Finite Group Databasebeta

← Group #72318988

Character table — Group #72318988

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100
size1111111122222222222244444444444488888888888888888888888888161616161616161616161616161616161616161616161616161616161616161616161616161632323232
order12222222444444444444444488888888248888888888888888888888882222444444448888888888161616161616161616161616161616164488
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ411111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ51111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1
χ61111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-111
χ71111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1
χ81111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111
χ911111111111111111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111
χ1011111111111111111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1
χ1111111111111111111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111
χ1211111111111111111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111111111111111-1-1-1-11111-1-1-1-111-1-1
χ1311111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111111111111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ1411111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ1511111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ1611111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ171111111111-1-1-1-111-1-1-1-111-1-111-1-1-1-1111-1ii−i−i11-1-1iiii−i−i−i−iiiii−i−i−i−i111111-1-1-1-1-1-1i−iii−i−iii−i−iii−i−iii−i−i11-1-111-1-1-11i−i
χ181111111111-1-1-1-111-1-1-1-111-1-111-1-1-1-1111-1ii−i−i11-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-111-1-1i−iii−i−i−i−iii−i−iii−i−iii-1-111-1-1111-1−ii
χ191111111111-1-1-1-111-1-1-1-111-1-111-1-1-1-1111-1ii−i−i11-1-1iiii−i−i−i−i−i−i−i−iiiii-1-111-1-111-1-111i−i−i−iiiii−i−i−i−iii−i−iii-1-111-1-111-11i−i
χ201111111111-1-1-1-111-1-1-1-111-1-111-1-1-1-1111-1ii−i−i11-1-1iiii−i−i−i−i−i−i−i−iiiii-1-1-1-1-1-1111111i−i−i−iii−i−iiiii−i−iii−i−i11-1-111-1-11-1−ii
χ211111111111-1-1-1-111-1-1-1-111-1-111-1-1-1-1111-1−i−iii11-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-111-1-111-1-111−iiii−i−i−i−iiiii−i−iii−i−i-1-111-1-111-11−ii
χ221111111111-1-1-1-111-1-1-1-111-1-111-1-1-1-1111-1−i−iii11-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-1-1-1111111−iiii−i−iii−i−i−i−iii−i−iii11-1-111-1-11-1i−i
χ231111111111-1-1-1-111-1-1-1-111-1-111-1-1-1-1111-1−i−iii11-1-1−i−i−i−iiiii−i−i−i−iiiii111111-1-1-1-1-1-1−ii−i−iii−i−iii−i−iii−i−iii11-1-111-1-1-11−ii
χ241111111111-1-1-1-111-1-1-1-111-1-111-1-1-1-1111-1−i−iii11-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-111-1-1−ii−i−iiiii−i−iii−i−iii−i−i-1-111-1-1111-1i−i
χ251111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-11ii−i−i-1-111−i−i−i−iiiiiiiii−i−i−i−i-1-1111111-1-1-1-1i−i−i−iii−i−iiiii−i−i−i−iii11-1-1-1-1111-1i−i
χ261111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-11ii−i−i-1-111−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-1111111-1-1i−i−i−iiiii−i−i−i−iiiii−i−i-1-11111-1-1-11−ii
χ271111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-11ii−i−i-1-111−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1-1-111i−iii−i−i−i−iii−i−iiiii−i−i-1-11111-1-11-1i−i
χ281111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-11ii−i−i-1-111−i−i−i−iiiii−i−i−i−iiiii11-1-1-1-1-1-11111i−iii−i−iii−i−iii−i−i−i−iii11-1-1-1-111-11−ii
χ291111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-11−i−iii-1-111iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1-1-111−ii−i−iiiii−i−iii−i−i−i−iii-1-11111-1-11-1−ii
χ301111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-11−i−iii-1-111iiii−i−i−i−iiiii−i−i−i−i11-1-1-1-1-1-11111−ii−i−iii−i−iii−i−iiiii−i−i11-1-1-1-111-11i−i
χ311111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-11−i−iii-1-111iiii−i−i−i−i−i−i−i−iiiii-1-1111111-1-1-1-1−iiii−i−iii−i−i−i−iiiii−i−i11-1-1-1-1111-1−ii
χ321111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-11−i−iii-1-111iiii−i−i−i−i−i−i−i−iiiii-1-1-1-1111111-1-1−iiii−i−i−i−iiiii−i−i−i−iii-1-11111-1-1-11i−i
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χ392222222222-2-2-2-222-2-2-2-2-2-222-2-22222-2-2-222i2i−2i−2i22-2-2−2i−2i2i2i2i2i−2i−2i00000000000000000000−2i2i0000000000000000000000000000
χ402222222222-2-2-2-222-2-2-2-2-2-222-2-22222-2-2-22−2i−2i2i2i22-2-22i2i−2i−2i−2i−2i2i2i000000000000000000002i−2i0000000000000000000000000000
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χ42222-2-2-2-222-22i2i−2i−2i2-22i2i−2i−2i00002-22i2i−2i−2i2-20000000000000000002ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ00-220000−2i2i000000000000−2ζ32ζ3−2ζ2ζ0000000000000000
χ43222-2-2-2-222-22i2i−2i−2i2-22i2i−2i−2i00002-22i2i−2i−2i2-2000000000000000000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ002-200002i−2i000000000000−2ζ32ζ3−2ζ2ζ0000000000000000
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χ998-8-8-888-8800000000000000000000000000000042−42000000000000000000000000000000000000000000000000000000000000
χ1008-8-8-888-88000000000000000000000000000000−4242000000000000000000000000000000000000000000000000000000000000

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