Finite Group Databasebeta

← Group #13140721

Character table — Group #13140721

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129
size11112222222222222222222222444444444444444444444444448888888888888888888888888888888888812121212121212121212121212121212121212122424242424242424363636363636363654547272108216
order12223344666666999181818181818181818366699912121212181818181818181818363636363636412121212121212121212363636363636363636363636363636363636363636363636448824242424727272727272727272727272121236363636363644882424242444121224
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ51111111111111111111111111111111111111111111111111111-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111111-1
χ61111111111111111111111111111111111111111111111111111-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-1-1-1-11
χ71111111111111111111111111111111111111111111111111111-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-11
χ81111111111111111111111111111111111111111111111111111-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-11-1
χ922222222222222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-100000000000000
χ1022222222222222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2111111111111-2-211111100000000000000
χ1122222222222222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-222-2-2-2-2111111-1-1-1-1-1-111111111111122-2-2-2-2-2-211111111111122-1-1-1-1-1-100000000000000
χ1222222222222222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-222-2-2-2-2111111-1-1-1-1-1-1111111111111-2-2222222-1-1-1-1-1-1-1-1-1-1-1-1-2-211111100000000000000
χ13222222-2-22222222222222222222222222-2-2-2-2222222222-2-2-2-2-2-200000-2-20000000000-2-2-2-2-2-20000000000000000000000000000000000000000000000002200-20
χ14222222-2-22222222222222222222222222-2-2-2-2222222222-2-2-2-2-2-200000-2-20000000000-2-2-2-2-2-2000000000000000000000000000000000000000000000000-2-20020
χ1522222-1222-12-1-12ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68-1-1-1-1ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ682-1-12ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ4−ζ44+ζ52−ζ4−ζ68−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68222-1-1-1-1-1-1-1-1ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ4−ζ44+ζ52−ζ4−ζ68−ζ4−ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ4−ζ44+ζ52−ζ4−ζ68−ζ4−ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ4−ζ44+ζ52ζ4−ζ44+ζ52ζ4−ζ44+ζ52−ζ4−ζ68−ζ4−ζ68−ζ4−ζ68−ζ4−ζ682222-1-1-1-1ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ4−ζ44+ζ52ζ4−ζ44+ζ52ζ4−ζ44+ζ52−ζ4−ζ68−ζ4−ζ68−ζ4−ζ68−ζ4−ζ68-1-1ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ4−ζ44+ζ52−ζ4−ζ68−ζ4−ζ6800000000000000
χ1622222-1222-12-1-12ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68-1-1-1-1ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ682-1-12ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ4−ζ44+ζ52−ζ4−ζ68−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68222-1-1-1-1-1-1-1-1ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ4−ζ44+ζ52−ζ4−ζ68−ζ4−ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ4−ζ44+ζ52−ζ4−ζ68−ζ4−ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ4−ζ44+ζ52ζ4−ζ44+ζ52ζ4−ζ44+ζ52−ζ4−ζ68−ζ4−ζ68−ζ4−ζ68−ζ4−ζ68-2-2-2-21111−ζ44+ζ52−ζ68−ζ44+ζ52−ζ68−ζ44+ζ52−ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52−ζ4+ζ44−ζ52−ζ4+ζ44−ζ52−ζ4+ζ44−ζ52ζ4+ζ68ζ4+ζ68ζ4+ζ68ζ4+ζ6811−ζ44+ζ52−ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52−ζ4+ζ44−ζ52ζ4+ζ68ζ4+ζ6800000000000000
χ1722222-1222-12-1-12ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68-1-1-1-1ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ682-1-12ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ4−ζ44+ζ52−ζ4−ζ68−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68-2-2-211-1-11111−ζ44+ζ52−ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52−ζ4+ζ44−ζ52ζ4+ζ68ζ4+ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ4−ζ44+ζ52−ζ4−ζ68−ζ4−ζ68−ζ44+ζ52−ζ68−ζ44+ζ52−ζ68−ζ44+ζ52−ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52−ζ4+ζ44−ζ52−ζ4+ζ44−ζ52−ζ4+ζ44−ζ52ζ4+ζ68ζ4+ζ68ζ4+ζ68ζ4+ζ6822-2-21111−ζ44+ζ52−ζ68−ζ44+ζ52−ζ68−ζ44+ζ52−ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52−ζ4+ζ44−ζ52−ζ4+ζ44−ζ52−ζ4+ζ44−ζ52ζ4+ζ68ζ4+ζ68ζ4+ζ68ζ4+ζ68-1-1ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ4−ζ44+ζ52−ζ4−ζ68−ζ4−ζ6800000000000000
χ1822222-1222-12-1-12ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68-1-1-1-1ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ682-1-12ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ4−ζ44+ζ52−ζ4−ζ68−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68-2-2-211-1-11111−ζ44+ζ52−ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52−ζ4+ζ44−ζ52ζ4+ζ68ζ4+ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ4−ζ44+ζ52−ζ4−ζ68−ζ4−ζ68−ζ44+ζ52−ζ68−ζ44+ζ52−ζ68−ζ44+ζ52−ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52−ζ4+ζ44−ζ52−ζ4+ζ44−ζ52−ζ4+ζ44−ζ52ζ4+ζ68ζ4+ζ68ζ4+ζ68ζ4+ζ68-2-222-1-1-1-1ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ4−ζ44+ζ52ζ4−ζ44+ζ52ζ4−ζ44+ζ52−ζ4−ζ68−ζ4−ζ68−ζ4−ζ68−ζ4−ζ6811−ζ44+ζ52−ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52−ζ4+ζ44−ζ52ζ4+ζ68ζ4+ζ6800000000000000
χ1922222-1222-12-1-12ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68-1-1-1-1ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ682-1-12ζ4−ζ44+ζ52ζ4−ζ44+ζ52−ζ4−ζ68−ζ4−ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68222-1-1-1-1-1-1-1-1ζ4−ζ44+ζ52ζ4−ζ44+ζ52−ζ4−ζ68−ζ4−ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ4−ζ44+ζ52−ζ4−ζ68−ζ4−ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ4−ζ44+ζ52ζ4−ζ44+ζ52ζ4−ζ44+ζ52−ζ4−ζ68−ζ4−ζ68−ζ4−ζ68−ζ4−ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ682222-1-1-1-1ζ4−ζ44+ζ52ζ4−ζ44+ζ52ζ4−ζ44+ζ52ζ4−ζ44+ζ52−ζ4−ζ68−ζ4−ζ68−ζ4−ζ68−ζ4−ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68-1-1ζ4−ζ44+ζ52ζ4−ζ44+ζ52−ζ4−ζ68−ζ4−ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ6800000000000000
χ2022222-1222-12-1-12ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68-1-1-1-1ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ682-1-12ζ4−ζ44+ζ52ζ4−ζ44+ζ52−ζ4−ζ68−ζ4−ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68222-1-1-1-1-1-1-1-1ζ4−ζ44+ζ52ζ4−ζ44+ζ52−ζ4−ζ68−ζ4−ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ4−ζ44+ζ52−ζ4−ζ68−ζ4−ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ4−ζ44+ζ52ζ4−ζ44+ζ52ζ4−ζ44+ζ52−ζ4−ζ68−ζ4−ζ68−ζ4−ζ68−ζ4−ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68-2-2-2-21111−ζ4+ζ44−ζ52−ζ4+ζ44−ζ52−ζ4+ζ44−ζ52−ζ4+ζ44−ζ52ζ4+ζ68ζ4+ζ68ζ4+ζ68ζ4+ζ68−ζ44+ζ52−ζ68−ζ44+ζ52−ζ68−ζ44+ζ52−ζ68−ζ44+ζ52−ζ6811−ζ4+ζ44−ζ52−ζ4+ζ44−ζ52ζ4+ζ68ζ4+ζ68−ζ44+ζ52−ζ68−ζ44+ζ52−ζ6800000000000000
χ2122222-1222-12-1-12ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68-1-1-1-1ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ682-1-12ζ4−ζ44+ζ52ζ4−ζ44+ζ52−ζ4−ζ68−ζ4−ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68-2-2-211-1-11111−ζ4+ζ44−ζ52−ζ4+ζ44−ζ52ζ4+ζ68ζ4+ζ68−ζ44+ζ52−ζ68−ζ44+ζ52−ζ68ζ4−ζ44+ζ52ζ4−ζ44+ζ52−ζ4−ζ68−ζ4−ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68−ζ4+ζ44−ζ52−ζ4+ζ44−ζ52−ζ4+ζ44−ζ52−ζ4+ζ44−ζ52ζ4+ζ68ζ4+ζ68ζ4+ζ68ζ4+ζ68−ζ44+ζ52−ζ68−ζ44+ζ52−ζ68−ζ44+ζ52−ζ68−ζ44+ζ52−ζ6822-2-21111−ζ4+ζ44−ζ52−ζ4+ζ44−ζ52−ζ4+ζ44−ζ52−ζ4+ζ44−ζ52ζ4+ζ68ζ4+ζ68ζ4+ζ68ζ4+ζ68−ζ44+ζ52−ζ68−ζ44+ζ52−ζ68−ζ44+ζ52−ζ68−ζ44+ζ52−ζ68-1-1ζ4−ζ44+ζ52ζ4−ζ44+ζ52−ζ4−ζ68−ζ4−ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ6800000000000000
χ2222222-1222-12-1-12ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68-1-1-1-1ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ682-1-12ζ4−ζ44+ζ52ζ4−ζ44+ζ52−ζ4−ζ68−ζ4−ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68-2-2-211-1-11111−ζ4+ζ44−ζ52−ζ4+ζ44−ζ52ζ4+ζ68ζ4+ζ68−ζ44+ζ52−ζ68−ζ44+ζ52−ζ68ζ4−ζ44+ζ52ζ4−ζ44+ζ52−ζ4−ζ68−ζ4−ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68−ζ4+ζ44−ζ52−ζ4+ζ44−ζ52−ζ4+ζ44−ζ52−ζ4+ζ44−ζ52ζ4+ζ68ζ4+ζ68ζ4+ζ68ζ4+ζ68−ζ44+ζ52−ζ68−ζ44+ζ52−ζ68−ζ44+ζ52−ζ68−ζ44+ζ52−ζ68-2-222-1-1-1-1ζ4−ζ44+ζ52ζ4−ζ44+ζ52ζ4−ζ44+ζ52ζ4−ζ44+ζ52−ζ4−ζ68−ζ4−ζ68−ζ4−ζ68−ζ4−ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ6811−ζ4+ζ44−ζ52−ζ4+ζ44−ζ52ζ4+ζ68ζ4+ζ68−ζ44+ζ52−ζ68−ζ44+ζ52−ζ6800000000000000
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Here ζ is a primitive root of unity of order 72 (ζ72 = 1); i = ζ18.