Finite Group Databasebeta

← Group #12026401

Character table — Group #12026401

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162C163C164C165C166C167C168C169C170C171C172C173C174C175C176
size11111111111111112222222222222222222222222222222222222222444444444444444444444444444444444444444444444444444444448888888888888888888888888888888888888888202020202020202020202020202020204040404040404040
order1222222222222222444444445510101010101010101010101010101010101010101010101010101010101044444444202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020444444442020202020202020202020202020202020202020202020202020202020202020444444444444444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-1
χ611111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-111
χ711111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-111-1-111
χ811111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111111111-1-1-1-111-1-111-1-1
χ91111111111111111-1-1-1-1-1-1-1-1111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111
χ101111111111111111-1-1-1-1-1-1-1-1111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1
χ111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ121111111111111111-1-1-1-1-1-1-1-1111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ131111111111111111-1-1-1-1-1-1-1-111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ141111111111111111-1-1-1-1-1-1-1-111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ151111111111111111-1-1-1-1-1-1-1-111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-11111-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ161111111111111111-1-1-1-1-1-1-1-111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-11111-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ17111-1-1-111-1-1-111-11-1iiii−i−i−i−i1111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1ii−i−i11-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i11111111-1-1-1-1-1-1-1-11-1i−ii−i1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-111-1-1ii−i−i11-1-1ii−i−i1-11-1i−ii−i
χ18111-1-1-111-1-1-111-11-1iiii−i−i−i−i1111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1ii−i−i11-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i11111111-1-1-1-1-1-1-1-11-1i−ii−i1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1-1-111−i−iii-1-111−i−iii-11-11−ii−ii
χ19111-1-1-111-1-1-111-11-1iiii−i−i−i−i1111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1ii−i−i11-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i11111111-1-1-1-1-1-1-1-1-11−ii−ii-11-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii-1-1-1-1111111-1-1ii−i−i11-1-1ii−i−i-11-11−ii−ii
χ20111-1-1-111-1-1-111-11-1iiii−i−i−i−i1111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1ii−i−i11-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i11111111-1-1-1-1-1-1-1-1-11−ii−ii-11-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111-1-111−i−iii-1-111−i−iii1-11-1i−ii−i
χ21111-1-1-111-1-1-111-11-1iiii−i−i−i−i1111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1−i−iii-1-111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1-1-1-1-1111111111-1−iii−i-111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii-1-1-1-1111111-1-1−i−iii-1-111ii−i−i1-1-11i−i−ii
χ22111-1-1-111-1-1-111-11-1iiii−i−i−i−i1111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1−i−iii-1-111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1-1-1-1-1111111111-1−iii−i-111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111-1-111ii−i−i11-1-1−i−iii-111-1−iii−i
χ23111-1-1-111-1-1-111-11-1iiii−i−i−i−i1111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1−i−iii-1-111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1-1-1-1-111111111-11i−i−ii1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-111-1-1−i−iii-1-111ii−i−i-111-1−iii−i
χ24111-1-1-111-1-1-111-11-1iiii−i−i−i−i1111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1−i−iii-1-111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1-1-1-1-111111111-11i−i−ii1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-1-111ii−i−i11-1-1−i−iii1-1-11i−i−ii
χ25111-1-1-111-1-1-111-11-1−i−i−i−iiiii1111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1ii−i−i-1-111−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1-1-1-1-1111111111-1i−i−ii-111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-1111111-1-1ii−i−i-1-111−i−iii1-1-11−iii−i
χ26111-1-1-111-1-1-111-11-1−i−i−i−iiiii1111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1ii−i−i-1-111−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1-1-1-1-1111111111-1i−i−ii-111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111-1-111−i−iii11-1-1ii−i−i-111-1i−i−ii
χ27111-1-1-111-1-1-111-11-1−i−i−i−iiiii1111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1ii−i−i-1-111−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1-1-1-1-111111111-11−iii−i1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-111-1-1ii−i−i-1-111−i−iii-111-1i−i−ii
χ28111-1-1-111-1-1-111-11-1−i−i−i−iiiii1111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1ii−i−i-1-111−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1-1-1-1-111111111-11−iii−i1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-1-111−i−iii11-1-1ii−i−i1-1-11−iii−i
χ29111-1-1-111-1-1-111-11-1−i−i−i−iiiii1111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1−i−iii11-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii11111111-1-1-1-1-1-1-1-11-1−ii−ii1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-111-1-1−i−iii11-1-1−i−iii1-11-1−ii−ii
χ30111-1-1-111-1-1-111-11-1−i−i−i−iiiii1111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1−i−iii11-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii11111111-1-1-1-1-1-1-1-11-1−ii−ii1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1-1-111ii−i−i-1-111ii−i−i-11-11i−ii−i
χ31111-1-1-111-1-1-111-11-1−i−i−i−iiiii1111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1−i−iii11-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii11111111-1-1-1-1-1-1-1-1-11i−ii−i-11-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i-1-1-1-1111111-1-1−i−iii11-1-1−i−iii-11-11i−ii−i
χ32111-1-1-111-1-1-111-11-1−i−i−i−iiiii1111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1−i−iii11-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii11111111-1-1-1-1-1-1-1-1-11i−ii−i-11-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111-1-111ii−i−i-1-111ii−i−i1-11-1−ii−ii
χ33222222222222222222222222−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−5222222222−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−5222222222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52000000000000000000000000
χ34222222222222222222222222−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−5222222222−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52-2-2-2-2-2-2-2-21−521−521+521+521−521−521+521+521−521−521+521+521−521−521+521+521−521−521+521+521−521−521+521+521−521−521+521+521−521−521+521+52000000000000000000000000
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χ36222222222222222222222222−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52-2-2-2-2-2-2-2-2−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−521−521−521−521−521+521+521+521+521−521−521−521−521+521+521+521+521−521−521−521−521+521+521+521+521−521−521−521−521+521+521+521+52-2-222-2-2221−521−521+521+521−521−521+521+521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52000000000000000000000000
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χ1714-4-4-4-444-444-4-4444-400000000−1−5−1+51+51+5−1−51+51−51−5−1+51−51+51+5−1−51+51−51−5−1+51−5−1−51+5−1−5−1+51−5−1+5−1−5−1−51+5−1−5−1+5−1+51−5−1+50000000000000000000000002ζ2−2ζ18−2ζ2+2ζ18−2ζ2+2ζ182ζ2−2ζ18−2ζ6+2ζ142ζ6−2ζ142ζ6−2ζ14−2ζ6+2ζ14−2ζ2+2ζ182ζ2−2ζ182ζ2−2ζ18−2ζ2+2ζ182ζ6−2ζ14−2ζ6+2ζ14−2ζ6+2ζ142ζ6−2ζ1400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1724-4-4-4-4-4444444-4-4-440000000044-4-4-44-4-4-44-4-4-44-4-4-4444-444-4444-4444-4000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1734-4-4-4-4-4444444-4-4-4400000000−1+5−1−51−51−51−5−1+51+51+51+5−1−51−51−51−5−1+51+51+51+5−1−5−1+5−1+51−5−1−5−1−51+5−1+5−1+5−1+51−5−1−5−1−5−1−51+50000000000000000000000002ζ6−2ζ14−2ζ6+2ζ142ζ6−2ζ14−2ζ6+2ζ142ζ2−2ζ18−2ζ2+2ζ182ζ2−2ζ18−2ζ2+2ζ18−2ζ6+2ζ142ζ6−2ζ14−2ζ6+2ζ142ζ6−2ζ14−2ζ2+2ζ182ζ2−2ζ18−2ζ2+2ζ182ζ2−2ζ1800000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1744-4-4-4-4-4444444-4-4-4400000000−1+5−1−51−51−51−5−1+51+51+51+5−1−51−51−51−5−1+51+51+51+5−1−5−1+5−1+51−5−1−5−1−51+5−1+5−1+5−1+51−5−1−5−1−5−1−51+5000000000000000000000000−2ζ6+2ζ142ζ6−2ζ14−2ζ6+2ζ142ζ6−2ζ14−2ζ2+2ζ182ζ2−2ζ18−2ζ2+2ζ182ζ2−2ζ182ζ6−2ζ14−2ζ6+2ζ142ζ6−2ζ14−2ζ6+2ζ142ζ2−2ζ18−2ζ2+2ζ182ζ2−2ζ18−2ζ2+2ζ1800000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1754-4-4-4-4-4444444-4-4-4400000000−1−5−1+51+51+51+5−1−51−51−51−5−1+51+51+51+5−1−51−51−51−5−1+5−1−5−1−51+5−1+5−1+51−5−1−5−1−5−1−51+5−1+5−1+5−1+51−5000000000000000000000000−2ζ2+2ζ182ζ2−2ζ18−2ζ2+2ζ182ζ2−2ζ182ζ6−2ζ14−2ζ6+2ζ142ζ6−2ζ14−2ζ6+2ζ142ζ2−2ζ18−2ζ2+2ζ182ζ2−2ζ18−2ζ2+2ζ18−2ζ6+2ζ142ζ6−2ζ14−2ζ6+2ζ142ζ6−2ζ1400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1764-4-4-4-4-4444444-4-4-4400000000−1−5−1+51+51+51+5−1−51−51−51−5−1+51+51+51+5−1−51−51−51−5−1+5−1−5−1−51+5−1+5−1+51−5−1−5−1−5−1−51+5−1+5−1+5−1+51−50000000000000000000000002ζ2−2ζ18−2ζ2+2ζ182ζ2−2ζ18−2ζ2+2ζ18−2ζ6+2ζ142ζ6−2ζ14−2ζ6+2ζ142ζ6−2ζ14−2ζ2+2ζ182ζ2−2ζ18−2ζ2+2ζ182ζ2−2ζ182ζ6−2ζ14−2ζ6+2ζ142ζ6−2ζ14−2ζ6+2ζ1400000000000000000000000000000000000000000000000000000000000000000000000000000000

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