Finite Group Databasebeta

← Group #72344007

Character table — Group #72344007

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100
size11111111222222222222444444444444444444444444888888888888888816161616161616161616161616161616161616161616161616161616161616163232323232323232
order12222222444444444444224444448888888888888888888888888888888822444444888888881616161616161616161616161616161624448888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ911111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11-11-1-1-111
χ1011111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-11-1111-1-1
χ1111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-1-11-1111-1-1
χ1211111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111111-11-1-1-111
χ1311111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111-11-111-1-1
χ1411111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-11-11-1-111
χ1511111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-11-11-1-111
χ1611111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-11-11-111-1-1
χ17111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1iiii−i−i−i−i11-1-111-1-1ii−i−iiiii−i−i−i−i11-1-1-1-111ii−i−iii−i−i11-1-111-1-1ii−i−iii−i−i11-1-1i−ii−i
χ18111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1iiii−i−i−i−i11-1-111-1-1ii−i−iiiii−i−i−i−i11-1-1-1-111ii−i−iii−i−i-1-111-1-111−i−iii−i−iii-1-111−ii−ii
χ19111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1iiii−i−i−i−i11-1-111-1-1ii−i−iiiii−i−i−i−i-1-11111-1-1−i−iii−i−iii11-1-111-1-1ii−i−iii−i−i-1-111−ii−ii
χ20111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1iiii−i−i−i−i11-1-111-1-1ii−i−iiiii−i−i−i−i-1-11111-1-1−i−iii−i−iii-1-111-1-111−i−iii−i−iii11-1-1i−ii−i
χ21111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1−i−i−i−iiiii11-1-111-1-1−i−iii−i−i−i−iiiii11-1-1-1-111−i−iii−i−iii11-1-111-1-1−i−iii−i−iii11-1-1−ii−ii
χ22111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1−i−i−i−iiiii11-1-111-1-1−i−iii−i−i−i−iiiii11-1-1-1-111−i−iii−i−iii-1-111-1-111ii−i−iii−i−i-1-111i−ii−i
χ23111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1−i−i−i−iiiii11-1-111-1-1−i−iii−i−i−i−iiiii-1-11111-1-1ii−i−iii−i−i11-1-111-1-1−i−iii−i−iii-1-111i−ii−i
χ24111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1−i−i−i−iiiii11-1-111-1-1−i−iii−i−i−i−iiiii-1-11111-1-1ii−i−iii−i−i-1-111-1-111ii−i−iii−i−i11-1-1−ii−ii
χ25111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1iiii−i−i−i−i11-1-1-1-111ii−i−i−i−i−i−iiiii1111-1-1-1-1−i−iiiii−i−i11-1-1-1-111ii−i−i−i−iii1-1-11−iii−i
χ26111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1iiii−i−i−i−i11-1-1-1-111ii−i−i−i−i−i−iiiii1111-1-1-1-1−i−iiiii−i−i-1-11111-1-1−i−iiiii−i−i-111-1i−i−ii
χ27111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1iiii−i−i−i−i11-1-1-1-111ii−i−i−i−i−i−iiiii-1-1-1-11111ii−i−i−i−iii11-1-1-1-111ii−i−i−i−iii-111-1i−i−ii
χ28111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1iiii−i−i−i−i11-1-1-1-111ii−i−i−i−i−i−iiiii-1-1-1-11111ii−i−i−i−iii-1-11111-1-1−i−iiiii−i−i1-1-11−iii−i
χ29111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1−i−i−i−iiiii11-1-1-1-111−i−iiiiiii−i−i−i−i1111-1-1-1-1ii−i−i−i−iii11-1-1-1-111−i−iiiii−i−i1-1-11i−i−ii
χ30111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1−i−i−i−iiiii11-1-1-1-111−i−iiiiiii−i−i−i−i1111-1-1-1-1ii−i−i−i−iii-1-11111-1-1ii−i−i−i−iii-111-1−iii−i
χ31111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1−i−i−i−iiiii11-1-1-1-111−i−iiiiiii−i−i−i−i-1-1-1-11111−i−iiiii−i−i11-1-1-1-111−i−iiiii−i−i-111-1−iii−i
χ32111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1−i−i−i−iiiii11-1-1-1-111−i−iiiiiii−i−i−i−i-1-1-1-11111−i−iiiii−i−i-1-11111-1-1ii−i−i−i−iii1-1-11i−i−ii
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χ3622222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222222222-2-222-2-20000000000000000000000000000000000000000
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χ39222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2222i2i2i2i−2i−2i−2i−2i-2-22222-2-2−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000000000
χ40222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-222−2i−2i−2i−2i2i2i2i2i-2-22222-2-22i2i−2i−2i2i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000000000
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χ998-8-8-888-8800000000000000008-800000000000000000000000000000000000000000000000000000000000000000000000000
χ1008-8-8-888-880000000000000000-8800000000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.