Finite Group Databasebeta

← Group #72258935

Character table — Group #72258935

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85
size1122233444444666888888888121212121212121216161616161616161616161616161616242424242424242424242424323232323232323232323232323232323232323232323232
order122242222444422422224444422444444336666661212121212121212224444444444666666666666121212121212121212121212
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+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
χ3111111111111111111111111111111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−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
χ4111111111-1-1-1-111111-1-11-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-11-1-1-1-11111-1-11111-1-111-1-1-1-111-1-1-1-1
χ5111111111-1-1-1-111111-1-11-1-1-1-11111-1-1-1-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i3211111-1-11-1-1-1-1−1−i32−1−i32−1−i32−1−i321+i321+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i321−i321−i321−i321−i32
χ6111111111-1-1-1-111111-1-11-1-1-1-11111-1-1-1-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i3211111-1-11-1-1-1-1−1+i32−1+i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i321+i321+i321+i321+i32
χ71111111-1-111-1-1111-1-11-1-111-1-1-1-11111-1-111-1-1-1-11111-1-111-1-1-1-1-1111-1111-1-111-1-11-111-1-11-11-111-1-11-111-1-1
χ81111111-1-111-1-1111-1-11-1-111-1-1-1-11111-1-1−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32-1-1-1111-1111-1-1−1−i32−1−i321+i321+i32−1−i321+i32−1+i32−1+i321−i321−i32−1+i321−i32−1−i321+i32−1−i32−1−i321+i321+i32−1+i321−i32−1+i32−1+i321−i321−i32
χ91111111-1-111-1-1111-1-11-1-111-1-1-1-11111-1-1−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32-1-1-1111-1111-1-1−1+i32−1+i321−i321−i32−1+i321−i32−1−i32−1−i321+i321+i32−1−i321+i32−1+i321−i32−1+i32−1+i321−i321−i32−1−i321+i32−1−i32−1−i321+i321+i32
χ101111111-1-1-1-111111-1-1-11-1-1-111-1-111-1-11111-1-1-1-111-1-111-1-111-1-1-111-111-1-11111-1-1-1111-1-1-111-1-1-1111-1-1-111
χ111111111-1-1-1-111111-1-1-11-1-1-111-1-111-1-111−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32-1-1-111-111-1-111−1−i32−1−i321+i321+i321+i32−1−i32−1+i32−1+i321−i321−i321−i32−1+i32−1−i321+i321+i321+i32−1−i32−1−i32−1+i321−i321−i321−i32−1+i32−1+i32
χ121111111-1-1-1-111111-1-1-11-1-1-111-1-111-1-111−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32-1-1-111-111-1-111−1+i32−1+i321−i321−i321−i32−1+i32−1−i32−1−i321+i321+i321+i32−1−i32−1+i321−i321−i321−i32−1+i32−1+i32−1−i321+i321+i321+i32−1−i32−1−i32
χ13111-1-1111111111-1-11-1-1-1-11-11-11111111111111111111111111-1-11-1-1-1-11-11-11-11-1-1-11-11-1-1-1-1-11-11-1-1-11-11-1
χ14111-1-1111111111-1-11-1-1-1-11-11-111111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321-1-11-1-1-1-11-11-1−1−i321+i32−1−i321+i321+i321+i32−1+i321−i32−1+i321−i321−i321−i321+i321+i32−1−i321+i32−1−i321+i321−i321−i32−1+i321−i32−1+i321−i32
χ15111-1-1111111111-1-11-1-1-1-11-11-111111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321-1-11-1-1-1-11-11-1−1+i321−i32−1+i321−i321−i321−i32−1−i321+i32−1−i321+i321+i321+i321−i321−i32−1+i321−i32−1+i321−i321+i321+i32−1−i321+i32−1−i321+i32
χ16111-1-11111-1-1-1-11-1-11-111-1-11-111111-1-1-1-111111111-1-1-1-1-1-1-1-11-1-11-111-1-11-111-11-1111-11-111-1-1-11-11-1-1-11-11
χ17111-1-11111-1-1-1-11-1-11-111-1-11-111111-1-1-1-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i321-1-11-111-1-11-11−1−i321+i32−1−i321+i32−1−i32−1−i32−1+i321−i32−1+i321−i32−1+i32−1+i321+i321+i321+i32−1−i321+i32−1−i321−i321−i321−i32−1+i321−i32−1+i32
χ18111-1-11111-1-1-1-11-1-11-111-1-11-111111-1-1-1-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i321-1-11-111-1-11-11−1+i321−i32−1+i321−i32−1+i32−1+i32−1−i321+i32−1−i321+i32−1−i32−1−i321−i321−i321−i32−1+i321−i32−1+i321+i321+i321+i32−1−i321+i32−1−i32
χ19111-1-111-1-111-1-11-1-1-11-1111-1-11-1-11111-1-111-1-1-1-11111-1-111-1-1-1111-1-11-11-1-111-1-11-111-1-11-11-111-1-11-111-1-11
χ20111-1-111-1-111-1-11-1-1-11-1111-1-11-1-11111-1-1−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32-1111-1-11-11-1-11−1−i321+i321+i32−1−i321+i32−1−i32−1+i321−i321−i32−1+i321−i32−1+i321+i32−1−i32−1−i321+i321+i32−1−i321−i32−1+i32−1+i321−i321−i32−1+i32
χ21111-1-111-1-111-1-11-1-1-11-1111-1-11-1-11111-1-1−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32-1111-1-11-11-1-11−1+i321−i321−i32−1+i321−i32−1+i32−1−i321+i321+i32−1−i321+i32−1−i321−i32−1+i32−1+i321−i321−i32−1+i321+i32−1−i32−1−i321+i321+i32−1−i32
χ22111-1-111-1-1-1-1111-1-1-111-11-111-1-1-111-1-11111-1-1-1-111-1-111-1-111-1111-11-1-1-111-11-1-111-11-1-111-1-11-111-1-11-111-1
χ23111-1-111-1-1-1-1111-1-1-111-11-111-1-1-111-1-111−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32-1111-11-1-1-111-1−1−i321+i321+i32−1−i32−1−i321+i32−1+i321−i321−i32−1+i32−1+i321−i321+i32−1−i321+i32−1−i32−1−i321+i321−i32−1+i321−i32−1+i32−1+i321−i32
χ24111-1-111-1-1-1-1111-1-1-111-11-111-1-1-111-1-111−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32-1111-11-1-1-111-1−1+i321−i321−i32−1+i32−1+i321−i32−1−i321+i321+i32−1−i32−1−i321+i321−i32−1+i321−i32−1+i32−1+i321−i321+i32−1−i321+i32−1−i32−1−i321+i32
χ2511-11-111111111-11-1-11-1-1-1-11-11111111111111111111111111-11-1-11-1-1-1-11-11-11-11-1-1-11-11-1-1-1-1-11-11-1-1-11-11
χ2611-11-111111111-11-1-11-1-1-1-11-1111111111−1−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+i32-11-1-11-1-1-1-11-111+i32−1−i321+i32−1−i321+i321+i321−i32−1+i321−i32−1+i321−i321−i321+i321+i321+i32−1−i321+i32−1−i321−i321−i321−i32−1+i321−i32−1+i32
χ2711-11-111111111-11-1-11-1-1-1-11-1111111111−1+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−i32-11-1-11-1-1-1-11-111−i32−1+i321−i32−1+i321−i321−i321+i32−1−i321+i32−1−i321+i321+i321−i321−i321−i32−1+i321−i32−1+i321+i321+i321+i32−1−i321+i32−1−i32
χ2811-11-11111-1-1-1-1-11-1-1111-11-11-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-1111-11-11-1-11-1111-11-1111-1-11-11-1-1-11-11-1
χ2911-11-11111-1-1-1-1-11-1-1111-11-11-11111-1-1-1-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32-11-1-1111-11-11-11+i32−1−i321+i32−1−i32−1−i32−1−i321−i32−1+i321−i32−1+i32−1+i32−1+i321+i321+i32−1−i321+i32−1−i321+i321−i321−i32−1+i321−i32−1+i321−i32
χ3011-11-11111-1-1-1-1-11-1-1111-11-11-11111-1-1-1-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32-11-1-1111-11-11-11−i32−1+i321−i32−1+i32−1+i32−1+i321+i32−1−i321+i32−1−i32−1−i32−1−i321−i321−i32−1+i321−i32−1+i321−i321+i321+i32−1−i321+i32−1−i321+i32
χ3111-11-111-1-111-1-1-11-11-1-111-111-1-1-11111-1-111-1-1-1-11111-1-111-1-11-11-11-11-1-111-1-111-1-11-111-1-11-11-111-1-11-111-1
χ3211-11-111-1-111-1-1-11-11-1-111-111-1-1-11111-1-1−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321-11-11-11-1-111-11+i32−1−i32−1−i321+i321+i32−1−i321−i32−1+i32−1+i321−i321−i32−1+i321+i32−1−i321+i32−1−i32−1−i321+i321−i32−1+i321−i32−1+i32−1+i321−i32
χ3311-11-111-1-111-1-1-11-11-1-111-111-1-1-11111-1-1−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321-11-11-11-1-111-11−i32−1+i32−1+i321−i321−i32−1+i321+i32−1−i32−1−i321+i321+i32−1−i321−i32−1+i321−i32−1+i32−1+i321−i321+i32−1−i321+i32−1−i32−1−i321+i32
χ3411-11-111-1-1-1-111-11-11-11-111-1-11-1-111-1-11111-1-1-1-111-1-111-1-1111-11-111-1-11-1-11-111-11-1-111-11-1-111-1-11-111-1-11
χ3511-11-111-1-1-1-111-11-11-11-111-1-11-1-111-1-111−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321-11-111-1-11-1-111+i32−1−i32−1−i321+i32−1−i321+i321−i32−1+i32−1+i321−i32−1+i321−i321+i32−1−i32−1−i321+i321+i32−1−i321−i32−1+i32−1+i321−i321−i32−1+i32
χ3611-11-111-1-1-1-111-11-11-11-111-1-11-1-111-1-111−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321-11-111-1-11-1-111−i32−1+i32−1+i321−i32−1+i321−i321+i32−1−i32−1−i321+i32−1−i321+i321−i32−1+i32−1+i321−i321−i32−1+i321+i32−1−i32−1−i321+i321+i32−1−i32
χ3711-1-1111111111-1-11-1-1111-1-1-1-1111111111111111111111111-1-11-1-1111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-1
χ3811-1-1111111111-1-11-1-1111-1-1-1-111111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-1-11-1-1111-1-1-1-11+i321+i321+i321+i32−1−i32−1−i321−i321−i321−i321−i32−1+i32−1+i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i321−i321−i321−i321−i32
χ3911-1-1111111111-1-11-1-1111-1-1-1-111111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-1-11-1-1111-1-1-1-11−i321−i321−i321−i32−1+i32−1+i321+i321+i321+i321+i32−1−i32−1−i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i321+i321+i321+i321+i32
χ4011-1-111111-1-1-1-1-1-11-1-1-1-1111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ4111-1-111111-1-1-1-1-1-11-1-1-1-1111111111-1-1-1-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32-1-11-1-1-1-1111111+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32
χ4211-1-111111-1-1-1-1-1-11-1-1-1-1111111111-1-1-1-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32-1-11-1-1-1-1111111−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32
χ4311-1-1111-1-111-1-1-1-11111-1-1-1-111-1-11111-1-111-1-1-1-11111-1-111-1-111-1-1-11-11-1-111-1-1111-1-1-1111-11-1-1-1111-1-1-111
χ4411-1-1111-1-111-1-1-1-11111-1-1-1-111-1-11111-1-1−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i3211-1-1-11-11-1-1111+i321+i32−1−i32−1−i32−1−i321+i321−i321−i32−1+i32−1+i32−1+i321−i32−1−i321+i321+i321+i32−1−i32−1−i32−1+i321−i321−i321−i32−1+i32−1+i32
χ4511-1-1111-1-111-1-1-1-11111-1-1-1-111-1-11111-1-1−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i3211-1-1-11-11-1-1111−i321−i32−1+i32−1+i32−1+i321−i321+i321+i32−1−i32−1−i32−1−i321+i32−1+i321−i321−i321−i32−1+i32−1+i32−1−i321+i321+i321+i32−1−i32−1−i32
χ4611-1-1111-1-1-1-111-1-1111-11-111-1-1-1-111-1-11111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-111-11-1-111-111-111-1-11-111-1-1
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.