Finite Group Databasebeta

← Group #72343103

Character table — Group #72343103

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116
size112222244444444444444444444444888888888888888888888888816161616161616161616161616161616161616161616161616161616163232323232323232323232323232323232323232323232326464646464646464
order1224488222224444488888161616161616161624444444448888888161616161616161688816161616161616161616323232323232323232323232323232328888888888888888323232323232323244448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111-1-111-1-11-1-1-1-1-1-1-1-1-11-111-1-1-1-1-11111-1-1-1-1-1-1-111111-1-111-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−i11-1-111-1-1
χ6111111111111111-1-111-1-11-1-1-1-1-1-1-1-1-11-111-1-1-1-1-11111-1-1-1-1-1-1-111111-1-111-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i-1-111-1-111
χ7111111111111111-1-111-1-11-1-1-1-1-1-1-1-1-11-111-1-1-1-1-11111-1-1-1-1-1-1-111111-1-111-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiii-1-111-1-111
χ8111111111111111-1-111-1-11-1-1-1-1-1-1-1-1-11-111-1-1-1-1-11111-1-1-1-1-1-1-111111-1-111-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii11-1-111-1-1
χ91111111111-1-11-1-11111111-1-1-1-1-1-1-1-1-11-1-1-1111-1-111-1-11-1-11111-1-1-1-1-11-111-1-111-1-111iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-11111-1-1-1-1ii−i−iii−i−ii−ii−ii−ii−i
χ101111111111-1-11-1-11111111-1-1-1-1-1-1-1-1-11-1-1-1111-1-111-1-11-1-11111-1-1-1-1-11-111-1-111-1-111iiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111-1-1-1-11111ii−i−iii−i−i−ii−ii−ii−ii
χ111111111111-1-11-1-11111111-1-1-1-1-1-1-1-1-11-1-1-1111-1-111-1-11-1-11111-1-1-1-1-11-111-1-111-1-111−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-11111-1-1-1-1−i−iii−i−iii−ii−ii−ii−ii
χ121111111111-1-11-1-11111111-1-1-1-1-1-1-1-1-11-1-1-1111-1-111-1-11-1-11111-1-1-1-1-11-111-1-111-1-111−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111-1-1-1-11111−i−iii−i−iiii−ii−ii−ii−i
χ131111111111-1-11-1-1-1-111-1-1111111111111-1-1-1-1-11111-1-1-111-1-1-1-1-1-1-1-1-1-11111111-1-1-1-11111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111−iii−i−iii−i
χ141111111111-1-11-1-1-1-111-1-1111111111111-1-1-1-1-11111-1-1-111-1-1-1-1-1-1-1-1-1-11111111-1-1-1-11111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111i−i−iii−i−ii
χ151111111111-1-11-1-1-1-111-1-1111111111111-1-1-1-1-11111-1-1-111-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1i−i−iii−i−ii
χ161111111111-1-11-1-1-1-111-1-1111111111111-1-1-1-1-11111-1-1-111-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-111111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1−iii−i−iii−i
χ1711111111-1-111111111111111111111-1-1-1-1-11-1-111-1-11111111111111-1-1-1-1-1-1-111-1-1-1-1111111111111111111-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111
χ1811111111-1-111111111111111111111-1-1-1-1-11-1-111-1-11111111111111-1-1-1-1-1-1-111-1-1-1-11111111111111111-1-111-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1
χ1911111111-1-111111111111111111111-1-1-1-1-11-1-111-1-11111111111111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-111111111-1-11111-1-1
χ2011111111-1-111111111111111111111-1-1-1-1-11-1-111-1-11111111111111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1111111111111-1-1-1-111
χ2111111111-1-111111-1-111-1-11-1-1-1-1-1-1-1-11-11-1-1-111-1-1-1-111-1-1-1-1-1-1-11111-111-1-11111-1-111iiiiiiii−i−i−i−i−i−i−i−iii−i−iii−i−i−i−iii−i−iii−i−i−i−iiiii1111-1-1-1-1
χ2211111111-1-111111-1-111-1-11-1-1-1-1-1-1-1-11-11-1-1-111-1-1-1-111-1-1-1-1-1-1-11111-111-1-11111-1-111iiiiiiii−i−i−i−i−i−i−i−i−i−iii−i−iiiii−i−iii−i−i−i−i−i−iiiii-1-1-1-11111
χ2311111111-1-111111-1-111-1-11-1-1-1-1-1-1-1-11-11-1-1-111-1-1-1-111-1-1-1-1-1-1-11111-111-1-11111-1-111−i−i−i−i−i−i−i−iiiiiiiiiii−i−iii−i−i−i−iii−i−iiiiiii−i−i−i−i-1-1-1-11111
χ2411111111-1-111111-1-111-1-11-1-1-1-1-1-1-1-11-11-1-1-111-1-1-1-111-1-1-1-1-1-1-11111-111-1-11111-1-111−i−i−i−i−i−i−i−iiiiiiiii−i−iii−i−iiiii−i−iii−i−iiiii−i−i−i−i1111-1-1-1-1
χ2511111111-1-1-1-11-1-11111111-1-1-1-1-1-1-1-11-11111-1-1-1-1-1-1-1-11-1-11111-1-1-1-11-11-1-1111111-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-1-1-11111-1-1-1-111−i−iii−i−iiii−i−ii−iii−i
χ2611111111-1-1-1-11-1-11111111-1-1-1-1-1-1-1-11-11111-1-1-1-1-1-1-1-11-1-11111-1-1-1-11-11-1-1111111-1-1iiii−i−i−i−iiiii−i−i−i−i-1-11111-1-1-1-11111-1-1−i−iii−i−iii−iii−ii−i−ii
χ2711111111-1-1-1-11-1-11111111-1-1-1-1-1-1-1-11-11111-1-1-1-1-1-1-1-11-1-11111-1-1-1-11-11-1-1111111-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-1-1-11111-1-1-1-111ii−i−iii−i−i−iii−ii−i−ii
χ2811111111-1-1-1-11-1-11111111-1-1-1-1-1-1-1-11-11111-1-1-1-1-1-1-1-11-1-11111-1-1-1-11-11-1-1111111-1-1−i−i−i−iiiii−i−i−i−iiiii-1-11111-1-1-1-11111-1-1ii−i−iii−i−ii−i−ii−iii−i
χ2911111111-1-1-1-11-1-1-1-111-1-1111111111-1-1-111-11111-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111ii−i−i−i−iii−i−iiiii−i−i-1-11111-1-1−ii−iii−ii−i
χ3011111111-1-1-1-11-1-1-1-111-1-1111111111-1-1-111-11111-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111−i−iiiii−i−iii−i−i−i−iii-1-11111-1-1i−ii−i−ii−ii
χ3111111111-1-1-1-11-1-1-1-111-1-1111111111-1-1-111-11111-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1ii−i−i−i−iii−i−iiiii−i−i11-1-1-1-111i−ii−i−ii−ii
χ3211111111-1-1-1-11-1-1-1-111-1-1111111111-1-1-111-11111-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1−i−iiiii−i−iii−i−i−i−iii11-1-1-1-111−ii−iii−ii−i
χ332222222222222222222222-2-2-2-2-2-2-2-222222222222222222-2-2-2-2-2-2-2-2222-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000
χ34222222222222222-2-222-2-2222222222-22-222-2-2-2-2-22222-2-2-22222-2-2-2-22-2-2-2-222-2-2-2-222000000000000000000000000000000000000000000000000
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χ362222222222-2-22-2-2-2-222-2-22-2-2-2-2-2-2-2-2222-2-2-2-2-22222-2-2-22222222222-2-22-2-2-2-2-2-22222000000000000000000000000000000000000000000000000
χ3722222222-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-22-2-222-2-222222-2-2-2-2-2-2-2-2-2-2-22222-2-22222000000000000000000000000000000000000000000000000
χ3822222222-2-222222-2-222-2-22222222222-22-2-2-222-2-2-2-222-2-2-22222-2-2-2-2-22222-2-2-2-222-2-2000000000000000000000000000000000000000000000000
χ3922222222-2-2-2-22-2-22222222222222222-22222-2-2-2-2-2-2-2-22-2-2-2-2-2-222222-2222-2-2-2-2-2-222000000000000000000000000000000000000000000000000
χ4022222222-2-2-2-22-2-2-2-222-2-22-2-2-2-2-2-2-2-2-2-2-222-22222-2-2-2-2-2222222222222-22222-2-2-2-2-2-2000000000000000000000000000000000000000000000000
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χ502222222-200-22-2-2222-2-22222222-2-2-2-200000-200-2200-22-2-22-2-22222-2-20000000-2200000000000000000000-22002-200-22002-2000000000000000000
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χ5822222-2-22222222222-2-2-2-2-2000000002222222222-2-2-2-2-2-2-200000000-2-2-20000000000−2−222−2−222−2−222−2−2220000000000000000−22−22−22−2200000000
χ5922222-2-222222222-2-2-2-222-200000000-22-222-2-2-2-2-2-2-2-2-222200000000-2220000000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000000000000000i2−i2i2−i2−i2i2−i2i200000000
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χ7222222-2-22-2-2-2-22-2-2-2-2-2-222-200000000-2-2-222-2222222222-2-200000000-2-220000000000−2−22222−2−222−2−2−2−22200000000000000002−2−22−222−200000000
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Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.