Finite Group Databasebeta

← Group #11722559

Character table — Group #11722559

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91
size1111112222222223333666666666666666666666666666666666666666666121212121212121212121212242424242424242424242424242424242424
order12336622466661212991818244466121212121212181818181818181818183636363636363636363636363636363636363636336699991818181866661212181818181818181836363636
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111−1+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−i32−1−i32−1+i32−1+i32−1−i32−1−i32
χ31111111111111111111111111111111111111111111111111111111111111−1−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+i32−1+i32−1−i32−1−i32−1+i32−1+i32
χ4111111111111111−1+i32−1−i32−1+i32−1−i32111111111111−1+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−i32−1−i32−1−i32−1−i32−1−i32−1−i321111−1+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
χ5111111111111111−1+i32−1−i32−1+i32−1−i32111111111111−1+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−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+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1−i32−1−i321111−1+i32−1+i32−1−i3211−1+i32
χ6111111111111111−1+i32−1−i32−1+i32−1−i32111111111111−1+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−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−i321−1−i32−1−i32−1+i32−1+i32−1−i32−1+i3211−1+i32−1+i32−1−i32−1−i32111−1+i32−1−i321
χ7111111111111111−1−i32−1+i32−1−i32−1+i32111111111111−1−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+i32−1+i32−1+i32−1+i32−1+i32−1+i321111−1−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
χ8111111111111111−1−i32−1+i32−1−i32−1+i32111111111111−1−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+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+i321−1+i32−1+i32−1−i32−1−i32−1+i32−1−i3211−1−i32−1−i32−1+i32−1+i32111−1−i32−1+i321
χ9111111111111111−1−i32−1+i32−1−i32−1+i32111111111111−1−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+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−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1+i32−1+i321111−1−i32−1−i32−1+i3211−1−i32
χ101111111-1-111-1-1-1-11111-111-1-1-11111-1-11-1-1-1-11-1-1-1-1111111-1-1-1-1111111-1-1-1-11111111111111-11-1-1-11-11-11-11-1-1-1-1-1
χ111111111-1-111-1-1-1-11111-111-1-1-11111-1-11-1-1-1-11-1-1-1-1111111-1-1-1-1111111-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i321−i32−1−i321+i321−i321+i32−1+i321−i32−1+i321−i32−1−i321+i32−1−i321+i321−i321−i321+i321+i32
χ121111111-1-111-1-1-1-11111-111-1-1-11111-1-11-1-1-1-11-1-1-1-1111111-1-1-1-1111111-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i321+i32−1+i321−i321+i321−i32−1−i321+i32−1−i321+i32−1+i321−i32−1+i321−i321+i321+i321−i321−i32
χ131111111-1-111-1-1-1-1−1+i32−1−i32−1+i32−1−i32-111-1-1-11111-1-1−1+i321−i321−i321−i321−i32−1−i321+i321+i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321-11-1-1-1−1+i321−i32−1−i321+i32−1+i321−i32−1−i321+i321−i321+i321−i321+i32
χ141111111-1-111-1-1-1-1−1+i32−1−i32−1+i32−1−i32-111-1-1-11111-1-1−1+i321−i321−i321−i321−i32−1−i321+i321+i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1−i32−1+i32−1−i32−1−i3211−1+i32−1−i3211−1+i32−1+i321−i32−1−i321+i321−i321+i32−1−i321+i321-11-1−1+i321−i321+i32-1-11−i32
χ151111111-1-111-1-1-1-1−1+i32−1−i32−1+i32−1−i32-111-1-1-11111-1-1−1+i321−i321−i321−i321−i32−1−i321+i321+i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1+i32−1−i32−1+i321−1+i32−1−i3211−1+i32−1−i321−1−i321+i32−1+i321−i321+i321−i321-1−1+i321−i32−1−i321+i321-1-11−i321+i32-1
χ161111111-1-111-1-1-1-1−1−i32−1+i32−1−i32−1+i32-111-1-1-11111-1-1−1−i321+i321+i321+i321+i32−1+i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321-11-1-1-1−1−i321+i32−1+i321−i32−1−i321+i32−1+i321−i321+i321−i321+i321−i32
χ171111111-1-111-1-1-1-1−1−i32−1+i32−1−i32−1+i32-111-1-1-11111-1-1−1−i321+i321+i321+i321+i32−1+i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1−i32−1+i32−1−i321−1−i32−1+i3211−1−i32−1+i321−1+i321−i32−1−i321+i321−i321+i321-1−1−i321+i32−1+i321−i321-1-11+i321−i32-1
χ181111111-1-111-1-1-1-1−1−i32−1+i32−1−i32−1+i32-111-1-1-11111-1-1−1−i321+i321+i321+i321+i32−1+i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1+i32−1−i32−1+i32−1+i3211−1−i32−1+i3211−1−i32−1−i321+i32−1+i321−i321+i321−i32−1+i321−i321-11-1−1−i321+i321−i32-1-11+i32
χ19111111-11-1-1-111-1-11111-11-11-1-111-1-111-11-1-1-1-11-1-1-1111-1-1-1111-1111-1-1-1111-1111111111111-11-11-1-1-11-11-11-11-1-1-1-1
χ20111111-11-1-1-111-1-11111-11-11-1-111-1-111-11-1-1-1-11-1-1-1111-1-1-1111-1111-1-1-1111-1−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321−i32−1+i321+i32−1−i321−i321+i321−i32−1+i321−i32−1+i321+i32−1−i321+i32−1−i321−i321−i321+i321+i32
χ21111111-11-1-1-111-1-11111-11-11-1-111-1-111-11-1-1-1-11-1-1-1111-1-1-1111-1111-1-1-1111-1−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321+i32−1−i321−i32−1+i321+i321−i321+i32−1−i321+i32−1−i321−i32−1+i321−i32−1+i321+i321+i321−i321−i32
χ22111111-11-1-1-111-1-1−1+i32−1−i32−1+i32−1−i32-11-11-1-111-1-1111−i32−1+i321−i321−i321−i321+i32−1−i321+i321+i321+i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i32−1+i321−i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i32−1−i321+i321111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-11-11-1-11−i32−1+i321+i32−1−i321−i32−1+i321+i32−1−i321−i321+i321−i321+i32
χ23111111-11-1-1-111-1-1−1+i32−1−i32−1+i32−1−i32-11-11-1-111-1-1111−i32−1+i321−i321−i321−i321+i32−1−i321+i321+i321+i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i32−1+i321−i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i32−1−i321+i32−1+i32−1−i32−1+i32−1−i32−1−i3211−1+i32−1−i3211−1+i321−i32−1+i321+i32−1−i321−i321+i321+i32−1−i32-11-111−i32−1+i321+i32-1-11−i32
χ24111111-11-1-1-111-1-1−1+i32−1−i32−1+i32−1−i32-11-11-1-111-1-1111−i32−1+i321−i321−i321−i321+i32−1−i321+i321+i321+i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i32−1+i321−i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i32−1−i321+i32−1−i32−1+i32−1−i32−1+i321−1+i32−1−i3211−1+i32−1−i3211+i32−1−i321−i32−1+i321+i321−i32-111−i32−1+i321+i32−1−i32-11-11−i321+i32-1
χ25111111-11-1-1-111-1-1−1−i32−1+i32−1−i32−1+i32-11-11-1-111-1-1111+i32−1−i321+i321+i321+i321−i32−1+i321−i321−i321−i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i32−1−i321+i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i32−1+i321−i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-11-11-1-11+i32−1−i321−i32−1+i321+i32−1−i321−i32−1+i321+i321−i321+i321−i32
χ26111111-11-1-1-111-1-1−1−i32−1+i32−1−i32−1+i32-11-11-1-111-1-1111+i32−1−i321+i321+i321+i321−i32−1+i321−i321−i321−i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i32−1−i321+i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i32−1+i321−i32−1+i32−1−i32−1+i32−1−i321−1−i32−1+i3211−1−i32−1+i3211−i32−1+i321+i32−1−i321−i321+i32-111+i32−1−i321−i32−1+i32-11-11+i321−i32-1
χ27111111-11-1-1-111-1-1−1−i32−1+i32−1−i32−1+i32-11-11-1-111-1-1111+i32−1−i321+i321+i321+i321−i32−1+i321−i321−i321−i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i32−1−i321+i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i32−1+i321−i32−1−i32−1+i32−1−i32−1+i32−1+i3211−1−i32−1+i3211−1−i321+i32−1−i321−i32−1+i321+i321−i321−i32−1+i32-11-111+i32−1−i321−i32-1-11+i32
χ28111111-1-11-1-1-1-111111111-1-11111-1-1-1-1-1-1111-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-11111111111111-1-1-1-111-1-1-1-1-1-1-1-11111
χ29111111-1-11-1-1-1-111111111-1-11111-1-1-1-1-1-1111-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-11−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32−1+i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32−1+i32−1+i32−1−i32−1−i32
χ30111111-1-11-1-1-1-111111111-1-11111-1-1-1-1-1-1111-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-11−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32−1−i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32−1−i32−1−i32−1+i32−1+i32
χ31111111-1-11-1-1-1-111−1+i32−1−i32−1+i32−1−i3211-1-11111-1-1-1-11−i321−i32−1+i32−1+i32−1+i321+i321+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i321111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-1-1-1111−i321−i321+i321+i321−i321−i321+i321+i32−1+i32−1−i32−1+i32−1−i32
χ32111111-1-11-1-1-1-111−1+i32−1−i32−1+i32−1−i3211-1-11111-1-1-1-11−i321−i32−1+i32−1+i32−1+i321+i321+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i3211−1+i32−1−i3211−1+i321−i321−i321+i321+i32−1+i32−1−i321+i321+i32-1-1-1-11−i321−i32−1−i3211−1+i32
χ33111111-1-11-1-1-1-111−1+i32−1−i32−1+i32−1−i3211-1-11111-1-1-1-11−i321−i32−1+i32−1+i32−1+i321+i321+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1+i32−1−i32−1+i321−1+i32−1−i3211−1+i32−1−i3211+i321+i321−i321−i32−1−i32−1+i32-1-11−i321−i321+i321+i32-1-11−1+i32−1−i321
χ34111111-1-11-1-1-1-111−1−i32−1+i32−1−i32−1+i3211-1-11111-1-1-1-11+i321+i32−1−i32−1−i32−1−i321−i321−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-1-1-1111+i321+i321−i321−i321+i321+i321−i321−i32−1−i32−1+i32−1−i32−1+i32
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χ874-444-4-4000000000−2−2i3−2+2i32+2i32−2i3000000000000000000000000000000000000000000-2-2221+i31−i31+i31−i3−1−i3−1+i3−1−i3−1+i3000000000000000000
χ884-444-4-4000000000−2−2i3−2+2i32+2i32−2i30000000000000000000000000000000000000000001−i31+i3−1+i3−1−i3-21+i31−i3-22−1−i3−1+i32000000000000000000
χ894-444-4-4000000000−2−2i3−2+2i32+2i32−2i30000000000000000000000000000000000000000001+i31−i3−1−i3−1+i31−i3-2-21+i3−1+i322−1−i3000000000000000000
χ9012-12−6+6i3−6−6i36−6i36+6i30000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9112-12−6−6i3−6+6i36+6i36−6i30000000000000000000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 9 (ζ9 = 1); i = ζ2.