Finite Group Databasebeta

← Group #147192

Character table — Group #147192

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size111122222222222222222244444444444444444444444444444444444444444444444444444416161616161616161616161616161616
order1244222222244444448888444444448888888888888816161616161616161616161616161616161616161616161616161616161616168888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111111111-1-1-1-1
χ9111111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i11-1-111-1-1ii−i−iii−i−i
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χ11111111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii11-1-111-1-1−i−iii−i−iii
χ12111111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii-1-111-1-111ii−i−iii−i−i
χ13111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii11-1-1-1-111ii−i−i−i−iii
χ14111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii-1-11111-1-1−i−iiiii−i−i
χ15111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i11-1-1-1-111−i−iiiii−i−i
χ16111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i-1-11111-1-1ii−i−i−i−iii
χ1711-1-11-111-1-1-1-11-1111-111-1-1ii−i−iii−i−iii−i−iii−i−i11-1-11-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−ii−ii−i1-11-1i−ii−i1-11-1
χ1811-1-11-111-1-1-1-11-1111-111-1-1ii−i−iii−i−iii−i−iii−i−i11-1-11-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−ii−ii-11-11−ii−ii-11-11
χ1911-1-11-111-1-1-1-11-1111-111-1-1ii−i−iii−i−iii−i−iii−i−i11-1-11-1-1-1-1-11111-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiiii−ii−i1-11-1−ii−ii-11-11
χ2011-1-11-111-1-1-1-11-1111-111-1-1ii−i−iii−i−iii−i−iii−i−i11-1-11-1-1-1-1-11111-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii−ii−ii-11-11i−ii−i1-11-1
χ2111-1-11-111-1-1-1-11-1111-111-1-1−i−iii−i−iii−i−iii−i−iii11-1-11-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiii−ii−i-11-11i−ii−i-11-11
χ2211-1-11-111-1-1-1-11-1111-111-1-1−i−iii−i−iii−i−iii−i−iii11-1-11-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−ii−ii1-11-1−ii−ii1-11-1
χ2311-1-11-111-1-1-1-11-1111-111-1-1−i−iii−i−iii−i−iii−i−iii11-1-11-1-1-1-1-11111-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−ii−ii−i-11-11−ii−ii1-11-1
χ2411-1-11-111-1-1-1-11-1111-111-1-1−i−iii−i−iii−i−iii−i−iii11-1-11-1-1-1-1-11111-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i−ii−ii1-11-1i−ii−i-11-11
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χ2611-1-11-1-1-111-1-1-1111-11-1-111ii−i−i−i−iiiii−i−i−i−iii11-1-1-11iiii−i−i−i−i−i−i−i−iiiii-1-1-1-111111111-1-1-1-1−iii−i-111-11-1-11−iii−i
χ2711-1-11-1-1-111-1-1-1111-11-1-111ii−i−i−i−iiiii−i−i−i−iii11-1-1-11−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-1-1-1-11111i−i−ii1-1-111-1-11−iii−i
χ2811-1-11-1-1-111-1-1-1111-11-1-111ii−i−i−i−iiiii−i−i−i−iii11-1-1-11−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-1-1-1-11111−iii−i-111-1-111-1i−i−ii
χ2911-1-11-1-1-111-1-1-1111-11-1-111−i−iiiii−i−i−i−iiiii−i−i11-1-1-11iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111i−i−ii-111-1-111-1−iii−i
χ3011-1-11-1-1-111-1-1-1111-11-1-111−i−iiiii−i−i−i−iiiii−i−i11-1-1-11iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111−iii−i1-1-111-1-11i−i−ii
χ3111-1-11-1-1-111-1-1-1111-11-1-111−i−iiiii−i−i−i−iiiii−i−i11-1-1-11−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-111111111-1-1-1-1i−i−ii-111-11-1-11i−i−ii
χ3211-1-11-1-1-111-1-1-1111-11-1-111−i−iiiii−i−i−i−iiiii−i−i11-1-1-11−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-111111111-1-1-1-1−iii−i1-1-11-111-1−iii−i
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χ8822-2-2-2-2-222-222-22-222-2000000000000−2i2i2i−2i2i−2i−2i2i000000−22−222−22−22−22−2−22−22i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i20000000000000000
χ898-88i−8i000000000000004i2−4i242−420000000000000000000000000000000000000000000000000000000000000000000000
χ908-88i−8i00000000000000−4i24i2−42420000000000000000000000000000000000000000000000000000000000000000000000
χ918-8−8i8i000000000000004i2−4i2−42420000000000000000000000000000000000000000000000000000000000000000000000
χ928-8−8i8i00000000000000−4i24i242−420000000000000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).