Finite Group Databasebeta

← Group #129102

Character table — Group #129102

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size111111112222222222222222222222222222222222224444444444444444444444444444444444444444444416161616161616161616161616161616
order122244442244444444448888888888888888888888884444444488888888888888888888888888888888888816161616161616161616161616161616
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ6111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111iiii−i−i−i−i−i−i−i−iiiii
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111−i−i−i−iiiiiiiii−i−i−i−i
χ911111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-1
χ1011111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111
χ1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-111-1-111
χ1211111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-111-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111ii−i−i−i−iiiii−i−i−i−iii
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−iiiii−i−i−i−iiiii−i−i
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1ii−i−i−i−iii−i−iiiii−i−i
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1−i−iiiii−i−iii−i−i−i−iii
χ1711111111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−i11-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i1-11-11-11-1i−ii−ii−ii−i
χ1811111111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−i11-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i-11-11-11-11−ii−ii−ii−ii
χ1911111111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii11-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii1-11-11-11-1−ii−ii−ii−ii
χ2011111111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii11-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii-11-11-11-11i−ii−ii−ii−i
χ2111111111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i-1-111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiii−ii−i−ii−ii-11-111-11-1
χ2211111111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i-1-111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii−ii−iii−ii−i1-11-1-11-11
χ2311111111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiii-1-111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−ii−ii−i−ii−ii1-11-1-11-11
χ2411111111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiii-1-111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−ii−iii−ii−i-11-111-11-1
χ2511111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1iiii−i−i−i−i11-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii1-1-111-1-11i−i−iii−i−ii
χ2611111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1iiii−i−i−i−i11-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii-111-1-111-1−iii−i−iii−i
χ2711111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1−i−i−i−iiiii11-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i1-1-111-1-11−iii−i−iii−i
χ2811111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1−i−i−i−iiiii11-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i-111-1-111-1i−i−iii−i−ii
χ2911111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111iiii−i−i−i−i-1-1111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−ii−i−ii−iii−i-111-11-1-11
χ3011111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111iiii−i−i−i−i-1-1111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i−iii−ii−i−ii1-1-11-111-1
χ3111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111−i−i−i−iiiii-1-1111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiii−i−ii−iii−i1-1-11-111-1
χ3211111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111−i−i−i−iiiii-1-1111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−iii−ii−i−ii-111-11-1-11
χ332222222222-2-2-2-222-2-2-2-200000000000000002222222222-2-222-2-2-2-2-2-2000000000000000022-2-222-2-2000000000000000000000000
χ342222222222-2-2-2-222-2-2-2-2000000000000000022222222-2-222-2-222-2-2-2-20000000000000000-2-222-2-222000000000000000000000000
χ352222222222-2-2-2-222-2-2-2-20000000000000000-2-2-2-2-2-2-2-222-2-222-2-222220000000000000000-2-222-2-222000000000000000000000000
χ362222222222-2-2-2-222-2-2-2-20000000000000000-2-2-2-2-2-2-2-2-2-222-2-2222222000000000000000022-2-222-2-2000000000000000000000000
χ3722222222-2-2-2-2-2-2-2-2222200000000000000002222-2-2-2-22i2i−2i−2i−2i−2i2i2i-2-22200000000000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ3822222222-2-2-2-2-2-2-2-2222200000000000000002222-2-2-2-2−2i−2i2i2i2i2i−2i−2i-2-2220000000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ3922222222-2-2-2-2-2-2-2-222220000000000000000-2-2-2-222222i2i−2i−2i−2i−2i2i2i22-2-20000000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ4022222222-2-2-2-2-2-2-2-222220000000000000000-2-2-2-22222−2i−2i2i2i2i2i−2i−2i22-2-200000000000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
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χ462222-2-2-2-222-2-222-2-2-2-2222i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i−2i−2i2i2i−2i−2i2i2i000000002i−2i2i−2i-2-222-2-2220000000000000000000000000000000000000000
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χ542222-2-2-2-2-2-2-2-2222222-2-22i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i−2i−2i2i2i2i2i−2i−2i000000002i−2i−2i2i-2-22222-2-20000000000000000000000000000000000000000
χ552222-2-2-2-2-2-2-2-2222222-2-2−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i2i2i−2i−2i−2i−2i2i2i00000000−2i2i2i−2i-2-22222-2-20000000000000000000000000000000000000000
χ562222-2-2-2-2-2-2-2-2222222-2-2−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i−2i−2i2i2i2i2i−2i−2i000000002i−2i−2i2i22-2-2-2-2220000000000000000000000000000000000000000
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χ6722-2-222-2-2-220000-220000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2-22-222-22-2002-200-220000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i200-22002-2i2−i2i2−i2−i2i2−i2i20000000000000000
χ6822-2-222-2-2-220000-220000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2-22-222-22-200-22002-20000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2002-200-22−i2i2−i2i2i2−i2i2−i20000000000000000
χ6922-2-222-2-2-220000-220000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i22-22-2-22-22002-200-220000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2002-200-22i2−i2i2−i2−i2i2−i2i20000000000000000
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χ1044-4-44−4i4i4i−4i00−4i4i4-400000000000000−4ζ34ζ34ζ3−4ζ3−4ζ4ζ4ζ−4ζ00000000000000000000000000000000000000000000000000000000000000000000

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