Finite Group Databasebeta

← Group #10595553

Character table — Group #10595553

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111222222222333333444444444444444444666666666888888888888888888121212121212161616161616161616161616
order1233664881212242424242266662333333466666666121248812122424242412121212121224242424242424242424242424661212666666121212121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+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
χ31111111111111111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−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
χ4111111111111111111111-1111111-1-1-1111111-1-1111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ5111111111111111111111-1−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-1-1−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-1111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−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+i321+i321−i321−i321−i321+i321+i321+i321−i321−i321−i32
χ6111111111111111111111-1−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-1-1−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-1111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+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−i321−i321+i321+i321+i321−i321−i321−i321+i321+i321+i32
χ71111111-1-111-1-1-1-11111111111111-111111111-1-11-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1111111-1-1-1-1-1-1
χ81111111-1-111-1-1-1-11111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-11-1-111-1-1-1-1−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i321-111-1-1−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321+i321+i321+i321−i321−i321−i32
χ91111111-1-111-1-1-1-11111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-11-1-111-1-1-1-1−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i321-111-1-1−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−i321−i321−i321+i321+i321+i32
χ101111111-1-111-1-1-1-1111111-11111111-1-1111111111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1-1-1-1-1111111
χ111111111-1-111-1-1-1-1111111-1−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321-1-1−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111-1-111-1-1-1-1−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i32-11-1-1111+i321+i321+i321−i321−i321−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32
χ121111111-1-111-1-1-1-1111111-1−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321-1-1−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111-1-111-1-1-1-1−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i32-11-1-1111−i321−i321−i321+i321+i321+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32
χ1311−1−i32−1+i32−1−i32−1+i32111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i3211−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32−1−i32−1+i32111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i3211−1−i32−1+i32−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32
χ1411−1−i32−1+i32−1−i32−1+i32111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i321−1+i321−1−i321−1−i32−1+i32−1−i32−1+i321−1+i321−1−i32−1−i32−1+i32111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321−1+i321−1−i32−1−i32−1−i32−1+i32−1+i3211−1+i32−1+i3211−1−i32−1−i3211−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321−1+i321−1−i32−1−i32−1+i321−1+i321−1−i32
χ1511−1−i32−1+i32−1−i32−1+i32111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1+i321−1−i32−1−i32−1+i3211−1−i32−1+i32−1+i321−1−i32−1−i32−1+i321−1−i32−1+i32111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1+i321−1−i32−1−i32−1+i321−1+i32−1+i3211−1−i32−1−i32−1−i32−1−i32−1+i32−1+i321111−1−i32−1+i32−1−i32−1+i32−1+i321−1−i32−1−i32−1+i321−1+i321−1−i32−1−i32−1+i321
χ1611−1−i32−1+i32−1−i32−1+i32111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i32-11−1−i32−1+i321−1−i32−1+i32-11+i321−i321−1−i32−1+i321−1−i32−1+i321+i321−i32111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i32-1-11+i321−i321+i321−i32-11+i321−i32-11+i321−i32-11+i321−i32-11+i321−i32
χ1711−1−i32−1+i32−1−i32−1+i32111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i32-1−1−i32−1+i321−1+i321−1−i32-11+i321−i32−1−i32−1+i321−1+i321−1−i321+i321−i32111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321−1+i321−1−i32−1−i32−1−i32−1+i32−1+i3211−1+i32−1+i3211−1−i32−1−i32-1-11+i321−i321+i321−i321+i321−i32-11−i32-11+i321+i321−i32-11−i32-11+i32
χ1811−1−i32−1+i32−1−i32−1+i32111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i32-1−1+i321−1−i32−1−i32−1+i321-11+i321−i32−1+i321−1−i32−1−i32−1+i3211+i321−i32111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1+i321−1−i32−1−i32−1+i321−1+i32−1+i3211−1−i32−1−i32−1−i32−1−i32−1+i32−1+i3211-1-11+i321−i321+i321−i321−i32-11+i321+i321−i32-11−i32-11+i321+i321−i32-1
χ1911−1−i32−1+i32−1−i32−1+i321-1-1−1−i32−1+i321+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i3211−1−i32−1+i321−1−i32−1+i32-1−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321+i321−i321-1-1−1−i32−1+i321+i321+i321−i321−i321−1−i32−1+i321−1−i32−1+i32-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i321-1−1−i32−1+i321+i321−i321−1−i32−1+i321−1−i32−1+i32-11+i321−i32-11+i321−i32
χ2011−1−i32−1+i32−1−i32−1+i321-1-1−1−i32−1+i321+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i321−1+i321−1−i32-1−1−i32−1+i32−1−i32−1+i321−1+i321−1−i321+i321−i321-1-1−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i321−1+i321−1−i321+i321+i321−i321−i32-1-11−i321−i32-1-11+i321+i321-1−1−i32−1+i321+i321−i32−1−i32−1+i321−1+i321−1−i321+i321−i32-11−i32-11+i32
χ2111−1−i32−1+i32−1−i32−1+i321-1-1−1−i32−1+i321+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i321−1+i321−1−i32−1−i32−1+i321-1−1−i32−1+i32−1+i321−1−i32−1−i32−1+i3211+i321−i321-1-1−1−i32−1+i321+i321+i321−i321−i32−1+i321−1−i32−1−i32−1+i3211−i321−i32-1-11+i321+i321+i321+i321−i321−i32-1-11-1−1−i32−1+i321+i321−i32−1+i321−1−i32−1−i32−1+i3211−i32-11+i321+i321−i32-1
χ2211−1−i32−1+i32−1−i32−1+i321-1-1−1−i32−1+i321+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i32-11−1−i32−1+i321−1−i32−1+i3211+i321−i321−1−i32−1+i321−1−i32−1+i32−1−i32−1+i321-1-1−1−i32−1+i321+i321+i321−i321−i321−1−i32−1+i321−1−i32−1+i32-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i32-111+i321−i32−1−i32−1+i32-11+i321−i32-11+i321−i321−1−i32−1+i321−1−i32−1+i32
χ2311−1−i32−1+i32−1−i32−1+i321-1-1−1−i32−1+i321+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i32-1−1−i32−1+i321−1+i321−1−i3211+i321−i32−1−i32−1+i321−1+i321−1−i32−1−i32−1+i321-1-1−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i321−1+i321−1−i321+i321+i321−i321−i32-1-11−i321−i32-1-11+i321+i32-111+i321−i32−1−i32−1+i321+i321−i32-11−i32-11+i32−1−i32−1+i321−1+i321−1−i32
χ2411−1−i32−1+i32−1−i32−1+i321-1-1−1−i32−1+i321+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i32-1−1+i321−1−i32−1−i32−1+i32111+i321−i32−1+i321−1−i32−1−i32−1+i321−1−i32−1+i321-1-1−1−i32−1+i321+i321+i321−i321−i32−1+i321−1−i32−1−i32−1+i3211−i321−i32-1-11+i321+i321+i321+i321−i321−i32-1-1-111+i321−i32−1−i32−1+i321−i32-11+i321+i321−i32-1−1+i321−1−i32−1−i32−1+i321
χ2511−1+i32−1−i32−1+i32−1−i32111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i3211−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32−1+i32−1−i32111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i3211−1+i32−1−i32−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32
χ2611−1+i32−1−i32−1+i32−1−i32111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1−i321−1+i32−1+i32−1−i3211−1+i32−1−i32−1−i321−1+i32−1+i32−1−i321−1+i32−1−i32111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1−i321−1+i32−1+i32−1−i321−1−i32−1−i3211−1+i32−1+i32−1+i32−1+i32−1−i32−1−i321111−1+i32−1−i32−1+i32−1−i32−1−i321−1+i32−1+i32−1−i321−1−i321−1+i32−1+i32−1−i321
χ2711−1+i32−1−i32−1+i32−1−i32111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i321−1−i321−1+i321−1+i32−1−i32−1+i32−1−i321−1−i321−1+i32−1+i32−1−i32111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−1−i321−1+i32−1+i32−1+i32−1−i32−1−i3211−1−i32−1−i3211−1+i32−1+i3211−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−1−i321−1+i32−1+i32−1−i321−1−i321−1+i32
χ2811−1+i32−1−i32−1+i32−1−i32111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i32-11−1+i32−1−i321−1+i32−1−i32-11−i321+i321−1+i32−1−i321−1+i32−1−i321−i321+i32111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i32-1-11−i321+i321−i321+i32-11−i321+i32-11−i321+i32-11−i321+i32-11−i321+i32
χ2911−1+i32−1−i32−1+i32−1−i32111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i32-1−1−i321−1+i32−1+i32−1−i321-11−i321+i32−1−i321−1+i32−1+i32−1−i3211−i321+i32111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1−i321−1+i32−1+i32−1−i321−1−i32−1−i3211−1+i32−1+i32−1+i32−1+i32−1−i32−1−i3211-1-11−i321+i321−i321+i321+i32-11−i321−i321+i32-11+i32-11−i321−i321+i32-1
χ3011−1+i32−1−i32−1+i32−1−i32111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i32-1−1+i32−1−i321−1−i321−1+i32-11−i321+i32−1+i32−1−i321−1−i321−1+i321−i321+i32111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−1−i321−1+i32−1+i32−1+i32−1−i32−1−i3211−1−i32−1−i3211−1+i32−1+i32-1-11−i321+i321−i321+i321−i321+i32-11+i32-11−i321−i321+i32-11+i32-11−i32
χ3111−1+i32−1−i32−1+i32−1−i321-1-1−1+i32−1−i321−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i3211−1+i32−1−i321−1+i32−1−i32-1−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−i321+i321-1-1−1+i32−1−i321−i321−i321+i321+i321−1+i32−1−i321−1+i32−1−i32-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i321-1−1+i32−1−i321−i321+i321−1+i32−1−i321−1+i32−1−i32-11−i321+i32-11−i321+i32
χ3211−1+i32−1−i32−1+i32−1−i321-1-1−1+i32−1−i321−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i321−1−i321−1+i32−1+i32−1−i321-1−1+i32−1−i32−1−i321−1+i32−1+i32−1−i3211−i321+i321-1-1−1+i32−1−i321−i321−i321+i321+i32−1−i321−1+i32−1+i32−1−i3211+i321+i32-1-11−i321−i321−i321−i321+i321+i32-1-11-1−1+i32−1−i321−i321+i32−1−i321−1+i32−1+i32−1−i3211+i32-11−i321−i321+i32-1
χ3311−1+i32−1−i32−1+i32−1−i321-1-1−1+i32−1−i321−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i321−1−i321−1+i32-1−1+i32−1−i32−1+i32−1−i321−1−i321−1+i321−i321+i321-1-1−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i321−1−i321−1+i321−i321−i321+i321+i32-1-11+i321+i32-1-11−i321−i321-1−1+i32−1−i321−i321+i32−1+i32−1−i321−1−i321−1+i321−i321+i32-11+i32-11−i32
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.