Finite Group Databasebeta

← Group #72277787

Character table — Group #72277787

Order 8064.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116
size112336666666666666777714141616161618181818181818181818181818181818181818182121212132324242424242424242424242424242424242425656565656569696969696969696112112112112112112112112168168168168168168224224224224224224224224224224224224224224224224
order122222222222227141414336666336614141414141414141414141414141414141414146666666666666666666666662466121221214242424242423333666644121212126666666666121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111−1+i32−1−i32−1+i32−1−i32111111111111111111111111−1+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−i32111111−1+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
χ4111111111111111111111111−1+i32−1−i32−1+i32−1−i32111111111111111111111111−1+i32−1−i32111111111111111111-1-1-1-1-1-1−1+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−i32-1-1-1-1-1-11−i321+i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i321−i321+i321−i321−i321+i321+i32
χ5111111111111111111111111−1−i32−1+i32−1−i32−1+i32111111111111111111111111−1−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+i32111111−1−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
χ6111111111111111111111111−1−i32−1+i32−1−i32−1+i32111111111111111111111111−1−i32−1+i32111111111111111111-1-1-1-1-1-1−1−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+i32-1-1-1-1-1-11+i321−i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i321+i321−i321+i321+i321−i321−i32
χ7111111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32111111111111111111111111−1+i32−1+i32−1−i32−1−i3211−1+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−i3211−1+i32−1−i32−1+i32−1−i3211111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i3211−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211−1+i32−1−i32−1+i32−1−i32
χ8111111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32111111111111111111111111−1+i32−1+i32−1−i32−1−i3211−1+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−i32-1-11−i321+i321−i321+i3211111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-11−i321−i321+i321+i32-1-1−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i32-1-11−i321+i321−i321+i32
χ9111111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211111111111111111111−1+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−i3211−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i3211−1+i32−1−i3211−1+i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1−i3211−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i3211−1+i32
χ10111111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211111111111111111111−1+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−i32-1-11−i321+i321−i321+i32−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i3211−1+i32−1−i3211−1+i32-1-11−i321−i321+i321+i321−i321+i32−1−i3211−1+i321+i32-1-11−i321−i321+i321+i32-1-11−i32
χ11111111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i3211111111111111111111−1+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−i3211−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321−1+i32−1−i3211−1+i32−1−i32111−1+i32−1+i32−1−i32−1−i32−1−i32−1+i321−1+i32−1−i3211−1+i32−1−i321−1−i32−1+i321−1+i32−1−i321
χ12111111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i3211111111111111111111−1+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−i32-1-11−i321+i321−i321+i32−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321−1+i32−1−i3211−1+i32−1−i321-1-11−i321−i321+i321+i321+i321−i321−1+i32−1−i321-11−i321+i32-11+i321−i32-11−i321+i32-1
χ13111111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32111111111111111111111111−1−i32−1−i32−1+i32−1+i3211−1−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+i3211−1−i32−1+i32−1−i32−1+i3211111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i3211−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211−1−i32−1+i32−1−i32−1+i32
χ14111111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32111111111111111111111111−1−i32−1−i32−1+i32−1+i3211−1−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+i32-1-11+i321−i321+i321−i3211111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-11+i321+i321−i321−i32-1-1−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i32-1-11+i321−i321+i321−i32
χ15111111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i3211111111111111111111−1−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+i3211−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−1−i32−1+i3211−1−i32−1+i32111−1−i32−1−i32−1+i32−1+i32−1+i32−1−i321−1−i32−1+i3211−1−i32−1+i321−1+i32−1−i321−1−i32−1+i321
χ16111111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i3211111111111111111111−1−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+i32-1-11+i321−i321+i321−i32−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−1−i32−1+i3211−1−i32−1+i321-1-11+i321+i321−i321−i321−i321+i321−1−i32−1+i321-11+i321−i32-11−i321+i32-11+i321−i32-1
χ17111111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211111111111111111111−1−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+i3211−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i3211−1−i32−1+i3211−1−i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1+i3211−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i3211−1−i32
χ18111111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211111111111111111111−1−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+i32-1-11+i321−i321+i321−i32−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i3211−1−i32−1+i3211−1−i32-1-11+i321+i321−i321−i321+i321−i32−1+i3211−1−i321−i32-1-11+i321+i321−i321−i32-1-11+i32
χ1911-1111111-1-1-1-1-111-1-11111-1-111111111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-11111-1-1-1-1-11-111-1-1111-1-11-1-1111111111-11-11-111-1-1-1-11111-1-1-1-1-1-1
χ2011-1111111-1-1-1-1-111-1-11111-1-111111111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-11111-1-1-1-1-1-11-1-111111-1-11-1-111111111-11-11-11-1-1-1-1-1-1-1-1-1-1111111
χ2111-1111111-1-1-1-1-111-1-11111-1-1−1+i32−1−i32−1+i32−1−i321111111111-1-1-1-1-1-1-1-1-1-111111−i321+i321111-1-1-1-1-11111-1-1-1-1-11-111-1-1−1+i32−1−i32−1+i321−i321−i32−1−i321+i321+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321-11-11-1−1+i32−1−i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i321−i321+i321−i321−i321+i321+i32
χ2211-1111111-1-1-1-1-111-1-11111-1-1−1+i32−1−i32−1+i32−1−i321111111111-1-1-1-1-1-1-1-1-1-111111−i321+i321111-1-1-1-1-11111-1-1-1-1-1-11-1-111−1+i32−1−i32−1+i321−i321−i32−1−i321+i321+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32-11-11-111−i321+i321−i321−i321+i321+i321−i321−i321+i321+i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32
χ2311-1111111-1-1-1-1-111-1-11111-1-1−1−i32−1+i32−1−i32−1+i321111111111-1-1-1-1-1-1-1-1-1-111111+i321−i321111-1-1-1-1-11111-1-1-1-1-11-111-1-1−1−i32−1+i32−1−i321+i321+i32−1+i321−i321−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321-11-11-1−1−i32−1+i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i321+i321−i321+i321+i321−i321−i32
χ2411-1111111-1-1-1-1-111-1-11111-1-1−1−i32−1+i32−1−i32−1+i321111111111-1-1-1-1-1-1-1-1-1-111111+i321−i321111-1-1-1-1-11111-1-1-1-1-1-11-1-111−1−i32−1+i32−1−i321+i321+i32−1+i321−i321−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32-11-11-111+i321−i321+i321+i321−i321−i321+i321+i321−i321−i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32
χ2511-1111111-1-1-1-1-111-1-1−1+i32−1−i32−1+i32−1−i321−i321+i3211111111111111-1-1-1-1-1-1-1-1-1-1−1+i32−1+i32−1−i32−1−i32-1-1−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321-1−1+i32−1−i321−i321+i32111-1-11-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321-1−1+i321−i32−1−i321+i32111−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i32-1-11−i321+i321−i321+i32
χ2611-1111111-1-1-1-1-111-1-1−1+i32−1−i32−1+i32−1−i321−i321+i3211111111111111-1-1-1-1-1-1-1-1-1-1−1+i32−1+i32−1−i32−1−i32-1-1−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i32-111−i321+i32−1+i32−1−i32111-1-11-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-111−i32−1+i321+i32−1−i32-1-11−i321+i321−i321+i321−i321+i321−i321+i3211−1+i32−1−i32−1+i32−1−i32
χ2711-1111111-1-1-1-1-111-1-1−1+i32−1−i32−1+i32−1−i321−i321+i32−1+i32−1−i32−1+i32−1−i321111111111-1-1-1-1-1-1-1-1-1-1−1+i32−1+i32−1−i32−1−i321−i321+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321-1−1+i32−1−i321−i321+i32−1+i32−1−i32−1+i321−i321−i32−1−i321+i321+i32−1−i3211−1+i32−1−i3211−1+i321-1−1+i321−i32−1−i321+i32−1+i32−1−i321+i32-1-11−i32−1−i3211−1+i321−i321+i321+i32-1-11−i32
χ2811-1111111-1-1-1-1-111-1-1−1+i32−1−i32−1+i32−1−i321−i321+i32−1+i32−1−i32−1+i32−1−i321111111111-1-1-1-1-1-1-1-1-1-1−1+i32−1+i32−1−i32−1−i321−i321+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i32-111−i321+i32−1+i32−1−i32−1+i32−1−i32−1+i321−i321−i32−1−i321+i321+i32−1−i3211−1+i32−1−i3211−1+i32-111−i32−1+i321+i32−1−i321−i321+i321+i32-1-11−i321+i32-1-11−i32−1+i32−1−i32−1−i3211−1+i32
χ2911-1111111-1-1-1-1-111-1-1−1+i32−1−i32−1+i32−1−i321−i321+i32−1−i32−1+i32−1−i32−1+i321111111111-1-1-1-1-1-1-1-1-1-1−1+i32−1+i32−1−i32−1−i321+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321-1−1+i32−1−i321−i321+i32−1−i32−1+i32−1−i321+i321+i32−1+i321−i321−i321−1+i32−1−i3211−1+i32−1−i3211-1−1+i321−i32−1−i321+i32−1−i32−1+i32-11−i321+i32-11−1+i32−1−i3211+i321−i32-11−i321+i32-1
χ3011-1111111-1-1-1-1-111-1-1−1+i32−1−i32−1+i32−1−i321−i321+i32−1−i32−1+i32−1−i32−1+i321111111111-1-1-1-1-1-1-1-1-1-1−1+i32−1+i32−1−i32−1−i321+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i32-111−i321+i32−1+i32−1−i32−1−i32−1+i32−1−i321+i321+i32−1+i321−i321−i321−1+i32−1−i3211−1+i32−1−i321-111−i32−1+i321+i32−1−i321+i321−i32-11−i321+i32-1-11−i321+i32-1−1−i32−1+i321−1+i32−1−i321
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Here ζ is a primitive root of unity of order 21 (ζ21 = 1); i = ζ5.