Finite Group Databasebeta

← Group #72226456

Character table — Group #72226456

Order 6400.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162C163C164C165C166C167C168C169C170C171C172C173C174C175C176C177C178C179C180C181C182C183C184C185C186C187C188C189C190C191C192C193C194C195C196C197C198C199C200C201C202C203C204C205C206C207C208C209C210C211C212C213C214C215C216C217C218C219C220
size11112222224444444444444444444444444444444444444444444444444444888888888888888888888888888888888888888888888888888888888888888888888888888816161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161625252525505050505050100100100100200200200200200200200200200200200200200200200200200200200200
order1244222444224455555510101010101010101010101010101010101020202020202020202020202020202020202020202020202024441010101010101010101010101010101010101010101010101010101010101010101010102020202020202020202020202020202020202020202020202020202020202020202020201010101010101010101010102020202020202020202020202020202020202020202020202020202020202020202020202244222444224424444444444488888888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ511111111111111111111111111111111111111111111111111111111111111-1-1-1-1111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111111111111111111111111111111111-1-1-1-1111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111111111111111111111111111111111111111111111111111-1-1-1-1111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−iii−i−i−i−iii−i−iii
χ811111111111111111111111111111111111111111111111111111111111111-1-1-1-1111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−iii−i−iiiii−i−iii−i−i
χ91111111111-1-1-1-111111111111111111111111111111111111111111111111111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111
χ101111111111-1-1-1-111111111111111111111111111111111111111111111111111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1
χ111111111111-1-1-1-111111111111111111111111111111111111111111111111111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-111ii−i−i−i−iii−i−iiiii−i−i
χ121111111111-1-1-1-111111111111111111111111111111111111111111111111111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-111−i−iiiii−i−iii−i−i−i−iii
χ131111111111-1-1-1-1111111111111111111111111111111111111111111111111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1
χ141111111111-1-1-1-1111111111111111111111111111111111111111111111111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111
χ151111111111-1-1-1-1111111111111111111111111111111111111111111111111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1ii−i−i−i−iiiii−i−i−i−iii
χ161111111111-1-1-1-1111111111111111111111111111111111111111111111111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1−i−iiiii−i−i−i−iiiii−i−i
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χ2188-8−8i8i000000-444i−4i-2-23+5−2+25−2−253−5−2525−2525−5+55−500005+5−5−522−3−52−252+25−3+52i−2i2i−2i−4ζ3−4ζ7−2ζ11−2ζ194ζ3+4ζ7+2ζ11+2ζ194ζ11+4ζ19−4ζ11−4ζ194ζ3+4ζ7−4ζ3−4ζ7−2ζ3−2ζ7−4ζ11−4ζ192ζ3+2ζ7+4ζ11+4ζ192i5−2i52i5−2i54ζ3+4ζ7+6ζ11+6ζ19−4ζ3−4ζ7−6ζ11−6ζ190000−6ζ3−6ζ7−4ζ11−4ζ196ζ3+6ζ7+4ζ11+4ζ1900000000000000001+5−1−51−5−1+51+5−1−51−5−1+51−5−1+5-441−5−1+51−5−1+51+5−1−51+5−1−5-441+5−1−5000000000000−2ζ3−2ζ72ζ3+2ζ7−2ζ11−2ζ192ζ11+2ζ19−2ζ3−2ζ72ζ3+2ζ7−2ζ11−2ζ192ζ11+2ζ19−2ζ11−2ζ192ζ11+2ζ194i−4i−2ζ11−2ζ192ζ11+2ζ19−2ζ11−2ζ192ζ11+2ζ19−2ζ3−2ζ72ζ3+2ζ7−2ζ3−2ζ72ζ3+2ζ74i−4i−2ζ3−2ζ72ζ3+2ζ70000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ2198-8−8i8i000000-444i−4i-2-2−2−253+53−5−2+2525−25−252500−5+55−55+5−5−500222+25−3−5−3+52−252i−2i2i−2i4ζ3+4ζ7−4ζ3−4ζ7−4ζ3−4ζ7−2ζ11−2ζ194ζ3+4ζ7+2ζ11+2ζ19−2ζ3−2ζ7−4ζ11−4ζ192ζ3+2ζ7+4ζ11+4ζ194ζ11+4ζ19−4ζ11−4ζ19−2i52i52i5−2i5004ζ3+4ζ7+6ζ11+6ζ19−4ζ3−4ζ7−6ζ11−6ζ19−6ζ3−6ζ7−4ζ11−4ζ196ζ3+6ζ7+4ζ11+4ζ190000000000000000001−5−1+51+5−1−51+5−1−51−5−1+51+5−1−51+5−1−51−5−1+5-44-441+5−1−51−5−1+51−5−1+5000000000000−2ζ11−2ζ192ζ11+2ζ19−2ζ3−2ζ72ζ3+2ζ7−2ζ3−2ζ72ζ3+2ζ7−2ζ11−2ζ192ζ11+2ζ19−2ζ3−2ζ72ζ3+2ζ7−2ζ3−2ζ72ζ3+2ζ7−2ζ11−2ζ192ζ11+2ζ194i−4i4i−4i−2ζ3−2ζ72ζ3+2ζ7−2ζ11−2ζ192ζ11+2ζ19−2ζ11−2ζ192ζ11+2ζ190000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ2208-8−8i8i000000-444i−4i-2-2−2−253+53−5−2+25−252525−25005−5−5+5−5−55+500222+25−3−5−3+52−252i−2i2i−2i4ζ3+4ζ7−4ζ3−4ζ7−4ζ3−4ζ7−2ζ11−2ζ194ζ3+4ζ7+2ζ11+2ζ19−2ζ3−2ζ7−4ζ11−4ζ192ζ3+2ζ7+4ζ11+4ζ194ζ11+4ζ19−4ζ11−4ζ192i5−2i5−2i52i500−4ζ3−4ζ7−6ζ11−6ζ194ζ3+4ζ7+6ζ11+6ζ196ζ3+6ζ7+4ζ11+4ζ19−6ζ3−6ζ7−4ζ11−4ζ190000000000000000001+5−1−51−5−1+51−5−1+51+5−1−51+5−1−51+5−1−5-441−5−1+51+5−1−5-441−5−1+51−5−1+5000000000000−2ζ3−2ζ72ζ3+2ζ7−2ζ11−2ζ192ζ11+2ζ19−2ζ11−2ζ192ζ11+2ζ19−2ζ3−2ζ72ζ3+2ζ7−2ζ3−2ζ72ζ3+2ζ7−2ζ3−2ζ72ζ3+2ζ74i−4i−2ζ11−2ζ192ζ11+2ζ19−2ζ3−2ζ72ζ3+2ζ74i−4i−2ζ11−2ζ192ζ11+2ζ19−2ζ11−2ζ192ζ11+2ζ190000000000000000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 20 (ζ20 = 1); i = ζ5.