111111111-1-1-1-11111-1-1-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−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−i321+i321+i321+i321+i32111111111111-1-1-1-11111-1-1-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−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−i321+i321+i321+i321+i32
χ28111111111111-1-1-1-1-1-1-1-11111−1+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+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−i32111111111111-1-1-1-1-1-1-1-11111−1+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+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−i32
χ2911-1-111-1-111-1-111-1-1ii−i−iii−i−i−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32ζ7ζ7−ζ7−ζ7ζ7ζ7−ζ7−ζ7−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32ζ11ζ11−ζ11−ζ11ζ11ζ11−ζ11−ζ1111-1-111-1-111-1-111-1-1ii−i−iii−i−i−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32ζ7ζ7−ζ7−ζ7ζ7ζ7−ζ7−ζ7−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32ζ11ζ11−ζ11−ζ11ζ11ζ11−ζ11−ζ11
χ3011-1-111-1-111-1-111-1-1−i−iii−i−iii−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−ζ7−ζ7ζ7ζ7−ζ7−ζ7ζ7ζ7−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−ζ11−ζ11ζ11ζ11−ζ11−ζ11ζ11ζ1111-1-111-1-111-1-111-1-1−i−iii−i−iii−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−ζ7−ζ7ζ7ζ7−ζ7−ζ7ζ7ζ7−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−ζ11−ζ11ζ11ζ11−ζ11−ζ11ζ11ζ11
χ3111-1-111-1-111-1-1-1-111ii−i−i−i−iii−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32ζ7ζ7−ζ7−ζ7−ζ7−ζ7ζ7ζ7−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32ζ11ζ11−ζ11−ζ11−ζ11−ζ11ζ11ζ1111-1-111-1-111-1-1-1-111ii−i−i−i−iii−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32ζ7ζ7−ζ7−ζ7−ζ7−ζ7ζ7ζ7−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32ζ11ζ11−ζ11−ζ11−ζ11−ζ11ζ11ζ11
χ3211-1-111-1-111-1-1-1-111−i−iiiii−i−i−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−ζ7−ζ7ζ7ζ7ζ7ζ7−ζ7−ζ7−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−ζ11−ζ11ζ11ζ11ζ11ζ11−ζ11−ζ1111-1-111-1-111-1-1-1-111−i−iiiii−i−i−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−ζ7−ζ7ζ7ζ7ζ7ζ7−ζ7−ζ7−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−ζ11−ζ11ζ11ζ11ζ11ζ11−ζ11−ζ11
χ331-11-11-11-11-11-1i−ii−i1-11-1i−ii−i−1+i321−i32−1+i321−i32−1+i321−i32−1+i321−i32−1+i321−i32−1+i321−i32ζ7−ζ7ζ7−ζ7−1+i321−i32−1+i321−i32ζ7−ζ7ζ7−ζ7−1−i321+i32−1−i321+i32−1−i321+i32−1−i321+i32−1−i321+i32−1−i321+i32ζ11−ζ11ζ11−ζ11−1−i321+i32−1−i321+i32ζ11−ζ11ζ11−ζ111-11-11-11-11-11-1i−ii−i1-11-1i−ii−i−1+i321−i32−1+i321−i32−1+i321−i32−1+i321−i32−1+i321−i32−1+i321−i32ζ7−ζ7ζ7−ζ7−1+i321−i32−1+i321−i32ζ7−ζ7ζ7−ζ7−1−i321+i32−1−i321+i32−1−i321+i32−1−i321+i32−1−i321+i32−1−i321+i32ζ11−ζ11ζ11−ζ11−1−i321+i32−1−i321+i32ζ11−ζ11ζ11−ζ11
χ341-11-11-11-11-11-1i−ii−i-11-11−ii−ii−1+i321−i32−1+i321−i32−1+i321−i32−1+i321−i32−1+i321−i32−1+i321−i32ζ7−ζ7ζ7−ζ71−i32−1+i321−i32−1+i32−ζ7ζ7−ζ7ζ7−1−i321+i32−1−i321+i32−1−i321+i32−1−i321+i32−1−i321+i32−1−i321+i32ζ11−ζ11ζ11−ζ111+i32−1−i321+i32−1−i32−ζ11ζ11−ζ11ζ111-11-11-11-11-11-1i−ii−i-11-11−ii−ii−1+i321−i32−1+i321−i32−1+i321−i32−1+i321−i32−1+i321−i32−1+i321−i32ζ7−ζ7ζ7−ζ71−i32−1+i321−i32−1+i32−ζ7ζ7−ζ7ζ7−1−i321+i32−1−i321+i32−1−i321+i32−1−i321+i32−1−i321+i32−1−i321+i32ζ11−ζ11ζ11−ζ111+i32−1−i321+i32−1−i32−ζ11ζ11−ζ11ζ11
χ351-11-11-11-11-11-1−ii−ii1-11-1−ii−ii−1+i321−i32−1+i321−i32−1+i321−i32−1+i321−i32−1+i321−i32−1+i321−i32−ζ7ζ7−ζ7ζ7−1+i321−i32−1+i321−i32−ζ7ζ7−ζ7ζ7−1−i321+i32−1−i321+i32−1−i321+i32−1−i321+i32−1−i321+i32−1−i321+i32−ζ11ζ11−ζ11ζ11−1−i321+i32−1−i321+i32−ζ11ζ11−ζ11ζ111-11-11-11-11-11-1−ii−ii1-11-1−ii−ii−1+i321−i32−1+i321−i32−1+i321−i32−1+i321−i32−1+i321−i32−1+i321−i32−ζ7ζ7−ζ7ζ7−1+i321−i32−1+i321−i32−ζ7ζ7−ζ7ζ7−1−i321+i32−1−i321+i32−1−i321+i32−1−i321+i32−1−i321+i32−1−i321+i32−ζ11ζ11−ζ11ζ11−1−i321+i32−1−i321+i32−ζ11ζ11−ζ11ζ11
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χ1402-2-222-2-22-222-2000000000000−1−i31+i31+i3−1−i3−1−i31+i31+i3−1−i31+i3−1−i3−1−i31+i3000000000000−1+i31−i31−i3−1+i3−1+i31−i31−i3−1+i31−i3−1+i3−1+i31−i3000000000000-222-2-222-22-2-220000000000001+i3−1−i3−1−i31+i31+i3−1−i3−1−i31+i3−1−i31+i31+i3−1−i30000000000001−i3−1+i3−1+i31−i31−i3−1+i3−1+i31−i3−1+i31−i31−i3−1+i3000000000000
χ1418888-1-1-1-10000000000000000−4−4i3−4−4i3−4−4i3−4−4i31+i321+i321+i321+i320000000000000000−4+4i3−4+4i3−4+4i3−4+4i31−i321−i321−i321−i320000000000000000-8-8-8-8111100000000000000004+4i34+4i34+4i34+4i3−1−i32−1−i32−1−i32−1−i3200000000000000004−4i34−4i34−4i34−4i3−1+i32−1+i32−1+i32−1+i320000000000000000
χ14288-8-8-1-1110000000000000000−4−4i3−4−4i34+4i34+4i31+i321+i32−1−i32−1−i320000000000000000−4+4i3−4+4i34−4i34−4i31−i321−i32−1+i32−1+i320000000000000000-8-88811-1-100000000000000004+4i34+4i3−4−4i3−4−4i3−1−i32−1−i321+i321+i3200000000000000004−4i34−4i3−4+4i3−4+4i3−1+i32−1+i321−i321−i320000000000000000
χ1438-88-8-11-110000000000000000−4−4i34+4i3−4−4i34+4i31+i32−1−i321+i32−1−i320000000000000000−4+4i34−4i3−4+4i34−4i31−i32−1+i321−i32−1+i320000000000000000-88-881-11-100000000000000004+4i3−4−4i34+4i3−4−4i3−1−i321+i32−1−i321+i3200000000000000004−4i3−4+4i34−4i3−4+4i3−1+i321−i32−1+i321−i320000000000000000
χ1448-8-88-111-10000000000000000−4−4i34+4i34+4i3−4−4i31+i32−1−i32−1−i321+i320000000000000000−4+4i34−4i34−4i3−4+4i31−i32−1+i32−1+i321−i320000000000000000-888-81-1-1100000000000000004+4i3−4−4i3−4−4i34+4i3−1−i321+i321+i32−1−i3200000000000000004−4i3−4+4i3−4+4i34−4i3−1+i321−i321−i32−1+i320000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.