Finite Group Databasebeta

← Group #12996180

Character table — Group #12996180

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107
size11112222222222444444444444444444888888888888888888888888888888888888101016161616161616161616161616161616202020202020202020202040404040404040404040
order1222445510101010101022444444881010101020202020444444488810102020202020202020202020202020202040404040404040404420202020202020202020202040404040244444444882244444888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111-1-11111111111-1-1-11-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1111111111-1-11-1-111-1-1-1-1-1
χ41111111111111111111111-1-11111111111-1-1-11-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-111111
χ5111111111111111111-1-1111111111111-1-1-1-1-1-1-1111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111111-1-1-1-1-1-1-1111
χ6111111111111111111-1-1111111111111-1-1-1-1-1-1-1111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-11111111-1-1-1
χ7111111111111111111-1-111-1-111111111-1-1111-11-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1-1-11111-1-1111-1-1-111-1-111-1-1-1
χ8111111111111111111-1-111-1-111111111-1-1111-11-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1111-1-111-1-1111
χ9111111111111111-11-111-1-111111111111-1-111-1-1-11-1-1-1-1-1-1-1111111-1-111111111111111-1-111-1-111-1-1-1-1-1-1-1-111-1-1-1-11-1-11111-11-11-11-1-1
χ10111111111111111-11-111-1-111111111111-1-111-1-1-11-1-1-1-1-1-1-1111111-1-1111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-111-1-1-1-11-11-11-111
χ11111111111111111-11-111-1-1-1-1111111111-11-1-1-111-11-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-111111111-1-1-1-11-1-1-1-11-111-1-11-111
χ12111111111111111-11-111-1-1-1-1111111111-11-1-1-111-11-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-11111-11111-11-1-111-11-1-1
χ13111111111111111-11-1-1-1-1-11111111111-111-1-111-11-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111111111-1-111-1-11111-1-1-1-111-1-1111-1-111-1-11-11-111-1-1
χ14111111111111111-11-1-1-1-1-11111111111-111-1-111-11-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-111-1-111-1-11111-1-1-1-1-1-111-1-1-111-1-111-11-11-1-111
χ15111111111111111-11-1-1-1-1-1-1-111111111-11-1111-11-11-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1111111-1-1111-1-1-1-1-11-1-111-1-111
χ16111111111111111-11-1-1-1-1-1-1-111111111-11-1111-11-11-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-111-1-1-111111-111-1-111-1-1
χ1711111111111111-11-1111-1-111-1-1-1-11111-1111-1-1-11-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-111-1-1-1-1111111-1-11-11-1-1-1-11-1111-1-1-1111-11-1
χ1811111111111111-11-1111-1-111-1-1-1-11111-1111-1-1-11-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-11-11111-11-1-1-1111-1-1-11-11
χ1911111111111111-11-1111-1-1-1-1-1-1-1-11111-11-1-11-11-11111-1-1-1-11111-1-1111111-1-1-1-1111111-1-1-1-111-1-111-1-1-1-1111-11-1-1-1-11-1-1-1111-11-1-11-11
χ2011111111111111-11-1111-1-1-1-1-1-1-1-11111-11-1-11-11-11111-1-1-1-11111-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-111-11-11111-1111-1-1-11-111-11-1
χ2111111111111111-11-11-1-1-1-111-1-1-1-111111-1-1-11111-1-111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-111-1-11-11-111-11-111-1111-1-1-1-11-1
χ2211111111111111-11-11-1-1-1-111-1-1-1-111111-1-1-11111-1-111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1-1-111-1-1-11-11-1-11-11-1-11-1-1-11111-11
χ2311111111111111-11-11-1-1-1-1-1-1-1-1-1-111111-111-11-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-111-1-111-1-1111-11-111-11-1-1-1-1-1-11-1111-11
χ2411111111111111-11-11-1-1-1-1-1-1-1-1-1-111111-111-11-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111-1-111-1-111-1-111-11-11-1-11-1111111-11-1-1-11-1
χ2511111111111111-1-1-1-1111111-1-1-1-11111-1-1-11-111-1-11-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1111-1-1111-1-11111-11-1-11-1-1-11
χ2611111111111111-1-1-1-1111111-1-1-1-11111-1-1-11-111-1-11-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-111-1-1-111-1-1-1-11-111-1111-1
χ2711111111111111-1-1-1-11111-1-1-1-1-1-11111-1-11-111-111-1-1-111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11-1-1111-1-11-1-111-1-1-1-1111-1
χ2811111111111111-1-1-1-11111-1-1-1-1-1-11111-1-11-111-111-1-1-111111111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111-1-1-111-1-1-111-111-1-11111-1-1-11
χ2911111111111111-1-1-1-1-1-11111-1-1-1-11111111-11-1-1-1-11-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1111111-1-1111-1-11-1-1-1-1111-11-111-11-1-11
χ3011111111111111-1-1-1-1-1-11111-1-1-1-11111111-11-1-1-1-11-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-111-11111-1-1-11-11-1-11-111-1
χ3111111111111111-1-1-1-1-1-111-1-1-1-1-1-1111111-11-1-1111-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111111111-1-111-1-11-1-11-1-1-1-11-1-1-1-11111-111-1
χ3211111111111111-1-1-1-1-1-111-1-1-1-1-1-1111111-11-1-1111-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-111-1-1-111-11111-11111-1-1-1-11-1-11
χ33222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−522222222222−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−522222222222−1+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+52−1−52−1−5200−1+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+52−1−52000000000000000000000
χ34222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−5222222222-2-2−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−5222-2-2-22-2-2-2-2−1+52−1−52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+5200−1+52−1−521−521+521−521+52−1+52−1−52−1+52−1−521−521+521−521+521−521+52000000000000000000000
χ35222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−522222-2-22222−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−52-2-2-2-2-2-2-2222−1+52−1−52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1−52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52001−521+521−521+521−521+521−521+521−521+521−521+52−1+52−1−52−1+52−1−52000000000000000000000
χ36222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−522222-2-222-2-2−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−52-2-2222-22-2-2-2−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−521−521−521+521+521−521−521+521+521−521−521+521+52001−521+52−1+52−1−52−1+52−1−521−521+521−521+52−1+52−1−521−521+521−521+52000000000000000000000
χ37222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−522-22-222-2-222−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−522-2-222-2-2-22-21−521+521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1−521−521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52001−521+52−1+52−1−521−521+52−1+52−1−521−521+521−521+521−521+521−521+52000000000000000000000
χ38222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−522-22-222-2-2-2-2−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−522-22-2-2-222-221−521+521−521−521+521+521−521−521+521+52−1+52−1−521−521+52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+52001−521+521−521+52−1+52−1−52−1+52−1−521−521+52−1+52−1−52−1+52−1−52−1+52−1−52000000000000000000000
χ39222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−522-22-2-2-2-2-222−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−52-222-2-222-22-21−521+521−521−521+521+521−521−521+521+52−1+52−1−521−521+521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5200−1+52−1−521−521+52−1+52−1−521−521+52−1+52−1−52−1+52−1−521−521+521−521+52000000000000000000000
χ40222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−522-22-2-2-2-2-2-2-2−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−52-22-2222-22-221−521+521−521−521+521+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+5200−1+52−1−52−1+52−1−521−521+521−521+52−1+52−1−521−521+52−1+52−1−52−1+52−1−52000000000000000000000
χ41222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-22-2222-2-2221−521−521+521+52−1+52−1−52−1+52−1−52-2222-2-2-22-2-2−1+52−1−521−521−521+521+521−521−521+521+521−521+52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521+521+52001−521+52−1+52−1−521−521+521−521+52−1+52−1−52−1+52−1−52−1+52−1−521−521+52000000000000000000000
χ42222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-22-2222-2-2-2-21−521−521+521+52−1+52−1−52−1+52−1−52-22-2-22-22-222−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521+52−1+52−1−52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−52001−521+521−521+52−1+52−1−521−521+52−1+52−1−521−521+521−521+52−1+52−1−52000000000000000000000
χ43222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-22-22-2-2-2-2221−521−521+521+52−1+52−1−52−1+52−1−522-2-2-22222-2-2−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521+52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+5200−1+52−1−521−521+52−1+52−1−52−1+52−1−521−521+521−521+52−1+52−1−521−521+52000000000000000000000
χ44222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-22-22-2-2-2-2-2-21−521−521+521+52−1+52−1−52−1+52−1−522-222-22-2-222−1+52−1−521−521−521+521+521−521−521+521+521−521+52−1+52−1−521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−5200−1+52−1−52−1+52−1−521−521+52−1+52−1−521−521+52−1+52−1−521−521+52−1+52−1−52000000000000000000000
χ45222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-2-2-2-22222221−521−521+521+52−1+52−1−52−1+52−1−52-2-2-22-222-2-221−521+52−1+52−1+52−1−52−1−521−521−521+521+521−521+521−521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521+521+5200−1+52−1−52−1+52−1−52−1+52−1−521−521+521−521+521−521+521−521+52−1+52−1−52000000000000000000000
χ46222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-2-2-2-22222-2-21−521−521+521+52−1+52−1−52−1+52−1−52-2-22-222-222-21−521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521+521−521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−5200−1+52−1−521−521+521−521+521−521+521−521+52−1+52−1−52−1+52−1−521−521+52000000000000000000000
χ47222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-2-2-2-2-2-222221−521−521+521+52−1+52−1−52−1+52−1−52222-22-2-2-2-221−521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521+521−521+521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52001−521+521−521+521−521+52−1+52−1−52−1+52−1−52−1+52−1−521−521+52−1+52−1−52000000000000000000000
χ48222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-2-2-2-2-2-222-2-21−521−521+521+52−1+52−1−52−1+52−1−5222-22-2-2222-21−521+52−1+52−1+52−1−52−1−521−521−521+521+521−521+521−521+521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−52001−521+52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−521−521+52−1+52−1−521−521+52000000000000000000000
χ49222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+522222222222−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+522222222222−1−52−1+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+5200−1−52−1+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+52000000000000000000000
χ50222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+5222222222-2-2−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+5222-2-2-22-2-2-2-2−1−52−1+52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−5200−1−52−1+521+521−521+521−52−1−52−1+52−1−52−1+521+521−521+521−521+521−52000000000000000000000
χ51222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+522222-2-22222−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+52-2-2-2-2-2-2-2222−1−52−1+52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1+52−1−52−1+521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52001+521−521+521−521+521−521+521−521+521−521+521−52−1−52−1+52−1−52−1+52000000000000000000000
χ52222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+522222-2-222-2-2−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+52-2-2222-22-2-2-2−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+521+521+521−521−521+521+521−521−521+521+521−521−52001+521−52−1−52−1+52−1−52−1+521+521−521+521−52−1−52−1+521+521−521+521−52000000000000000000000
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χ60222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52-22-22-2-2-2-2-2-21+521+521−521−52−1−52−1+52−1−52−1+522-222-22-2-222−1−52−1+521+521+521−521−521+521+521−521−521+521−52−1−52−1+521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+5200−1−52−1+52−1−52−1+521+521−52−1−52−1+521+521−52−1−52−1+521+521−52−1−52−1+52000000000000000000000
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χ734444-4-4−1+5−1−5−1+5−1+5−1−5−1−5−1+5−1−544-4-4004-400−1+5−1+5−1−5−1−51−51+51−51+50000000000−1+5−1−5−1+51−5−1−51+500001−51+51−51+5000000000000000000000000000000000000000000000000000
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χ9788-8-8-88−2+25−2−252−252−252+252+25−2+25−2−25000000000000002−252+25−2+25−2−25000000000000000000000000000000000000000000000000000000000000000000000000000
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χ1008-88-800−2+25−2−252−25−2+252+25−2−252−252+2500000000004ζ12−4ζ28−4ζ12+4ζ28−4ζ4+4ζ364ζ4−4ζ360000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1018-88-800−2+25−2−252−25−2+252+25−2−252−252+250000000000−4ζ12+4ζ284ζ12−4ζ284ζ4−4ζ36−4ζ4+4ζ360000000000000000000000000000000000000000000000000000000000000000000000000000000
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χ1048-8-8800−2+25−2−25−2+252−25−2−252+252−252+250000000042−42000000000000000000000000000000000000−2ζ7+2ζ13−2ζ23+2ζ372ζ7−2ζ13+2ζ23−2ζ372ζ21+2ζ29−2ζ31−2ζ39−2ζ21−2ζ29+2ζ31+2ζ390000000000000000000000000000000000000000000
χ1058-8-8800−2+25−2−25−2+252−25−2−252+252−252+2500000000−42420000000000000000000000000000000000002ζ7−2ζ13+2ζ23−2ζ37−2ζ7+2ζ13−2ζ23+2ζ37−2ζ21−2ζ29+2ζ31+2ζ392ζ21+2ζ29−2ζ31−2ζ390000000000000000000000000000000000000000000
χ1068-8-8800−2−25−2+25−2−252+25−2+252−252+252−250000000042−420000000000000000000000000000000000002ζ21+2ζ29−2ζ31−2ζ39−2ζ21−2ζ29+2ζ31+2ζ39−2ζ7+2ζ13−2ζ23+2ζ372ζ7−2ζ13+2ζ23−2ζ370000000000000000000000000000000000000000000
χ1078-8-8800−2−25−2+25−2−252+25−2+252−252+252−2500000000−4242000000000000000000000000000000000000−2ζ21−2ζ29+2ζ31+2ζ392ζ21+2ζ29−2ζ31−2ζ392ζ7−2ζ13+2ζ23−2ζ37−2ζ7+2ζ13−2ζ23+2ζ370000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 40 (ζ40 = 1); i = ζ10.